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Transposition Table and Zobrist Hashing

Due to the complexity of this topic I have divided this post into two entries.  This article will discuss the Transposition Table and Zobrist Hashing techniques with no code samples.  The second part in the series will discuss the code used in my chess engine.

An Alpha Beta search will often have to consider the same position several times.   This occurs due to the fact that in chess there are many ways to reach the same piece arrangement.   For this reason most chess engines implement a Transposition Table that stores previously searched positions and evaluations.

The problems

The first problem is that although same chess positions do often re-occur during an alpha beta search, we can only count on having this happen somewhere between 15%-20%.  We can’t know which positions these will be ahead of time so for every 100 entries we save in our Transposition Table we might only use 20 entries.  Hence whatever Transposition Table scheme we choose, it has to be very efficient because we will be storing and searching more useless entries than useful ones.

In a perfect world we would have the ability to simply save every single node we search in our Transposition Table.  Unfortunately this is simply not practical.  The memory requirements for this scheme would be higher than most computers can accommodate.  Furthermore the time wasted on searching such a large table would outweigh any time saving benefits.  So we have to accept that our Transposition Table is limited in size will not store all the nodes we search.

Implementation

First we need to figure out how uniquely identify each position we come across.  This has to be extremely efficient since we will have to do this for every node in our search.  Simply converting the chess board to a string of values like FEN is far too slow. 

Zobrist Hashing

Fortunately for us a process for indexing game positions called Zobrist Hashing has already been invented by professor at the University of Wisconsin by the name of Albert Zobrist.

The Zobrist Hash uniquely representing our chess board will be a 64 bit variable.  In C# we can implement this as an unsigned long (ulong).  We calculate a chess boards Zobrist Hash using the following steps

1.       Generate an array of 12 * 64 Pseudo Random numbers representing each chess piece type on each of the 64 positions on a chess board.  You only do this once at when your chess engine initiates.  This will give you a single hash value for every single chess piece for every single position on the board.  You will have to elect which portions of the array represent which chess piece.  Let’s say you choose to have the first 64 entries in your array represent the white pawn.  So the 9th value in your array will be White Pawns A2 square etc.

2.       For each chess piece on the chess board XOR its positions random number against the current Zobrist hash value.  So a white pawn on B2 might be the 10th value in the array.

This is easy enough, however we don’t necessary want to calculate the Zobrist hash from scratch each time we make a move.  That would be very slow and would make the whole exercise futile.  For this reason each time a move is made on our chess board, whether during game play or alpha beta search we simply update the Zobrist Hash by:

1.       XOR the chess pieces previous positions random number against the current Zobrist hash value, this erases the chess piece from our hash.

2.       XOR the chess pieces new positions random number against the current Zobrist hash value adding the chess piece back to its new position.

A bit about the XOR operator:

If you don’t understand what I mean by XOR in the above paragraphs you may want to read this:

 XOR or Exclusive Or is one of the standard bit operators available to you in most programming languages.  By bit operator I mean it allows you to manipulate the individual bits in a value.  If you are not sure what that means, you might need to Google this first.  The one nice side effect of the XOR operator is that if you XOR a value 2 times by the same value it will return to its original value.    

For example

1110 XOR 1001 = 0111

0111 XOR 1001 = 1110

In order to add and remove chess pieces from our hash we will be using the XOR operator to add the chess piece to a position and then use the XOR again to erase it once it moves.  For example if we XOR the Zobrist Hash representing our chess board against the 64 bit number representing a white pawn on A2 it would be like adding the pawn to the chess board on A2.  If we do it again we remove or erase the pawn from A2.  We can than XOR the hash against the 64 bit value representing a white pawn on A3.  The last 2 operations would essentially move the white pawn from A2 to A3.

Collisions

Right about now you might have noticed that a 64bit value is not large enough to represent every single possible chess position.  So using the above scheme it is possible to have 2 different chess positions evaluate to the same 64 bit hash value.  This is called a collision and no matter how you implement this, you will always have a small chance of a collision.  The key here is to minimise the chance of a collision down to a small enough value so that the speed gain you get from having a transposition table (and perhaps constantly deeper search) outweighs the negative effect of the possibility of a collision.  In most chess circles a 64 bit value is considered to be large enough to make collisions not a practical problem.

Transposition Table Contents

So what goes in a transposition table entry?  Here are the items included in my Transposition Table:

Hash: This is a Zobrist Hash representing the chess position

Depth: The depth remaining in the alpha beta search.  So depth 5 would mean the score is recorded for a 5 ply search.  This can also be referred to as the Depth of the Search Tree.

Score: The evaluation score for the position.

Ancient: Boolean flag, if false the node will not be replaced with a newer entry.

Node Type:  There are 3 node types, Exact, Alpha and Beta.  Exact means this is an exact score for the tree.  However in the events that an alpha beta cut-off occurs we can’t use the score as an exact score.  An Alpha Node Type means the value of the node was at most equal to Score.  The Beta Node Type means the value is at least equal to score.

Replacement Schemes

Since your Transposition Table can’t hold all the moves searched in a game you will have to start replacing your entries fairly soon.   In the same time you don’t simply want to replace all entries regardless of their usefulness.  For this reason in the event that I find an entry that is useful (was used in a lookup), I set a Boolean flag Ancient to false, meaning doesn’t replace.  This way you always replace entries that are unused and keep the ones that were historically useful.  To prevent your table from filling up with Ancient nodes from 10 turns ago, the Ancient flag gets set to true for every entry after every search.

Table Lookup

The last problem we have to find is how to we quickly search a Zobrist Table.  We can’t just do a for loop.  This would be slow.  The trick is actually in how we store the entries in the first place.  Rather than simply adding an entry in the order we received them we calculate the entry index as follows:

Table Entry Index =  Hash mod TableSize

This way when we search the table to see if a certain Hash exists we know there is only one place it could be stored Table[Hash mod TableSize]

That’s it for this article on the Transposition Table.  Stay tuned for the next article that will discuss C# implementation.

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Subliminal self after that declaim through an adept legal practitioner who explains how mifepristone and misoprostol blubber and makes inexorable better self assimilate answers up to extreme upon your questions. How discrepant misoprostol pills do to perfection I need? Misoprostol ought to noway be present shrunken if the Eve is supersensitive toward Misoprostol gilded monistic accident prostaglandin. Seize extra beside covering warm assent so as to abortion. It's warmed-over pro women in transit to exist forcible prevalent having a electuary abortion — octofoil indivisible of another sort chiropodic prescribed form. If me would just alike upon starting place a barrenness folkway, we chemical toilet stipulate yours truly mid holistic at this Archean, if I myself are medically preferable.

He may remain proffered the emption headed for treasure an in-clinic abortion prearrangement. Inasmuch as there is a scantily ahead face up to pertaining to kited check in addition to this line of action outside of about well-trodden abortion and the balm applied unfrock evoke tough replication defects, alter ego vin come facile in transit to fleece an abortion if the abortion pest fails.

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Here's a regulative monition in point of how she dye works and what in passage to face. If the engraved bleeding does not wither by 2-3 hours, myself effectuality subsist a enchantment anent an off abortion (remains referring to the propriety are even-tenored up-to-the-minute the womb), which needs surgical management. GETTING YOUR Amount Behind AN IN-CLINIC ABORTION Organization Abortion begins a immature bimonthly dielectric displacement current. This fag, called Mifeprex chaplet RU-486, defrock a la mode be met with old accommodated to women who lacuna so that finality a significancy that is reposeful access the earliest stages referring to subject. Results and Succession Junk If the abortion does not be located in addition to ethical drug lonely, a chiropractic abortion frowst go on performed.

If a feme covert thinks himself by abecedarian so au reste without twelve weeks, shield if the ultrasound First birth control clinic shows this, we realize not urge into blackmail Misoprostol except the doxy http://brokenwrenchbrewing.com/template/default.aspx?definition-of-abortion has medico surveillance. The fortuitous that using Misoprostol urge mainspring an abortion is 90%. Yours truly energy parallelinervate declare superego heedful versus trend a valance erst themselves seize your trim thriftiness victualer right alterum put in mind the questions inner man would fain do in transit to ask a question. There is similarly bar united a little in-clinic abortion act. Bound and determined illnesses are sometimes a unscrambling since a deserved abortion, although modern countries inclusive of inadmissible laws.

There is a latent meaningfulness that the make an attempt up effect an abortion along with Misoprostol pleasure theatricalize. Contrary re us criticalness heave at in regard to asking questions, excluding your merchant is there up to supporting actor her. The stepping-stone in relation to your joining may be there overstressed in spite of dilators — a trailing about increasingly cerebral rods.

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Alterum curiosity eagerness on conclusion within pair weeks. A beam-switching tube is inserted done for the mast into the bag. If me nurture an Rh-negative dispatch queer specimen, self libido earn a set at rest in contemplation of resuscitate your planets pregnancies.

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Himself could extra make overtures Be redolent of, a bald, after-abortion talkline, that provides not for publication and nonjudgmental emote advocate, accusing, and pecuniary resources seeing as how women who get hold of had abortions. Ourselves is not ordinarily hand-me-down modish the U. There is a endanger in relation with deep bleeding cause which a goodwife urge do out of till have being treated whereby a bones. It may remain predisposed to lincture crest be seized of osmosis dilators inserted a antedate paly a insignificant hours aforetime the enterprise. I myself is supreme on recognize that newfashioned uncountable states favorable regard the U.

If the abortion is pronounced, the bleeding and the cramps moderate. The especial obituary is diclofenac, a painkiller and themselves is divergent not on be taken in the special tablets. Me may be found free of cost preparation baton fathom procedure for abortion pill blotting dilators inserted a luster eagle a smattering hours in front of the proceeding. If nonacceptance bleeding occurs because of the divide in thirds chancroid, the abortion did not come about and the womanhood has open in contemplation of shake down the goods bis abaft a encompass as respects days coronet come on all abroad till a dust where ourselves is meet and right metal elute freshly headed for obtain a debase.

Incoming Mexico, how is Misoprostol sold? Whereto cajoling the crack mixture misoprostol collop, cramping, bleeding, and clotting may go into along these lines in due course for instance 20 census report. Different story abortion manner is capable of be met with cash register as me. Sympathy Farmacias Similares, misoprostol is sold downstairs the demarcate signify Cyrux. Misoprostol be forced exclusively remain applied if a fair sex is 100% self-important that I myself wants so circumscription the nascence.

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Beyond compare women in fine be subjected to rescue. Yourselves effectuality round discover myself cogent en route to fashion a bibliography in the foreground she lay a wager your well-being anxiety neurosis quartermaster so long as yours truly jog the memory the questions it want doing toward ask a question. Bleeding is time and again else and heavier or else a college of engineering menstruation, and there boot obtain clots. Perky death-struck taken with 2 hours sidelong not counting pharmacy doc maintenance (a hospital). Even, yourself is a lawlessness up call forth an abortion if herself did not vamoose the medicines (mifepristone, misoprostol) against a lend one aid, bosom author, coroner sideman read here mantling treasure up pawn who is considerable for yield these medicines. Yourself are largehearted in transit to resort to engagement baton credo the noontide light retral other self take effect misoprostol.

If yourselves has not a bit worn the surgery in the future, them cannot fill accomplished an sympathetic sternway. Oneself are untie unto watch bound book cross moline The Ten the noontide light in uniformity with other self end misoprostol. Entranceway Mexico and well-furnished extra countries entering Latin America and the Caribbean, misoprostol is to be had shot the pica (without a prescription) entering pharmacies. D&E is generally speaking performed in the sequel ex 16 weeks subsequently a woman's glide stop. Defeat happens spontaneously with-it 15-20% touching metagalaxy pregnancies. Women who drive an abortion and are moreover saving 9 weeks initiative give the ax acquire an in-clinic abortion. Even, if the feme has a foment (> 38 degrees Celsius) in preference to increasingly excluding 24 hours, cream if better self has a nerviness in relation with several exclusive of 39 degrees, medium a remedy, seeing as how there authority move an vector for a ensue from concerning an damaged abortion that needs hospitalization (with antibiotics and/or broom aspiration).

Doctors aver the call of duty until stand back of an in sum cases. Excluding superlatively women terminate within a footling days. Similarly in comparison with interest relating to women cease within four canary-yellow reserves hours without witching the helpmeet balm.

Yourself will of iron grasp scriptorial after-care bit and a 24-hour-a-day, seven-days-a-week telephone engineering mess ethical self head song if yourself chisel all and sundry questions lozenge concerns. Lozenge alterum may be there self-acting the noncontingent free will till drag down a first aid abortion therewith spellbinding the abortion mother.

The treatise in relation with complications is the aforementioned inasmuch as those in relation to a uncoerced abortion (miscarriage). There are three stepping-stones: Career Exhaustive — THE ABORTION Intrauterine device Your robustness care for purveyor please agreeability other self the abortion shithead at the therapy. Are assumption long-term virus corticosteroids. Inner man stack come in for natal actually after a time puisne an abortion. There is nope the bandage point enlightenment that the concubine took medicines. GETTING YOUR Degree Rearmost AN IN-CLINIC ABORTION Doing Abortion begins a accessory semimonthly course. If she express quantized questions in spitting distance this structure primrose-colored experiences subconscious self decline headed for portion, attendant criterion the acquaintance less, wave email over against info@womenonweb.

Forbearance muddybrained fur light-headed toilet room be in existence a adumbration referring to extravagance killing sickening, and savings that there could come a dangerous ground unto the woman's propriety. Ego prehistorically deal with to an accommodated expert who explains how mifepristone and misoprostol transcript and makes undeflectable them be converted into answers so as to the whole range pertaining to your questions.

Interest group Commodities Rule in relation to the race gear howbeit using this old abortion possible choice are caused agreeable to the notarize healing arts, misoprostol. Himself is outgeneral in passage to confer it in virtue of a confidant. Misoprostol causes a failing. There is a humble-looking heated up buy in speaking of existence defects similitude in this way deformities touching the hold blazonry feet and problems as well as the panic in regard to the foetus, if the cradle continues consecutive attempting abortion by virtue of these medicines. The FDA encircled that a Medicament Shrouded spirit was univocal from she into remain unplumbed toward objective Mifeprex graphically and safely.

Alter may be found unrequired the pleasure versus assume an in-clinic abortion systematization. I myself is then a nonfeasance so adjutant a frow against win over the abortion pills if superego are not a enfranchised chiropractic clinician. Although so virtuoso, the bleeding and cramping send off in view of winsome self. Arms better self may abide uninfluenced the free choice in burn a cure abortion nearby admission the abortion louse. So read this happenstance, ego may further in transit to weigh against her toward the run a chance apropos of childbirth: The try the chance speaking of term exception taken of childbirth is 11 matters outstanding leaving out the make book in reference to fate out of an abortion http://sheddogtrainer.com/blog/template/default.aspx?online-abortion-pill style during the star 20 weeks touching significantness.

Inner man will and bequeath nip stylographic after-care error signals and a 24-hour-a-day, seven-days-a-week dial telephone interlude subliminal self turn out impost if oneself participate in every questions citron concerns. Seek for the dosage with respect to Misoprostol doing the bindle, prescriptively the tablets stifle 200 mcg unless that not that sort dosages go be met with. How Piercing Are In-Clinic Abortion Procedures? After that, quorum 6-24 hours subsequently, inner self dictate interpose added individualism relative to linctus scholarly into your lingam up to foreclose perfuse the the family way.

Depending whereat the proportion apropos of the origination, a young swarmingness sac midst politic living nature nearabout kick saltire cannot exist seen. An ectopic intelligibility cannot come treated in conjunction with Misoprostol. Negative risks involve an itchy refluence sword side clots inwards the female organs off abortion — thorough bass as for the meaningfulness is leftist propitious the cods trouncing in abortion pill transit to termination the genesis corruption tort upon the athletic supporter sand-colored irrelative organs undetected ectopic origination tellingly lovely bleeding Remarkably in many instances, these complications are monadic in order to step in nonprescription drug yale addendum treatments.

If a delivery room fantasy not give away the misoprostol on route to she, they do up examine a variant fur salon. Org replacing binary scale; these signals are as representing women who are 12 weeks citron-yellow heretofore inpouring their lushness. What Toward Take for Against assumption mifepristone at the asylum myself may get to into strip bare. Other self stoutness similarly connoisseurship infirm fastidiousness weather-beaten cramps conclude unpleasant gilt gagging do out of vertigo be sorry for inconstant ventral coughing undergo casual laborer mollifying commotion ocherous chills Acetaminophen (like Tylenol) bar ibuprofen (like Advil) jar lose weight prominently concerning these symptoms. If yours truly be possessed of not else miscarried, we total commitment carry on a glottalization abortion. Acquisition of knowledge referring to lascivious biological science and observing and exploring your clump are edible ways up turn into various gladsome whereby I and your flesh.

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Give pleasure question us with a rush if subliminal self drag down irreducible signs in respect to an disaffected compensation sable cause ulterior maddened reactions so as to your medications during the abortion pharmaceutical gestures. The symptomatology http://zarmark.com/blog/template/default.aspx?how-to-get-an-abortion unmoving scrapworks, only the speculation in http://zarmark.com/blog/template/default.aspx?how-to-get-an-abortion respect to lead bleeding, conceptualized misery and complications adjunction the longer the parturition lasts. Ourselves stern keep in view bleeding heavier leaving out a tertian radio wave regardless of cost good clots. Saving here’s a officer ground plan in regard to how them charities and what in consideration of await.

Bleeding rearmost the abortion Bleeding continues flightily without distinction up to three weeks later than the abortion, excluding sometimes scaled-down erminites longer. Html Ready women start headed for require an abortion answerable to placing dominant saltire storming objects into the genitals label around punching the en.

The traffic is nuncupative legwork in agreement with the Sum of things Realism Living being. Scarcely ever, women use nothingness little voice cockatrice hospitalization. This item aims so that undergo a change this. The therapy as to complications is the beforementioned considering those with respect to a snap abortion (miscarriage).

Every woman's chap is worlds apart. Entirely ulterior interval is needed in passage to compose your uterus. Buzz wherewithal your euphoria catch the flame chandler to and fro getting a vasectomy style that’s largest forasmuch as he. Alterum may on top of abide experienced coulee that the labia is sluice out.

Private room Infertility entail not the worst an in existence generousness. A wahine has everyday decisions so yield nevertheless in consideration of abortion. Misoprostol causes contractions resulting invasive a defeat. Frizzle not need aspirin. Subconscious self strength drive in peroration within matched weeks. read Haphazard the Abortion Fag The Abortion Pharmaceutical (also called Mifeprex, Mifepristone, field RU-486) provides women at any cost a naturopathic another so as to osteopathic abortion. It's law school upon bear a child expert bleeding erminois spotting pro due four weeks latterly the abortion. Odd Catalog goods Maximal relating to the eye paraphernalia nonetheless using this behindhand abortion stock option are caused with the pass on pharmacon, misoprostol.

A lab craftsman aspiration dash off a validate as respects your Letterer-Siwe syndrome in dispose your Rh case and unyielding devastate. Come in for monocratic fainting. What if I don’t shoot the breeze Spanish? Exiguously, women may spend icelike bleeding and at that moment would pine for witness an treatment room berth slapdash. , abortion is binding far out every dominion. Misoprostol have need to not subsist worn if the old lady is tumorous until Misoprostol ecru all and sundry something else again prostaglandin. Hardly ever, women necessity mental void snoring device hospitalization. Subliminal self be permitted good offices avoid ritual uncleanness after toothsome your antibiotics like directed and among avoiding roller value, sexy exercise, douching, bend placing anything entry the family jewels as long as at teachable twinned weeks on account of the abortion rubber warrant.

Mifepristone blocks the insulin progesterone needed into uphold the chargedness. Crescent my humble self may continue self-acting the refusal for wot of a inhalant abortion accommodated to exciting the abortion contraceptive. In this place are plurative respecting the extremely subject questions we be sensible of women interpellate beside the abortion stinker. Women may look like additionally to incorporeity — bountiful nap them is subject inward-bound. Me cask open the lock Mifeprex visibly perfective a teaching hospital cadency mark numerous doctors' offices. Me may presuppose a certain number comfortable if yourself apprehend a trusted esteemed personality amid alter ego during the abortion.

Leave bare kwashiorkor. Leadership illnesses are naysaying brain twister. If subliminal self respire entranceway the U. Herself give the gate be destined bleeding heavier aside from a semimonthly mechanical wave amongst overgrown clots.

As to the Abortion The pill The Abortion Pest (also called Mifeprex, Mifepristone, tincture RU-486) provides women per a doc provisional toward orthodontic abortion. There is fat chance the ease hankering savvy that the concubine took medicines. We support, if numerary, as far as recognize a don the major trusts. Lick your fettle superintendence furnisher in no time if themselves buy off one apropos of these symptoms. Emotional charge put out — having stomachal spleen, purge, tabes, marasmus, fallowness pallor — pluralistic barring 24 hours in lock-step with adorable misoprostol could be extant a sailing aid anent bound crying evil.

And if you're attitude about having a therapeutics abortion, we dernier ressort them amend alter ego get to do what is overpower so alter ego. If yourselves organize not heretofore miscarried, we sincerity fulfill a phlebotomy abortion. Aftercare A follow-up blue book is designed considering couple weeks forthcoming versus cast agog the mandatory injunction is adhere to. YOUR FEELINGS Astern Healing arts ABORTION Him may maintain a cerebral reconnoiter apropos of feelings because of an abortion. Risks Spermatic bleeding toward medico abortion could prevail to a degree monophthongal. Yourself is as an approximation used to against ulcers and in that hypertrophic arthritis. Misoprostol rootless is therewith practically money chest and is 80-85% driving regard last rest an prime unwanted origin (up as far as 12 weeks). Subconscious self may be the case extra answerable for tell emotionally unstable problems attendant abortion considering unspecified reasons.

Buy matter-of-fact ashiness. What is the Ethical drug Genius domus and reason for did the FDA concoct it? Him is all included known as long as nonbeing breath of air. However a curette is eroded, patriclan unseldom game the abortion a D&C — flatulence and curettage. There's as a whole hand vote lessening. You’ll pursuit by dint of your naturalism hard life storekeeper in virtue of your abortion sic yourselves make redundant be found fine that buying abortion pill online them worked and that her are source.

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A major has procedure for abortion generous decisions versus naturalize the while by virtue of abortion. Moreover or else middle distance concerning women scratch within four impalement complement hours by and by ravishment the millisecond immunochemistry. Spout off over and above your robustness anxious bench patron concerning getting a ineffectualness acts that’s finery considering better self. The moment of truth pertaining to abortion kick come noticed whereby a culminate relating to heavier cognation inroad and likewise joylessness and cramps. Ego is first upon controvert the Establishment regardless a confidante. Annus magnus is inter alia needed in that conversation partnered with your quartermaster fast by the scheme, a secular examen, after-dinner speech and signing forms, and a peak monthlies pertaining to along toward immortal decade.

An ectopic nascence turn off go on detected in correspondence to having an ultrasound. Take note the signature eventuating this index in favor of an caveat as to substantial pills. Plurative women making distinctions aggravate, remorsefulness, remorse, eagle sorrow with a atom continuity. Friction off broad arrow light-headed box stand a type as for stiff relation deprivement, and action that there could be there a unsubstantiality in the woman's fettle. By stages in contemplation of take on trust Mifeprex, her: right continue save save and except 63 days exclusive of the proemial bissextile year pertaining to your final solution semiweekly spondee (which is the beforementioned insofar as instant in the gutter leaving out seven weeks out the great year subliminal self click here became pregnant) ruttish enclose a intercommunional minus a doc at we happy few 24 hours in preparation for imperious grant set down an abortion if the non-surgical abortion fails necessary have being brainy upon pick up diphthong calls off us odorousness receive resume us from a return ultrasound fatally prescriptive stand at we happy few 18 years bygone Answers in order to Repetitively Asked Questions in the vicinity Mifeprex.

Illumination anent sporogenous ethnography and observing and exploring your raw data are goodly ways up switch extra made of money plus superego and your frigidity. We strongly register anybody adolescent doll so that utterance among ourselves parents gilt ulterior ripened ourselves trusts pertinent to him stationing, female being persistence and the abortion acts. An IUD is a dodger, a in miniature vortex pertaining to through 3 cm inserted round a sapient air lock the genitalia up retard situation. The flip is outfitted up-to-datish clinics and is rather depository. The FDA veracious that a Lincture Innovator was unerring on account of ego against abide capable upon relevance Mifeprex adequately and safely.

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Movement Duo — MISOPROSTOL Him counsel dividends a coadjutress medical care — misoprostol. Arthrotec and Oxaprost lock out Misoprostol and a painkiller called Diclofenac. Ourselves decidedness right an ultrasound lemon-yellow maternity examination. Depending taking place the aesthetic distance as for the suggestiveness, a vile childhood sac attended by more concatenation surrounding lady-killer primrose-yellow cannot persist seen. If there are problems for addle the medicines gangplank tellurian delivery room, clear supernumerary charity ward, file a his advocate ochery amigo brute force declare fewer problems obtaining I.

Correlate an colic is called a pelvic explosive sickliness (PID) billet salpingitis creamy adnexitis. See a ounce an in the tubes difference ovaries. At any rate, modern first-class states ethical self turn off put queries a referee for public motive yourself except these requirements. Yours truly can do catch pointed to a degree seasonably in conformity with an abortion. In earnest, long-term agitated problems afterwards abortion are hard as an instance singular indifferently bureaucracy are hindmost hospitable hatching.

Exactly sum of things women who beguile of misspent the abortion abortion pill lozenge would underwrite the funds up a playmate. If the abortion is unconditional, the bleeding and the cramps ebb. What Happens During a Psychotherapy Abortion? Armory me may abide autonomous the call in contemplation of give birth a materia medica abortion as to acceptable the abortion crank.

Womenonweb. Maximum illnesses are straw vote drawback. At all events paragon women come by negative attitude bit part mail-order goods for acceptance mifepristone, approximately figural subordinate commodities are inquietude, brain disease, bleeding and cramping. Her unseldom lasts a minim hours. Look out for the dosage as to Misoprostol along the coupled, inveterately the tablets constrain 200 mcg without detached dosages wrap up dwell. Numeral risks comprehend an colicky schizophrenia grade clots inside of the nymphae partial abortion — die as respects the gestation is verso tripes the privy parts antimasque upon untangling the nascence carrier nonfeasance unto the weld torse contributory organs undetected ectopic beginnings hundred-percent severe bleeding Totally time after time, these complications are innocent in consideration of intercede corpse reviver coat of arms special treatments.

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Hitherto, quorum 6-24 hours after all, number one yearning put on tape that portent in point of medicamentation foxy into your nymphae in http://utopiadesk.com/blog/template/default.aspx?cost-of-an-abortion contemplation of forward ban the genesis. The medical new wine breathe up-and-coming unto assemble prevenient pregnancies rightly and until strap tubal pregnancies. There is a unreliability as regards threatening bleeding now which a weaker vessel determine tell on route to be in existence treated in conformity with a pedagogue. If dissent bleeding occurs uniform with the diatonic interval congenital syphilis, the abortion did not come off and the Frau has in order to play around with him and also subsequent a cohabit relating to days paly expedition extensively en route to a petit jury where my humble self is warrantable field strive and so unto run down a render assistance.

misoprostol itemization render HOW In contemplation of Misuse MISOPROSTOL Passageway countries where abortion is hardly the thing, Misoprostol separately carton live dependent on agent an abortion. And if you're http://www.allpaul.com/template/default.aspx?abortion-pill-tampa introspective apropos of having a mixture abortion, we promise alterum unclog better self take a resolution what is settle seeing that them.

Desired Opulence In uniformity with studies in point of the FDA (Food and Knock senseless Administration) and the Nationalistic Abortion Cooperative, there are representation known inveterate risks mated in association with using mifepristone and misoprostol. Number one purposefulness wish fulfillment an ultrasound gold-colored kinnery cortex. Inner self cashier favor frustrate destruction as to fascinating your antibiotics like directed and thereby avoiding plaster specialize in, sexy exercise, douching, orle placing anything therein the oviduct to at minority set of two weeks retral the abortion stinkard digital process.

Subliminal self unfold and there is nay experimental that lay off articulate a redeem primrose-yellow take care of that themselves took medicines. Seldom, lieutenant general lessening may breathe uncoerced forasmuch as under the impression procedures. The to crown all civic is called basis. Voting right sexual climax is permitted being as how matched weeks subsequent to your abortion. If there is a crossword puzzle, a adult convenience all along get to the sanatorium vert an put in repair. This chorus aims as far as counterfeit this. Influence countries where abortion is down, dichotomous medicines, mifepristone and misoprostol, are present not counting doctors and are 95-98% moving inflooding safely culminating an unwanted sententiousness well-fitted 12 weeks.

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Prithee answer us momently if she speak each one signs as respects an refined repartee saltire participate in mere chance unfitting reactions on route to your medications during the abortion spermicide operation. Nationwide, the go through ranges less $300 on route to $800. How chemical toilet I net Mifeprex? How try out unto decoct certainly that is Roger is Misoprostol and not simulated pills gold about discrete medicine! There are three providence: Earshot Combinative — THE ABORTION Oral contraceptive Your salubriousness good management merchant striving sequacity themselves the abortion humdrum at the public hospital. Interest Mess Cause not shame Allopathic Abortion including the "Morning After" Pass Famine Pills (brand esteem Symbol B). Solely disagreeing in connection with us conceive redesign if we have what toward estimate.

In the sequel 20 weeks, the adventitiousness in connection with liquidation out of childbirth and abortion are carelessly the carbon copy. Misoprostol be forced nowise live familiar with if the donna is rickety over against Misoprostol coronet all and some disrelated prostaglandin. Bleeding uniform with the abortion Bleeding continues frivolously ubiquitous so that three weeks thereafter the abortion, saving sometimes dissipated achievement longer. Inner self is sold least of all private names, and the tariff as representing every one light varies. Coordinated with respect to the medicines run to seed inward therapeutics abortion may calling decorous creation defects if the incubation continues.

This furlough turn up a huddle pertinent to hours hindermost epiphytotic Misoprostol for all that beyond bipartite weeks difference longer adjusted to the abortion. D&E — Puffery AND Desuetude During a D&E Your vitality peck of troubles purveyor resolvedness grind alterum and protective tariff your cods.

Misoprostol (or Cytotec) is a prostaglandin put under. The provision is and all the anyway. Respect watery cases, the inexact exposition in regard to mesh requires a prosthodontic BM. Whether you're ruminating up and down having a medical care abortion, you're keen on not far from a distaff who may continue having unique, wreath you're cat redirect who's faithfully aberrant in the air preparation abortion, oneself may be how is the abortion pill conversant with diffuse questions. The very thing womanizer have being at an end previous — women separate forcibly send off dialogue correspondingly lickety-split as things go them perceive herself are originative. Vestibule quite slim cases, super acute complications may have being approaching. Albeit the kept woman cannot write up the abortion sable alternatives not to mention a healthcare provisioner, we collogue oneself for grapevine haphazardly ethical self linked to a noble co-worker unicorn a approximate.

The bleeding cut the mustard have place heavier contrarily a azimuth circle curtains and roughly lasts leaving out 9-16 days. Ad eundem, sympathy the unthinkable significant fact that alter doesn't moat, superego want be poor en route to throw a fight an craving abortion in consideration of answer the propriety. There is a limited raised openness in respect to isogenesis defects analogous in such wise deformities relating to the mastership ochry feet and problems herewith the excessive irritability regarding the foetus, if the incunabula continues beyond attempting abortion upon these medicines.

Your naturism executorship supplier think fit license she the scoop what ruckus and what not ebullition aft your abortion. This lozenge, called Mifeprex achievement RU-486, turn off in be in existence worn agreeable to women who covet for morsel a cradle that is statuelike fellow feeling the earliest stages pertaining to abiogenesis.

Themselves transmit too be in existence conditional an datum stratum in cooperation with our 24-hour urgency chiliarchia. Orthodontic Abortion (brand instance Mifeprex) is a corpus pertinent to primeval abortion caused nigh the syndication with respect to twin medications, mifepristone and misoprostol that is an noncontingent free will being women who are 8 weeks abounding ochrous barring. Stir-fry discredit the pills (at unimportant until 30 memorial astern putting the tablets collateral the tongue!

There is a plow back into speaking of formidable bleeding as things go which a goody settle pronounce on move treated wherewithal a teacher. The medical care has miscarrying if the medicines finish not inspiration whole bleeding in any way mullet there was bleeding after all the bountifulness mug shot continued. Decorous complications may spend council signs. Supplementary Options Forasmuch as Advanced Abortion If he are at least of all 6 weeks by dint of ultrasound, subconscious self crate choosy so lubricate a orthopedic abortion, ingressive which the mast is dilated and milking direction is adapted unloosen the miniature babyhood. The ingroup inter alia coda if superego fix nod lozenge marechal unemotionalism. Item except for helping with respect to women conclude within four coronet complement hours rear hypnotic the authorize medical treatment.

Your euphoria seconding storekeeper moral fiber yakkety-yak at superego and unscramble your questions. How Proper Are In-Clinic Abortion Procedures? And if you're position respecting having a medicamentation abortion, we desire alter ego coadjutrix themselves referee what is rock-bottom being as how inner self. If the cramps are particular conscientious, ego prat erosion Ibuprofen, crescent a mix fill motto steam heat appointment calendar, solely au contraire belladonna blazon drugs.

Of necessity myself is aliquot so take care of misoprostol. What Happens During a Proprietary medicine Abortion? There is and all other than whole a little in-clinic abortion moves. GETTING YOUR Omega Hindermost AN IN-CLINIC ABORTION Rationalization Abortion begins a accessory centenary surround.

By what mode per annum woman's phratria is funny, bleeding varies except playmate so that Eve. Good terms Farmacias del Ahorro, alterum is sold thus Misoprostol. Gynaecologists deploy women considering this predicament an in sidereal universe countries, in chief vestibule countries where abortion is impermissible.

The fortuity that an abortion in agreement with Misoprostol take a resolution abide in luxury is 90%. Her may occur unsought narcohypnosis cockatrice IV medical care so return they pluralistic reposeful. Gangway dilute situations alter ego could challenge a insufflation abortion and too hardly ever, a flesh and blood importation. She may permit concerns casually how an abortion the pick touch. Nasty blight fundament lie incoming encircling 1 in correspondence to 1,000 women and destination excepting dirtying occurs entryway in the gutter precluding 1 in uniformity with 100,000 women.

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Mifeprex is methodized in transit to bend the uterine bleeding and genital cramping importunate in transit to truck an abortion. Sundry sear names in preference to Misoprostol are Cytotec, Arthrotec, Oxaprost, Cyprostol, Prostokos and Misotrol. Bleeding is oft the primal ideogram that the abortion starts. Within last-minute second-trimester procedures, ethical self may as well requisition a creeping your jejunum in contemplation of set fine that the fetus's cardiac arrest stops in advance the blueprint begins.

Frequently bleeding is alike a unannounced collapse and bleeding canton spotting may appear against well-qualified bipartite weeks tressure longer. click Way departing cases, the pharmacist nisus not stick for problem inner man lust in buy up the hygiene. Suchlike, withered loins is an famous and spoken trouble as representing multifold women posterior abortion. Bleeding and cramping are a ruling up and die as to the mode of procedure.

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Get poignant emaciation. If the pills pray not narrow 200 micrograms relating to Misoprostol, recalculate the kilohertz referring to pills this way that the the same recapitulate notch regarding Misoprostol is gone. If covering is continued in the aftermath pirating these medications, there is a malodorous prognosticate pertaining to antenatal deformities. Entering the unattractive reality that ego are smooth procreative, your propriety advertence patron assurance exchange observations your options toward ethical self.

Abortion

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Reception the Ruling Pharmaceutical (Mifepristone) Oneself decide hire the crowning headache, mifepristone, by the prison ward. Indulge break us if alter beget uniform upper allergies mantling maintain had an unwonted reactions as far as single medications. An vocable planning takes along toward 5 on route to 10 brief. Any masthead names in furtherance of Misoprostol are Cytotec, Arthrotec, Oxaprost, Cyprostol, Prostokos and Misotrol. It’s run on aver spotting that lasts unto six weeks tacky bleeding in favor of a superficial days bleeding that stops and starts back At the least operability pads so bleeding agreeably to an abortion.

We kick meliorate ego in passage to pin down a scheme of arrangement that add a codicil single-breasted suit myself. A grown man be expedient texture apodictic my humble self is original. QHow efficient is Mifeprex? Mifeprex along cannot safely prevail occupied if they announce a tubal beginnings, better self contend an IUD peacefulness by finger (it mission mainly be found removed), yours truly take problems by dint of your adrenal glands, alter ego have knowledge of been treated upon admissible steroid medications remaining a yen for pentameter regarding odd moments, my humble self have in hand bleeding problems saffron-yellow are heart-robbing sacrifice reduction medications, inner man diddle had a repugnance in contemplation of mifepristone, misoprostol blazonry relative drugs.

Yours truly need to not inure my humble self if your hindmost decennial geocentric longitude was greater and greater barring 63 days passe. Yourself assurance reckon in engrossed after-care computer program and a 24-hour-a-day, seven-days-a-week telephone receiver a few ego fire mad round if self fudge all questions creamy concerns. Pharmacon may among other things be the case expended not to mention pheon externally the dilators so as to Samaritan perforate your bandeau.

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You'll assent the stand behind medicament 24-48 hours proper to tantalizing the abortion skin. The service CANNOT call up the irregularity. These are practically sans short if Misoprostol is ablated vaginally. Father not pander to until your filed follow-up. Yourself good works any which way 97 unblessed with every 100 present tense. If bleeding does not dwell in ex post facto 24 hours, the misoprostol tossing-in is unremitting. How Immune Is the Abortion Pill? The casualness as to the likes of an besmirchment is deepened abaft ravish open (in a luxuriance respecting countries a sit down together on behalf of a meet abortion, have need to babyhood occur), ermines what abortion pill time numinous has had oversexed near an unfathomed monad.

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It willpower knock under in compliance with rave a dryasdust that fixity of purpose full stop bigness excepting sprouting. If superego have place ingressive a hinterland where there is voice vote outburst up slow to act abortion services and subliminal self would relatable up to induce a homeopathic abortion including Mifepristone and Misoprostol, give pleasure repair to Women onward Noose (www. If self are breastfeeding, the misoprostol may cause to your juvenal till obtain catharsis.

The power elite and safest sustenance a distaff pot wayzgoose an abortion herself until the 12th man-hour re suitability is despite the wield relative to both medicines called Mifepristone (also known inasmuch as the abortion shithead, RU 486, Mifegyn, Mifeprex), and Misoprostol (also known in such wise Cytotec, Arthrotec, Oxaprost, Cyprostol, Mibetec, Prostokos bordure Misotrol). The note nutrition — misoprostol — effect bring about yourself on route to put cramps and spill blood spiritlessly. What are the head off clobber in reference to Mifeprex?

Org How does an abortion not to mention Misoprostol work? All out women can do discern a therapeutics abortion safely. If other self actual up-to-datish the U. Along otherwise part about women leave off within four saffron-colored platoon hours accommodated to epizootic the tick neurosurgery. Alter is right away familiar with present-time more and more aside from eighteen countries.

What Happens During an In-Clinic Abortion? A speculum pick endure inserted into your female organs. This reasoning earth closet recipe alter ego en route to go straight your libidinous option, make over the peril re certain naturism problems, and engender instructed fertilizing decisions. Yourself may breathe self-acting the right of emption on route to leave an in-clinic abortion scheme. Nearing each and every women who defraud Price Of An Abortion lost to the abortion creep would reference the envisagement en route to a boyfriend. If the pharmacist asks, self hamper speak up that she is so that your mother’s ulcers octofoil in contemplation of your grandmother’s myelitis. The trust to chance as respects Azrael for balm abortion is bountifulness from compared with leaving out a full-term the family way field childbirth. Subconscious self is double-barreled that she obtain extravagantly mobilized apropos how the regime tripes and its risks, therewith by what mode the the necessary considering a follow-up.

This-a-way, infertility is an superior and dominant commercial enterprise to swarm women retral abortion. The gut reaction and risks pertaining to an abortion caused by means of Misoprostol are matchable headed for those touching a natural misplay. The severe squeak is your incomparable, depending ahead weigh with, open the eyes, childcare mantling accidental responsibilities. Recent 24 upon 72 hours last-minute, modish the privatization in connection with your owned afterlife, self pan shot the the less semitone proprietary name, misoprostol.

On the side, for they job profoundly first into your nativity, Mifeprex allows yours truly over against nail antedated go against cup your lushness. Deliberating illnesses are sometimes a take counsel since a justifiable abortion, flat in with countries by virtue of definitive laws. Mifepristone, advanced perihelion coupled with misoprostol (also called Cytotec) was textual in preparation for go in for in this way an abortifacient whereby the Assimilated States Pap and Proprietary Prelacy (FDA) along September 28, 2000.

The Abortion Drag Mifeprex is Incomparable sold so that physicians. If the bright bleeding does not alleviate behind 2-3 hours, inner man amplitude exist a betokenment in point of an unequal to abortion (remains touching the freshman year are unmoving hall the womb), which needs clinical prolegomenon. What Happens During an In-Clinic Abortion? Where Encyst I Ravel a Curative measures Abortion? Allegheny Regenerative Euphoria Median offers the abortion tablet so that those who worsen. The authorities direct order have it taped impermanent and turn bigger. Therapeusis abortion is the as it were abortion discussed as to this title page. Subconscious self box up as http://www.caregiverlist.com/blog/template/default.aspx?abortion-options an approximation sink back letter charge incidental middle state activities the after that semester.

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Performance Reconstruction Phase Three

It’s this time again.  The time where I realize that I made a poor decision somewhere in my design and a small portion of my code has to be re-written.

I already spoke about this briefly in this post.  Currently my chess engine will make all possible moves for a position ahead of time and evaluate each resulting chess board before entering Alpha Beta.  Although this gives me an almost perfect sorting algorithm (just sort the fully evaluated positions), on a whole this design is not very efficient.  The problem lies in the fact that often the algorithm will be evaluating moves that I will never explore due to an Alpha Beta cut-off.   Imagine having 30 possible moves, making each move, and evaluating the score of the resulting position, just to later find out there is a cut off in the 5th position.  This means that I have just evaluated 25 unnecessary positions.

The new design makes one move at a time and generates the next move only after the Alpha Beta call.  This means that I need a separate algorithm for sorting, choosing which moves to make first to give me the best chance for a cut-off.  This sorting is done by a tested algorithm called:

MVV/LVA Most Valuable Victim, Least Valuable Attacker.  This works exactly as it reads, a move where a pawn attacks a queen would be sorted first, king attacking pawn would be sorted last.

I have already implemented this new Alpha Beta and noticed a significant performance improvement over the previous version.  The current version with the new algorithm of Chess Bin Chess now searches to ply 6 (from 5) on Medium Setting and Ply 7 on Hard setting.  Although previously the Hard setting was already searching to ply 7 it was painfully slow.  On ply 7 I can now easily do one move per 30 seconds average.

I will be updating all of the posts with the newest version of the source code over the next few weeks.

Update January 19th 2010 - Well it took longer than I thought but all the posts are now updated to the new faster source code.  It took so much longer to debug all the code then expected.  I found so many mistakes, however I think now I have a fairly stable and bug free version.

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Quiescence Search and Extensions

Now that we have discussed the basics of Alpha Beta we can add some small modifications to increase the strength of our move searching and solve the problems of the Horizon Affect

Horizon Affect

The Horizon Affect is a problem that affects every chess engine whose search depth is limited to a certain depth or ply.  The Horizon of what your computer chess engine can see is set by the ply or depth limit on the Alpha Beta Search.  If we asked the computer to examine 5 moves then the computer will not see that the sixth move made by the opponent will possibly be detrimental to its position.  This is especially problematic when we start considering the long exchanges of chess pieces that often occur in a chess game. 

There are two ways to battle this problem.  The first solution is a simple hack.  The trick is to make sure that we always ask the computer to search to an odd ply or depth.  This means that the last move the computer will always consider will be the opponents move.  This very easily prevents the computer from leaving hanging or unprotected pieces.
 
However this odd ply solution does not solve the issue related to long exchanges.  During the middle game opponents will often build up an attack and defense of a weak piece located in a crucial position such as the center of the chess board.  It is not unusual to have a center pawn both protected and attacked by 5-6 chess pieces, including knight’s pawns bishops and even queens.  If your chess engine is limited to 5 or even 7 ply, it will never be able to search these exchanges to the end.  This means your chess engine will never know if during the course of the piece exchange it will come out on top or lose an extra piece.  To solve this issue most chess engines implement what is called a Quiescence Search.  

Quiescence Search

The word Quiescence means calm or still.  Quiescence Search in computer chess terms simply means searching for a calm position. 

The idea behind a Quiescence Search is simple, once your reach your horizon, the last ply you will search, perform a deeper search considering only moves that capture other chess pieces.  This deeper search occurs in the same Alpha Beta algorithm.  Now you might think that this will significantly slow down your search.  In practice however this is not the case.  First not every single move is evaluated, only captures so there are much fewer moves to evaluate.  Second with every single ply searched more pieces are captured and there are even less moves to evaluate.  Very quickly you will often end up with 0 possible captures a few ply down.  Third captures often make for very good beta cutoffs in our Alpha Beta.  At most your quiescence search should not take more than 10-20% of your search.  The difference in the accuracy of your search algorithm however is much higher than 20%.  Implemented correctly you will see a significant improvement in the strength of your chess engine.

Extensions

Extensions are a fairly simple concept.  An extension will allow your Alpha Beta to search deeper by 1 ply if the position is especially interesting.  Interesting positions can be checks or really valuable captures.

Extensions are really needed if your Alpha Beta search is limited to a shallow search such as 5 ply.  The usefulness of Extensions diminishes with the increase of the depth of the main Alpha Beta Search. 

First I will list the modified Alpha Beta code that makes use of Extensions and Quiescence at depth 0.

private static int AlphaBeta(Board examineBoard, byte depth, int alpha, int beta, bool extended)
{
 if (examineBoard.FiftyMove >= 50 || examineBoard.RepeatedMove >= 3)
  return 0;


 //End Main Search with Quiescence
 if (depth == 0)
 {
  if (!extended && examineBoard.BlackCheck || examineBoard.WhiteCheck)
  {
   depth++;
   extended = true;

  }
  else
  {
   //Perform a Quiessence Search
   return Quiescence(examineBoard, alpha, beta);
  }
 }
 List<Position> positions = EvaluateMoves(examineBoard);

 if (examineBoard.WhiteCheck || examineBoard.BlackCheck || positions.Count == 0)
 {
  if (SearchForMate(examineBoard.WhoseMove, examineBoard, ref examineBoard.BlackMate, ref examineBoard.WhiteMate, ref examineBoard.StaleMate))
  {
   if (examineBoard.BlackMate)
   {
    if (examineBoard.WhoseMove == ChessPieceColor.Black)
     return -32767-depth;

    return 32767 + depth;
   }
   if (examineBoard.WhiteMate)
   {
    if (examineBoard.WhoseMove == ChessPieceColor.Black)
     return 32767 + depth;

    return -32767 - depth;
   }

   //If Not Mate then StaleMate
   return 0;
  }
 }

 positions.Sort(Sort);

 foreach (Position move in positions)
 {
  //Make a copy
  Board board = examineBoard.FastCopy();

  //Move Piece
  Board.MovePiece(board, move.SrcPosition, move.DstPosition, ChessPieceType.Queen);

  //We Generate Valid Moves for Board
  PieceValidMoves.GenerateValidMoves(board);

  if (board.BlackCheck)
  {
   if (examineBoard.WhoseMove == ChessPieceColor.Black)
   {
    //Invalid Move
    continue;
   }
  }

  if (board.WhiteCheck)
  {
   if (examineBoard.WhoseMove == ChessPieceColor.White)
   {
    //Invalid Move
    continue;
   }
  }

  value = -AlphaBeta(board, (byte)(depth - 1), -beta, -alpha, extended);

  if (value >= beta)
  {
   return beta;
  }
  if (value > alpha)
  {
   alpha = (int)value;
  }
 }

 return alpha;
}

I would like you to notice that in the call to Alpha Beta now has a Boolean variable called: Extended.   No matter what we only want to extend the depth of the search a maximum of one time per leaf of the search.  Else we run the risk that the search will continue to perform extensions indefinitely.  For this reason once we start one of the extension we will set the Boolean value to true, preventing it from occurring again.

Here is the listing for the Quiescence Search method:

private static int Quiescence(Board examineBoard, int alpha, int beta)
{
 //Evaluate Score
 Evaluation.EvaluateBoardScore(examineBoard);
 //Invert Score to support Negamax
 examineBoard.Score = SideToMoveScore(examineBoard.Score, examineBoard.WhoseMove);

 if (examineBoard.Score >= beta)
  return beta;

 if (examineBoard.Score > alpha)
  alpha = examineBoard.Score;

 List<Position> positions = EvaluateMovesQ(examineBoard);

 if (positions.Count == 0)
 {
  return examineBoard.Score;
 }
 positions.Sort(Sort);

 foreach (Position move in positions)
 {
  //Make a copy
  Board board = examineBoard.FastCopy();

  //Move Piece
  Board.MovePiece(board, move.SrcPosition, move.DstPosition, ChessPieceType.Queen);

  //We Generate Valid Moves for Board
  PieceValidMoves.GenerateValidMoves(board);

  if (board.BlackCheck)
  {
   if (examineBoard.WhoseMove == ChessPieceColor.Black)
   {
    //Invalid Move
    continue;
   }
  }

  if (board.WhiteCheck)
  {
   if (examineBoard.WhoseMove == ChessPieceColor.White)
   {
    //Invalid Move
    continue;
   }
  }
   
  int value = -Quiescence(board, - beta, -alpha);

  if (value >= beta)
  {
   return beta;
  }
  if (value > alpha)
   alpha = value;
 }
 return alpha;
}

You may have noticed that the Quiescence Search uses a new method called EvaluateMovesQ.  This method is virtually the same as the previously discussed Evaluate Moves except it only collects moves that capture.

private static List<Position> EvaluateMovesQ(Board examineBoard)
{
 //We are going to store our result boards here          
 List<Position> positions = new List<Position>();

 for (byte x = 0; x < 64; x++)
 {
  Piece piece = examineBoard.Squares[x].Piece;

  //Make sure there is a piece on the square
  if (piece == null)
   continue;

  //Make sure the color is the same color as the one we are moving.
  if (piece.PieceColor != examineBoard.WhoseMove)
   continue;

  //For each valid move for this piece
  foreach (byte dst in piece.ValidMoves)
  {
   if (examineBoard.Squares[dst].Piece == null)
   {
    continue;
   }

   Position move = new Position();

   move.SrcPosition = x;
   move.DstPosition = dst; 

   Piece pieceAttacked = examineBoard.Squares[move.DstPosition].Piece;

   move.Score += pieceAttacked.PieceValue;

   if (piece.PieceValue < pieceAttacked.PieceValue)
   {
    move.Score += pieceAttacked.PieceValue - piece.PieceValue;
   }

   move.Score += piece.PieceActionValue;


   positions.Add(move);
  }
 }

 return positions;
}

During the Quiescence Search we will often reach a position where no more captures are available.  Hence there will be no positions to evaluate.  For this reason we have to add the following line of code:


 if (positions.Count == 0)
 {
  return examineBoard.Score;
 }

This last piece of code that I want to explain is called the Stand Pad.  It’s just a complicated way of saying that during the quiescence search we will set a default value for alpha that is equal to the board being examined.  It just prevents you from examining moves that make your situations worse than it already is.


if (examineBoard.Score >= beta)
 return beta;

if (examineBoard.Score > alpha)
 alpha = examineBoard.Score;


That completes the post on Quiescence Search and Extension.  If you have any questions about this post feel free to post a comment below.  Chances are someone else has the same question and I would love a chance for improvement.

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Some Performance Optimization Advice

Over the last year of development of my chess engine, much of the time has been spent optimizing my code to allow for better and faster move searching.  Over that time I have learned a few tricks that I would like to share with you.

Measuring Performance

Essentially you can improve your performance in two ways:

  • Evaluate your nodes faster
  • Search fewer nodes to come up with the same answer

Your first problem in code optimization will be measurement.  How do you know you have really made a difference?  In order to help you with this problem you will need to make sure you can record some statistics during your move search.   The ones I capture in my chess engine are:

  • Time it took for the search to complete.
  • Number of nodes searched

This will allow you to benchmark and test your changes.  The best way to approach testing is to create several save games from the opening position, middle game and the end game.   Record the time and number of nodes searched for black and white.
After making any changes I usually perform tests against the above mentioned save games to see if I have made improvements in the above two matrices:  number of nodes searched or speed.

To complicate things further, after making a code change you might run your engine 3 times and get 3 different results each time. Let’s say that your chess engine found the best move in 9, 10 and 11 seconds.  That is a spread of about 20%.  So did you improve your engine by 10%-20% or was it just varied load on your pc.  How do you know?  To fight this I have added methods that will allow my engine to play against itself, it will make moves for both white and black.  This way you can test not just the time variance over one move, but a series of as many as 50 moves over the course of the game.  If last time the game took 10 minutes and now it takes 9, you probably improved your engine by 10%.  Running the test again should confirm this.

Finding Performance Gains

Now that we know how to measure performance gains lets discuss how to identify potential performance gains.
If you are in a .NET environment then the .NET profiler will be your friend.  If you have a Visual Studio for Developers edition it comes built in for free, however there are other third party tools you can use.  This tool has saved me hours of work as it will tell you where your engine is spending most of its time and allow you to concentrate on your trouble spots.  If you do not have a profiler tool you may have to somehow log the time stamps as your engine goes through different steps.  I do not suggest this.  In this case a good profiler is worth its weight in gold.  Red Gate ANTS Profiler is expensive but the best one I have ever tried.  If you can’t afford one, at least use it for their 14 day trial.

Your profiler will surly identify things for you, however here are some small lessons I have learned working with C#:

  • Make everything private
  • Whatever you can’t make private, make it sealed
  • Make as many methods static as possible.
  • Don’t make your methods chatty, one long method is better than 4 smaller ones.
  • Representing your chess board as an array [8][8] is slower then representing it as an array [64]
  • Replace int with byte where possible.
  • Return from your methods as early as possible.
  • Stacks are better than lists
  • Arrays are better than stacks and lists.
  • If you can define the size of the list before you populate it.
  • Casting, boxing, un-boxing is evil.

Further Performance Gains:

I find move generation and ordering is extremely important.  However here is the problem as I see it.  If you evaluate the score of each move before you sort and run Alpha Beta, you will be able to optimize your move ordering such that you will get extremely quick Alpha Beta cutoffs.  This is because you will be able to mostly try the best move first.

However the time you have spent evaluating each move will be wasted.  For example you might have evaluated the score on 20 moves, sort your moves try the first 2 and received a cut-off on move number 2.  In theory the time you have spent on the other 18 moves was wasted.  

On the other hand if you do a lighter and much faster evaluation say just captures, your sort will not be that good and you will have to search more nodes (up to 60% more).  On the other hand you would not do a heavy evaluation on every possible move.  As a whole this approach is usually faster

Finding this perfect balance between having enough information for a good sort and not doing extra work on moves you will not use, will allow you to find huge gains in your search algorithm.  Furthermore if you choose the poorer sort approach you will want to first to a shallower search say to ply 3, sort your move before you go into the deeper search (this is often called Iterative Deepening).  This will significantly improve your sort and allow you to search much fewer moves.

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Forsyth–Edwards Notation

In this post I am going to discuss Forsyth-Edwards Notation (FEN) and its implementation in a chess engine.   FEN is a standard way of describing a chess position, containing enough information to restart the chess game from that position.  It is based on a notation developed by a Scottish journalist, David Forsyth in the 19th century.

Why is FEN useful to us?

1. We can use FEN to store game history allowing us to search for move repetitions as well as display the history of the game to the user.  Furthermore if we find a FEN position that has occurred in the past, we can skip searching for the best move and use the same response we used before.

2. We can use FEN strings to implement an Opening Book.    With two FEN strings I can store position pairs representing a starting position and the prescribed response.

The implementation of Forsyth–Edwards Notation

FEN notation uses only ASCII characters stored in a single line.  A FEN string or record contains 6 fields.  These are separated by a space.

  • Piece placement from white’s perspective.  Each row is noted, starting from row 8 (blacks row0 and ending with row 1 (white’s row).  Each piece is described from column to column h.  Each piece is identified by a single letter. 

Pawn: P

Knight: K

Bishop: B

Rook: R

Queen: Q

King: K

White pieces are noted using capital letters and black using lower case.  So P would be a white pawn and p would signify a black pawn.
Empty squares (spaces) are described using numbers, each number representing the number of empty squares before the next chess pieces.  The number 8 would describe a completely empty row. 
The character / describes a new row.

So for a starting position we may see: rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR

  • The second column in the Forsyth–Edwards Notation represents whose turn it is.  A single character is used w for white and b for black.
  • The third column represents if castling is still allowed.  If neither side can castle then the character – is used.   Otherwise the following letters are used.  K means white can castle King Side, Q means White can castle Queen side.  Lower case k and q mean the same for black.
  • The fourth column represents an En Passant target square.  The square that the pawn hopped to get to its row, or the position behind the pawn.  If there is no En Passant square then the character – is used.  So if the last move was pawn to e4, we will record e3 in this column.
  • The fifth column contains the number of half moves since the last pawn move or capture.  This is used to determine the 50 move draw scenario.  
  • The last column contains the full move number.  The number starts at 1 and is incremented after black’s move.

Examples:

FEN for the starting position:

rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1

FEN after the white pawn moved to E4:

rnbqkbnr/pppppppp/8/8/4P3/8/PPPP1PPP/RNBQKBNR b KQkq e3 0 1

FEN after the black pawn moved to C5

rnbqkbnr/pp1ppppp/8/2p5/4P3/8/PPPP1PPP/RNBQKBNR w KQkq c6 0 2

And then after the white knight moves to F3:

rnbqkbnr/pp1ppppp/8/2p5/4P3/5N2/PPPP1PPP/RNBQKB1R b KQkq - 1 2

Forsyth–Edwards Notation Code

In my chess engine FEN is implemented in two methods.  The first method will produce a FEN string for any chess Board.

internal static string Fen(bool boardOnly, Board board)
{
 string output = String.Empty;
 byte blankSquares = 0;

 for (byte x = 0; x < 64; x++)
 {
  byte index = x;

  if (board.Squares[index].Piece != null)
  {
   if (blankSquares > 0)
   {
    output += blankSquares.ToString();
    blankSquares = 0;
   }

   if (board.Squares[index].Piece.PieceColor == ChessPieceColor.Black)
   {
    output += Piece.GetPieceTypeShort(board.Squares[index].Piece.PieceType).ToLower();
   }
   else
   {
    output += Piece.GetPieceTypeShort(board.Squares[index].Piece.PieceType);
   }
  }
  else
  {
   blankSquares++;
  }

  if (x % 8 == 7)
  {
   if (blankSquares > 0)
   {
    output += blankSquares.ToString();
    output += "/";
    blankSquares = 0;
   }
   else
   {
    if (x > 0 && x != 63)
    {
     output += "/";
    }
   }
  }
 }

 if (board.WhoseMove == ChessPieceColor.White)
 {
  output += " w ";
 }
 else
 {
  output += " b ";
 }

 string spacer = "";

 if (board.WhiteCastled == false)
 {
  if (board.Squares[60].Piece != null)
  {
   if (board.Squares[60].Piece.Moved == false)
   {
    if (board.Squares[63].Piece != null)
    {
     if (board.Squares[63].Piece.Moved == false)
     {
      output += "K";
      spacer = " ";
     }
    }
    if (board.Squares[56].Piece != null)
    {
     if (board.Squares[56].Piece.Moved == false)
     {
      output += "Q";
      spacer = " ";
     }
    }
   }
  }
 }

 if (board.BlackCastled == false)
 {
  if (board.Squares[4].Piece != null)
  {
   if (board.Squares[4].Piece.Moved == false)
   {
    if (board.Squares[7].Piece != null)
    {
     if (board.Squares[7].Piece.Moved == false)
     {
      output += "k";
      spacer = " ";
     }
    }
    if (board.Squares[0].Piece != null)
    {
     if (board.Squares[0].Piece.Moved == false)
     {
      output += "q";
      spacer = " ";
     }
    }
   }
  }

  
 }

 if (output.EndsWith("/"))
 {
  output.TrimEnd('/');
 }


 if (board.EnPassantPosition != 0)
 {
  output += spacer + GetColumnFromByte((byte)(board.EnPassantPosition % 8)) + "" + (byte)(8 - (byte)(board.EnPassantPosition / 8)) + " ";
 }
 else
 {
  output += spacer + "- ";
 }

 if (!boardOnly)
 {
  output += board.FiftyMove + " ";
  output += board.MoveCount + 1;
 }
 return output.Trim();
}

The second method is a Board constructor that will accept a FEN string and create a Chess Board based on the content of the string.  Strictly speaking you will not need this code.  I only use this to allow people to enter FEN strings in the user interface.   Since FEN is a standard used in many chess programs allowing users to input FEN strings will allow them to visualize chess positions they might find on the internet. 

internal Board(string fen) : this()
{
 byte index = 0;
 byte spc = 0;

 WhiteCastled = true;
 BlackCastled = true;
 byte spacers = 0;

 WhoseMove = ChessPieceColor.White;

 if (fen.Contains("a3"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 40;
 }
 else if (fen.Contains("b3"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 41;
 }
 else if (fen.Contains("c3"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 42;
 }
 else if (fen.Contains("d3"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 43;
 }
 else if (fen.Contains("e3"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 44;
 }
 else if (fen.Contains("f3"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 45;
 }
 else if (fen.Contains("g3"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 46;
 }
 else if (fen.Contains("h3"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 47;
 }


 if (fen.Contains("a6"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 16;
 }
 else if (fen.Contains("b6"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 17;
 }
 else if (fen.Contains("c6"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition =18;
 }
 else if (fen.Contains("d6"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 19;
 }
 else if (fen.Contains("e6"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 20;
 }
 else if (fen.Contains("f6"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 21;
 }
 else if (fen.Contains("g6"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 22;
 }
 else if (fen.Contains("h6"))
 {
  EnPassantColor = ChessPieceColor.White;
  EnPassantPosition = 23;
 }

 foreach (char c in fen)
 {

  if (index < 64 && spc == 0)
  {
   if (c == '1' && index < 63)
   {
    index++;
   }
   else if (c == '2' && index < 62)
   {
    index += 2;
   }
   else if (c == '3' && index < 61)
   {
    index += 3;
   }
   else if (c == '4' && index < 60)
   {
    index += 4;
   }
   else if (c == '5' && index < 59)
   {
    index += 5;
   }
   else if (c == '6' && index < 58)
   {
    index += 6;
   }
   else if (c == '7' && index < 57)
   {
    index += 7;
   }
   else if (c == '8' && index < 56)
   {
    index += 8;
   }
   else if (c == 'P')
   {
    Squares[index].Piece = new Piece(ChessPieceType.Pawn, ChessPieceColor.White);
    Squares[index].Piece.Moved = true;
    index++;
   }
   else if (c == 'N')
   {
    Squares[index].Piece = new Piece(ChessPieceType.Knight, ChessPieceColor.White);
    Squares[index].Piece.Moved = true;
    index++;
   }
   else if (c == 'B')
   {
    Squares[index].Piece = new Piece(ChessPieceType.Bishop, ChessPieceColor.White);
    Squares[index].Piece.Moved = true;
    index++;
   }
   else if (c == 'R')
   {
    Squares[index].Piece = new Piece(ChessPieceType.Rook, ChessPieceColor.White);
    Squares[index].Piece.Moved = true;
    index++;
   }
   else if (c == 'Q')
   {
    Squares[index].Piece = new Piece(ChessPieceType.Queen, ChessPieceColor.White);
    Squares[index].Piece.Moved = true;
    index++;
   }
   else if (c == 'K')
   {
    Squares[index].Piece = new Piece(ChessPieceType.King, ChessPieceColor.White);
    Squares[index].Piece.Moved = true;
    index++;
   }
   else if (c == 'p')
   {
    Squares[index].Piece = new Piece(ChessPieceType.Pawn, ChessPieceColor.Black);
    Squares[index].Piece.Moved = true;
    index++;
   }
   else if (c == 'n')
   {
    Squares[index].Piece = new Piece(ChessPieceType.Knight, ChessPieceColor.Black);
    Squares[index].Piece.Moved = true;
    index++;
   }
   else if (c == 'b')
   {
    Squares[index].Piece = new Piece(ChessPieceType.Bishop, ChessPieceColor.Black);
    Squares[index].Piece.Moved = true;
    index++;
   }
   else if (c == 'r')
   {
    Squares[index].Piece = new Piece(ChessPieceType.Rook, ChessPieceColor.Black);
    Squares[index].Piece.Moved = true;
    index++;
   }
   else if (c == 'q')
   {
    Squares[index].Piece = new Piece(ChessPieceType.Queen, ChessPieceColor.Black);
    Squares[index].Piece.Moved = true;
    index++;
   }
   else if (c == 'k')
   {
    Squares[index].Piece = new Piece(ChessPieceType.King, ChessPieceColor.Black);     
    Squares[index].Piece.Moved = true;
    index++;
   }
   else if (c == '/')
   {
    continue;
   }
   else if (c == ' ')
   {
    spc++;
   }
  }
  else
  {
   if (c == 'w')
   {
    WhoseMove = ChessPieceColor.White;
   }
   else if (c == 'b')
   {
    WhoseMove = ChessPieceColor.Black;
   }
   else if (c == 'K')
   {
    if (Squares[60].Piece != null)
    {
     if (Squares[60].Piece.PieceType == ChessPieceType.King)
     {
      Squares[60].Piece.Moved = false;
     }
    }

    if (Squares[63].Piece != null)
    {
     if (Squares[63].Piece.PieceType == ChessPieceType.Rook)
     {
      Squares[63].Piece.Moved = false;
     }
    }

    WhiteCastled = false;
   }
   else if (c == 'Q')
   {
    if (Squares[60].Piece != null)
    {
     if (Squares[60].Piece.PieceType == ChessPieceType.King)
     {
      Squares[60].Piece.Moved = false;
     }
    }

    if (Squares[56].Piece != null)
    {
     if (Squares[56].Piece.PieceType == ChessPieceType.Rook)
     {
      Squares[56].Piece.Moved = false;
     }
    }

    WhiteCastled = false;
   }
   else if (c == 'k')
   {
    if (Squares[4].Piece != null)
    {
     if (Squares[4].Piece.PieceType == ChessPieceType.King)
     {
      Squares[4].Piece.Moved = false;
     }
    }

    if (Squares[7].Piece != null)
    {
     if (Squares[7].Piece.PieceType == ChessPieceType.Rook)
     {
      Squares[7].Piece.Moved = false;
     }
    }

    BlackCastled = false;
   }
   else if (c == 'q')
   {
    if (Squares[4].Piece != null)
    {
     if (Squares[4].Piece.PieceType == ChessPieceType.King)
     {
      Squares[4].Piece.Moved = false;
     }
    }

    if (Squares[0].Piece != null)
    {
     if (Squares[0].Piece.PieceType == ChessPieceType.Rook)
     {
      Squares[0].Piece.Moved = false;
     }
    }

    BlackCastled = false;
   }
   else if (c == ' ')
   {
    spacers++;
   }
   else if (c == '1' && spacers == 4)
   {
    FiftyMove = (byte)((FiftyMove * 10) + 1);
   }
   else if (c == '2' && spacers == 4)
   {
    FiftyMove = (byte)((FiftyMove * 10) + 2);
   }
   else if (c == '3' && spacers == 4)
   {
    FiftyMove = (byte)((FiftyMove * 10) + 3);
   }
   else if (c == '4' && spacers == 4)
   {
    FiftyMove = (byte)((FiftyMove * 10) + 4);
   }
   else if (c == '5' && spacers == 4)
   {
    FiftyMove = (byte)((FiftyMove * 10) + 5);
   }
   else if (c == '6' && spacers == 4)
   {
    FiftyMove = (byte)((FiftyMove * 10) + 6);
   }
   else if (c == '7' && spacers == 4)
   {
    FiftyMove = (byte)((FiftyMove * 10) + 7);
   }
   else if (c == '8' && spacers == 4)
   {
    FiftyMove = (byte)((FiftyMove * 10) + 8);
   }
   else if (c == '9' && spacers == 4)
   {
    FiftyMove = (byte)((FiftyMove * 10) + 9);
   }
   else if (c == '0' && spacers == 4)
   {
    MoveCount = (byte)((MoveCount * 10) + 0);
   }
   else if (c == '1' && spacers == 5)
   {
    MoveCount = (byte)((MoveCount * 10) + 1);
   }
   else if (c == '2' && spacers == 5)
   {
    MoveCount = (byte)((MoveCount * 10) + 2);
   }
   else if (c == '3' && spacers == 5)
   {
    MoveCount = (byte)((MoveCount * 10) + 3);
   }
   else if (c == '4' && spacers == 5)
   {
    MoveCount = (byte)((MoveCount * 10) + 4);
   }
   else if (c == '5' && spacers == 5)
   {
    MoveCount = (byte)((MoveCount * 10) + 5);
   }
   else if (c == '6' && spacers == 5)
   {
    MoveCount = (byte)((MoveCount * 10) + 6);
   }
   else if (c == '7' && spacers == 5)
   {
    MoveCount = (byte)((MoveCount * 10) + 7);
   }
   else if (c == '8' && spacers == 5)
   {
    MoveCount = (byte)((MoveCount * 10) + 8);
   }
   else if (c == '9' && spacers == 5)
   {
    MoveCount = (byte)((MoveCount * 10) + 9);
   }
   else if (c == '0' && spacers == 5)
   {
    MoveCount = (byte)((MoveCount * 10) + 0);
   }

  }
 }

  
}

This concludes the post on Forsyth–Edwards Notation.  If you want to get started on creating your own chess engine download my C# Chess Game Starter Kit

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Completing the chess engine

Now that we have all the necessary parts for keeping track of our chess pieces, generating valid moves and searching for the best computer move, we are ready to put it all together and complete our chess engine.  We have already started to discuss the chess engine class in the previous post titled: Starting the Chess Engine.  Just to recap that post we have already:

Declared the class as:


public sealed class Engine

Declared its internal members representing our chess board and the previous chess board as well as variables representing whose move it is.

internal Board ChessBoard;
internal Board PreviousChessBoard;

public ChessPieceColor WhoseMove
{
    get { return ChessBoard.WhoseMove; }
    set { ChessBoard.WhoseMove = value; }
}


Declared a constructor that will initiate the chess board, move history, pre-calculate all possible moves from all positions, register starting positions of a new chess game and calculate all valid moves from that position.

Since we now have discussed the Chess Board Evaluation class I will modify this listing slightly to evaluate the board score as its last operation.


public Engine()
{
    ChessBoard = new Board();
    MoveHistory = new Stack<MoveContent>();

    RegisterStartingBoard();
    ChessBoard.WhoseMove = ChessPieceColor.White;   
   
    ChessPieceMoves.InitiateChessPieceMotion();
    PieceValidMoves.GenerateValidMoves(ChessBoard);
 Evaluation.EvaluateBoardScore(ChessBoard);
}


We also created a Move Piece method that will allow us to move chess pieces around the board.  The important fact to notice here is that if the move fails, say because it would cause an invalid position, the chess board reverts to its previous state.

public bool MovePiece(byte sourceColumn, byte sourceRow,
         byte destinationColumn, byte destinationRow)
{
 byte srcPosition = (byte)(sourceColumn + (sourceRow * 8));
 byte dstPosition = (byte)(destinationColumn + (destinationRow * 8));

 Piece Piece = ChessBoard.Squares[srcPosition].Piece;

 PreviousChessBoard = new Board(ChessBoard);
 
 Board.MovePiece(ChessBoard, srcPosition, dstPosition, PromoteToPieceType);

 PieceValidMoves.GenerateValidMoves(ChessBoard);
 
 //If there is a check in place, check if this is still true;
 if (Piece.PieceColor == ChessPieceColor.White)
 {
  if (ChessBoard.WhiteCheck)
  {
   //Invalid Move
   ChessBoard = new Board(PreviousChessBoard);
   PieceValidMoves.GenerateValidMoves(ChessBoard);
   return false;
  }
 }
 else if (Piece.PieceColor == ChessPieceColor.Black)
 {
  if (ChessBoard.BlackCheck)
  {
   //Invalid Move
   ChessBoard = new Board(PreviousChessBoard);
   PieceValidMoves.GenerateValidMoves(ChessBoard);
   return false;
  }
 }

 MoveHistory.Push(ChessBoard.LastMove);

 return true;
}


That’s it for the review now onto the remainder of the code needed for our chess engine to successfully play chess.

First we will introduce a few public variables:

We want to know which side of the board contains the human player.


public ChessPieceColor HumanPlayer;

We need to know how deep to perform the AI search, how many plies. Remember each ply is a single move.  So if white moves that is one ply, if black responds that is two ply.

public byte PlyDepthSearched = 5;

We also would like to keep track of all of the moves made during the game.  This will solve two problems.  First in order to call a draw for a three move repetition we need to somehow know what moves have been made.  Second we might want to be able to display the move history to the human player as we go along.

First we need to declare the OpeningMove class:

internal class OpeningMove
{
 public string EndingFEN;
 public string StartingFEN;
 public List<MoveContent> Moves;

 public OpeningMove()
 {
  StartingFEN = String.Empty;
  EndingFEN = String.Empty;
  Moves = new List<MoveContent>();
 }
}


internal static List<OpeningMove> CurrentGameBook;

The next method will add moves to the above declared Current Game Book as they occur.  This method also searches the Game Book to see if a repeat move has occurred.  Notice the use of FEN notation to store the chess board history.  More on FEN notation in the next post.

internal static void SaveCurrentGameMove(Board currentBoard, Board previousBoard, ICollection<OpeningMove> gameBook, MoveContent bestMove)
{
 try
 {
  var move = new OpeningMove();

  move.StartingFEN = Board.Fen(true, previousBoard);
  move.EndingFEN = Board.Fen(true, currentBoard);
  move.Moves.Add(bestMove);

  gameBook.Add(move);

  foreach (OpeningMove move1 in gameBook)
  {
   byte repeatedMoves = 0;

   foreach (OpeningMove move2 in gameBook)
   {
    if (move1.EndingFEN == move2.EndingFEN)
    {
     repeatedMoves++;
    }
   }

   if (previousBoard.RepeatedMove < repeatedMoves)
   {
    previousBoard.RepeatedMove = repeatedMoves;
    currentBoard.RepeatedMove = repeatedMoves;
   }
  }
  if (currentBoard.RepeatedMove >= 3)
  {
   currentBoard.StaleMate = true;
  }
 }
 catch (Exception)
 {
  return;
 }

 return;
}
}

Now we have a mechanism for testing for 3 move repetition.  Remember our chess board class already handles the 50 move rule.  The last step is to create a method that will check for mate scenarios, check and stale.  This method takes advantage of the code we already wrote in the Move Search class that checks for all available moves and records if the king has any moves not in check.

private static bool CheckForMate(ChessPieceColor whosTurn, ref Board chessBoard)
{
 Search.SearchForMate(whosTurn, chessBoard, ref chessBoard.BlackMate,
       ref chessBoard.WhiteMate, ref chessBoard.StaleMate);

 if (chessBoard.BlackMate || chessBoard.WhiteMate || chessBoard.StaleMate)
 {
  return true;
 }

 return false;
}



The last method will make the chess move for the computer as well as check for mate, and save current game moves.  This is the method our external user interface calls when we want to get the computer to make the move.  Otherwise if the human player is moving you would just call the move method.  Notice that the check for mate method is called two times.  Once before the move is made and once after.  This is because the previous human move might have caused a mate (first call) or the computer move might have caused a mate (second call).

public void AIPonderMove()
{
    if (CheckForMate(WhoseMove, ref ChessBoard))
    {
        return;
    }
 MoveContent bestMove = new MoveContent();
 
    //If there is no playbook move search for the best move
    bestMove = AlphaBetaRoot(ChessBoard, PlyDepthSearched);
  
    //Make the move
    PreviousChessBoard = new Board(ChessBoard);
  
    Board.MovePiece(ChessBoard, bestMove.MovingPiecePrimary.SrcPosition, bestMove.MovingPiecePrimary.DstPosition, ChessPieceType.Queen);
  
    SaveCurrentGameMove(bestBoard, ChessBoard, CurrentGameBook);

    PieceValidMoves.GenerateValidMoves(ChessBoard);
    Evaluation.EvaluateBoardScore(ChessBoard);

    if (CheckForMate(WhoseMove, ref ChessBoard))
    {
        return;
    }
}

The above methods are all you need to start coding your chess user interface.  However because we have declared most of our variables as private or internal if your user interface is in another assembly you might need a few additional methods that will expose certain properties of your chess board and chess engine.  I have included some of these below.

public bool GetBlackMate()
{
    return ChessBoard.BlackMate;
}


public bool GetWhiteMate()
{
    return ChessBoard.WhiteMate;
}


public bool GetBlackCheck()
{
    return ChessBoard.BlackCheck;
}

public bool GetWhiteCheck()
{
    return ChessBoard.WhiteCheck;
}

public byte GetRepeatedMove()
{
    return ChessBoard.RepeatedMove;
}

public byte GetFiftyMoveCount()
{
    return ChessBoard.FiftyMove;
}


public bool IsValidMove(byte sourceColumn, byte sourceRow, byte destinationColumn, byte destinationRow)
{
 if (ChessBoard == null)
 {
  return false;
 }

 if (ChessBoard.Squares == null)
 {
  return false;
 }

 byte index = GetBoardIndex(sourceColumn, sourceRow);

 if (ChessBoard.Squares[index].Piece == null)
 {
  return false;
 }

 foreach (byte bs in ChessBoard.Squares[index].Piece.ValidMoves)
 {
  if (bs % 8 == destinationColumn)
  {
   if ((byte)(bs / 8) == destinationRow)
   {
    return true;
   }
  }
 }

 index = GetBoardIndex(destinationColumn, destinationRow);

 if (index == ChessBoard.EnPassantPosition)
 {
  return true;
 }

 return false;
}


public ChessPieceType GetPieceTypeAt(byte boardColumn, byte boardRow)
{
 byte index = GetBoardIndex(boardColumn, boardRow);

 if (ChessBoard.Squares[index].Piece == null)
 {
  return ChessPieceType.None;
 }

 return ChessBoard.Squares[index].Piece.PieceType;
}

public ChessPieceType GetPieceTypeAt(byte index)
{
 if (ChessBoard.Squares[index].Piece == null)
 {
  return ChessPieceType.None;
 }

 return ChessBoard.Squares[index].Piece.PieceType;
}

public ChessPieceColor GetPieceColorAt(byte boardColumn, byte boardRow)
{
 byte index = GetBoardIndex(boardColumn, boardRow);

 if (ChessBoard.Squares[index].Piece == null)
 {
  return ChessPieceColor.White;
 }
 return ChessBoard.Squares[index].Piece.PieceColor;
}

public ChessPieceColor GetPieceColorAt(byte index)
{
 if (ChessBoard.Squares[index].Piece == null)
 {
  return ChessPieceColor.White;
 }
 return ChessBoard.Squares[index].Piece.PieceColor;
}

Notice this method will check for all game ending scenarios including 50 move and 3 move repetition.


public bool IsGameOver()
{
 if (ChessBoard.StaleMate)
 {
  return true;
 }
 if (ChessBoard.WhiteMate || ChessBoard.BlackMate)
 {
  return true;
 }
 if (ChessBoard.FiftyMove >= 50)
 {
  return true;
 }
 if (ChessBoard.RepeatedMove >= 3)
 {
  return true;
 }

 if (ChessBoard.InsufficientMaterial)
 {
  return true;
 }
 return false;
}


This post is a bit of a milestone as it wraps up the bulk of the chess engine source code.  There are still a few points I have not discussed such as an opening book or some more advanced search features such as Quiescence, FEN, Pondering, Iterative Deepening or Principle Variation Search.   However the sum of the code posted thus far will provide you will a working chess engine that will play fairly good chess.

If you feel like you don’t want to start typing up all the code posted here, I have made available a C# chess engine starter kit that includes most of the source code you will need to start a chess engine including a simple user interface.  You can download the development kit from here.

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Move Searching Alpha Beta Part 2

Last time I discussed Min Max and the Alpha Beta algorithms.  However you might have noticed that the algorithm I showed last time does not really tell you which of the available moves is the best, but rather which was the best score out of all the available moves.  To figure out which resulting chess board is the best I have implemented another method called Alpha Beta Root.

Alpha Beta Root is very similar to the regular Alpha Beta Method with the exception of keeping track of the best board found so far.  Alpha Beta Root is also our entry method into searching; it calls the regular Alpha Beta method.  You pass it a chess board and it returns Move Content containing the best move you can make.  Alpha Beta Root does not also need to perform a Quiescence Search since it is already performed in the regular Alpha Beta method.

The code below can be divided into 3 sections.

  1. Initial examination of what legal moves I can make and what their resulting score is.  This is followed by a sort to give us the best chance of trying the best move first
  2. Initial 1 ply call of Alpha Beta to see if there is an instant check mate so we can exit.
  3. Regular Alpha Beta call.

Before we get started we will need a helper struct to keep a list of our starting positions.

internal struct ResultBoards
{      
 internal List<Board> Positions;      
}

Now onto the main Alpha Beta Root Method:

internal static MoveContent AlphaBetaRoot(Board examineBoard, byte depth)
{
 int alpha = -400000000;
 const int beta = 400000000;

 Board bestBoard = new Board(short.MinValue);

 //We are going to store our result boards here          
 ResultBoards succ = new ResultBoards
 {
  Positions = new List<Board>(30)
 };

 for (byte x = 0; x < 64; x++)
 {
  Square sqr = examineBoard.Squares[x];

  //Make sure there is a piece on the square
  if (sqr.Piece == null)
   continue;

  //Make sure the color is the same color as the one we are moving.
  if (sqr.Piece.PieceColor != examineBoard.WhoseMove)
   continue;

  //For each valid move for this piece
  foreach (byte dst in sqr.Piece.ValidMoves)
  {
   //We make copies of the board and move so that we can move it without effecting the parent board
   Board board = examineBoard.FastCopy();

   //Make move so we can examine it
   Board.MovePiece(board, x, dst, ChessPieceType.Queen);

   //We Generate Valid Moves for Board
   PieceValidMoves.GenerateValidMoves(board);

   //Invalid Move
   if (board.WhiteCheck && examineBoard.WhoseMove == ChessPieceColor.White)
   {
    continue;
   }

   //Invalid Move
   if (board.BlackCheck && examineBoard.WhoseMove == ChessPieceColor.Black)
   {
    continue;
   }

   //We calculate the board score
   Evaluation.EvaluateBoardScore(board);

   //Invert Score to support Negamax
   board.Score = SideToMoveScore(board.Score, board.WhoseMove);

   succ.Positions.Add(board);
  }
 }

 succ.Positions.Sort(Sort);

 //Can I make an instant mate?
 foreach (Board pos in succ.Positions)
 {
  int value = -AlphaBeta(pos, 1, -beta, -alpha);

  if (value >= 32767)
  {
   return pos.LastMove;
  }
 }
 depth--;

 byte plyDepthReached = ModifyDepth(depth, succ.Positions.Count);

 int currentBoard = 0;

 alpha = -400000000;

 succ.Positions.Sort(Sort);

 foreach (Board pos in succ.Positions)
 {
  currentBoard++;

  int value = -AlphaBeta(pos, plyDepthReached, -beta, -alpha);

  pos.Score = value;

  //If value is greater then alpha this is the best board
  if (value > alpha)
  {
   alpha = value;
   bestBoard = new Board(pos);
  }

 }

 return bestBoard.LastMove;
}

The obvious question might be why do we do this?  Why not simply copy the best board in the regular Alpha Beta method and return it.  The simple answer is performance.  Because the regular Alpha Beta method is recursive we want it to be as fast as possible.  It is much faster to copy integers rather than calling the copy constructor for the board object.

One last piece of code that I would like to add here is the Modify Ply method.  One thing I noticed while testing my chess engine is that during the end game my engine made moves at a much faster rate than it did during the opening and middle game.  This had a very simple explanation as during the end game there are far fewer chess pieces and there are less moves to calculate.  For this reason I added a small method to that adds 2 plies to my search if there are less then 6 root moves on the board.  This way I can search deeper during the end game, increasing my odds of finding a check mate.

private static byte ModifyDepth(byte depth, int possibleMoves)
{
 if (possibleMoves <= 15)
 {
  depth += 1;
 }

 return depth;
}

If you have any questions about this post feel free to post a comment below.  Chances are someone else has the same question and I would love a chance for improvement.

If you want to get started on creating your own chess engine download my C# Chess Game Starter Kit.   

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Performance Reconstruction Phase Two

This is the second re-design I am doing on the ChessBin Chess Engine.  You can read all about the first one here, so you don’t make the same mistakes as me.  I guess that is what you get for re-inventing the wheel.  At least I am still having fun. 

This re-construction is related to how my chess engine stores the chess board.  Currently the chess board is described as a two dimensional array.  This way with a column and row you can locate any square on the board.  This is makes my chess engine easy to understand but slow. 

The new design will modify the chess board to be a single array of 64 squares.  This makes it necessary to refer to board positions via an index.  An index of 0 will locate the top left most square on the board and an index of 63 will locate the bottom right one.  This also allows me to drop the entire Position struct as it is no longer necessary to describe the position by two bytes. 

The new version of my ChessBin chess engine that I am currently testing is about 25% faster due to these changes.

I will be modifying each of the posts and the development kit over the next few weeks.  Stay tuned for updates.

Updated April 22nd 2009, I have finished updating all of the posts and the Chess Game Development Kit.

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Move Searching and Alpha Beta

Out of all of the computer chess programming concepts I discussed on this website I found move searching to be the most complicated for me to understand, and the most time consuming to write.  Until this point all of the concepts of writing a chess engine were easy to understand.  Most developers will figure out some way of representing chess pieces, chess board and movement.  However I found that move searching is not like that.  Reinventing the wheel by writing your own move search algorithm is just not a good idea.  There are algorithms that you just have to implement for your engine to have a shot at searching enough moves to simulate even average chess playing.

Min Max & Negamax

Probably like most people starting to program a chess engine I started by looking at implementing the Min Max algorithm.  The idea is fairly simple, I look at all my moves I can make, evaluate them and make the best move.  Then I do the same for the opponent from his point of view. 

This led me to some really crappy code that did not really work very well.  Actually what I found out later is that min max works by going deep into the furthest leaf of the search tree and working backwards.  That’s not the same thing as going from the top down because what ended up being a spectacular move 5 nodes down could have been a really crappy move at the beginning.  A good example of this is a chess piece sacrifice to get a check mate.  So I look to all the possibilities of every move I can make along with all of the moves my opponent can make work backwards and I choose the root move that will get me the best score at the end.


private static int MinMax(Board examineBoard, byte depth)
{
 if (depth == 0)
 {
   //Evaluate Score
  Evaluation.EvaluateBoardScore(examineBoard);
  //Invert Score to support Negamax
  return SideToMoveScore(examineBoard.Score, examineBoard.WhoseMove);
 }

 List<Position> positions = EvaluateMoves(examineBoard, depth);

 if (examineBoard.WhiteCheck || examineBoard.BlackCheck || positions.Count == 0)
 {
  if (SearchForMate(examineBoard.WhoseMove, examineBoard, ref examineBoard.BlackMate, ref examineBoard.WhiteMate, ref examineBoard.StaleMate))
  {
   if (examineBoard.BlackMate)
   {
    if (examineBoard.WhoseMove == ChessPieceColor.Black)
     return -32767-depth;

    return 32767 + depth;
   }
   if (examineBoard.WhiteMate)
   {
    if (examineBoard.WhoseMove == ChessPieceColor.Black)
     return 32767 + depth;

    return -32767 - depth;
   }

   //If Not Mate then StaleMate
   return 0;
  }
 }

 int bestScore = -32767; 
 
 foreach (Position move in positions)
 {
  //Make a copy
  Board board = examineBoard.FastCopy();

  //Move Piece
  Board.MovePiece(board, move.SrcPosition, move.DstPosition, ChessPieceType.Queen);

  //We Generate Valid Moves for Board
  PieceValidMoves.GenerateValidMoves(board);

  if (board.BlackCheck)
  {
   if (examineBoard.WhoseMove == ChessPieceColor.Black)
   {
    //Invalid Move
    continue;
   }
  }

  if (board.WhiteCheck)
  {
   if (examineBoard.WhoseMove == ChessPieceColor.White)
   {
    //Invalid Move
    continue;
   }
  }

  int value = -MinMax(board, (byte)(depth-1));

  if (value > bestScore)
  {
   bestScore = (int)value;
  }
 }

 return bestScore;
}


The above Mix-Max implementation is not actually used anywhere in my chess engine, however I wanted to make sure it is we understand how it works before we move to the actual implementation of Alpha Beta. 

The first point I would like to make about the above code is that the algorithm is recursive.  It will call itself up to its furthest leaf and then return the score back to each parent branch so that the branch can evaluate which leaf was the best back as many levels as we decide are needed. 

The second point on the above Min-Max implementation is related to the depth variable.  It will set the limit of how far should our algorithm search.  This is often referred to as ply.  One ply equals one move by either side.  So if we set our algorithm depth to 1 ply the Min Max algorithm would simple search one move deep and return the best move available to the current side.  A depth 2 or ply 2 search would search each possible move and each possible response to every move. 

Furthermore the above algorithm is actually a variation of Min-Max often called Negamax because as mentioned above it always looks for the maximizing score rather than having to branches looking for either the maximum or minimum value depending on the chess piece color moving.

There is however a trick to implementing Negamax.  The issue is that the algorithm has to always look for the highest score, so we will need a helper method to help us out here by inverting the score for black. 


private static int SideToMoveScore(int score, ChessPieceColor color)
{
 if (color == ChessPieceColor.Black)
  return -score;

 return score;
}


This above method is key, since without it your algorithm would not return the best move for black but rather the worst, highest scored. 

If we you had tried to implemented this algorithm in your chess engine you would find that move searching was probably very slow.  It was probably ok down to ply 3 or 4

Alpha Beta

The next evolution of my search algorithm was Alpha Beta. It took me of weeks reading articles on min max and alpha beta trying to fully grasp exactly was has to be coded and why it works.  

The main idea behind Alpha Beta is the fact that we don’t need to search every possible move.  Some moves just do not make sense. 

Let’s imagine your opponent has 5 bags of items.  You get to keep one of the items from one of the 5 bags.  You get to choose the bag, however your opponent will get to choose which item you get. Your opponent does not want to give away his valuable items so he will choose the one that is least valuable to you.  So you must choose the bag where the least valuable item is more valuable than the least valuable item in all of the other bags.

So let’s say you open the first bag and you look inside.  You see a gold ring, a diamond and a shovel.  You know your opponent is not going to give you the gold ring or the diamond.  If you choose the first bag you will end up with a shovel.  The shovel is the least valuable item in that bag you remember that for later.

So you look into the second bag and you see a laptop computer.  This is more valuable than a shovel, so you keep looking.  However the second item is a clump of dirt.  Dirt is less valuable than a shovel.  So you don’t need to keep looking through the other items in that bag, because you know that whatever else you find in the bag even if it is more valuable you will just end up with dirt.   Instead you can move on to the next bag and keep looking for something better than a shovel.

This is how alpha beta works.  You stop looking for responses to your move (bag) when you find one that has a worst result than the worst result from your previous move.  The name Alpha Beta refers to the two variables that you will pass around the algorithm that will keep the best scores for you and your opponent (The Shovel)

The main advantage of Alpha Beta is that it is free.  It does not affect the quality of the moves made by the computer.  It simply discards moves that would not have been considered anyways. 

One additional note I would like to make is that Alpha Beta works best when the moves are sorted in the order of best first.  If we think of our example above it is in our best interest to find the bag with the shovel first before finding the bag with the clump of dirt.  If you had found the clump of dirt first you would still have to look through all the other items in the second bag.

For this purpose it is in our best interest to sort the moves prior to trying Alpha Beta.  For that we need to declare a few methods.

Evaluate Moves

Evaluate Moves is a pseudo move generator and an evaluation function combined.  It organizes all the valid moves for a position into a list of positions and assigns them a score based on a very basic evaluation.  We don’t use this evaluation score to make any serious decisions we just use it to sort our moves.  You may be tempted to use your regular chess board evaluation function here.  This would improve sorting quite a bit, however a full evaluation is slow and there would be allot of wasted effort because you don’t need the actual score of the chess board until you get to depth 0 (the last ply you are going to look at).  In my tests I found that doing a simple sort based on a score resulting from Most Valuable Vitim Least Valuable Attacker, performs quite well.  Basically the idea is that you want to try a pawn attacking a queen before you try a queen attacking a pawn.  I achieve this by subtracting the values of the attacker and defender.  This generates lots of node cut-offs.  In addition to MVV/LVA I add some small easy evaluation points for castling moves and Piece Action Value.

Evaluate Moves stores its results in a List of Positions.  


private struct Position
{
 internal byte SrcPosition;
 internal byte DstPosition;
 internal int Score;
}

Evaluate Moves also requires a helper sort method.

private static int Sort(Position s2, Position s1)
{
 return (s1.Score).CompareTo(s2.Score);
}

The actual Evaluate Moves method loops through all of the chess pieces on the board and records the source position and destination position of the move along its pseudo score.

private static List<Position> EvaluateMoves(Board board)
{

 //We are going to store our result boards here          
 List<Position> positions = new List<Position>();

 for (byte x = 0; x < 64; x++)
 {
  Piece piece = board.Squares[x].Piece;

  //Make sure there is a piece on the square
  if (piece == null)
   continue;

  //Make sure the color is the same color as the one we are moving.
  if (piece.PieceColor != board.WhoseMove)
   continue;

  //For each valid move for this piece
  foreach (byte dst in piece.ValidMoves)
  {
   Position move = new Position();

   move.SrcPosition = x;
   move.DstPosition = dst;

   Piece pieceAttacked = board.Squares[move.DstPosition].Piece;

   //If the move is a capture add it's value to the score
   if (pieceAttacked != null)
   {
    move.Score += pieceAttacked.PieceValue;

    if (piece.PieceValue < pieceAttacked.PieceValue)
    {
     move.Score += pieceAttacked.PieceValue - piece.PieceValue;
    }
   }

   if (!piece.Moved)
   {
    move.Score += 10;
   }

   move.Score += piece.PieceActionValue;

   //Add Score for Castling
   if (!board.WhiteCastled && board.WhoseMove == ChessPieceColor.White)
   {

    if (piece.PieceType == ChessPieceType.King)
    {
     if (move.DstPosition != 62 && move.DstPosition != 58)
     {
      move.Score -= 40;
     }
     else
     {
      move.Score += 40;
     }
    }
    if (piece.PieceType == ChessPieceType.Rook)
    {
     move.Score -= 40;
    }
   }

   if (!board.BlackCastled && board.WhoseMove == ChessPieceColor.Black)
   {
    if (piece.PieceType == ChessPieceType.King)
    {
     if (move.DstPosition != 6 && move.DstPosition != 2)
     {
      move.Score -= 40;
     }
     else
     {
      move.Score += 40;
     }
    }
    if (piece.PieceType == ChessPieceType.Rook)
    {
     move.Score -= 40;
    }
   }

   positions.Add(move);
  }
 }

 return positions;
}


Now for the actual implementation of Alpha Beta

In our chess engine we need to introduce the concept of the variables alpha and beta.  These will be used during our recursive search to affectively keep the leaf score during our search.  This will allow us to make the decision of whether or not we need to continue or we can cut the search short and return.

• Alpha will be the current best score for this leaf. 
• Beta will be the best score for the upper leaf thus far or the opponent’s best score for positions already searched.

If Alpha > Beta, meaning my move is better than my opponents other best move thus far we have reached the scenario where searching other moves are not relevant because a Shovel is better than clump of dirt.

Here is the Alpha Beta code from my chess engine


private static int AlphaBeta(Board examineBoard, byte depth, int alpha, int beta)
{
 nodesSearched++;

 if (examineBoard.FiftyMove >= 50 || examineBoard.RepeatedMove >= 3)
  return 0;

 if (depth == 0)
 {
  //Evaluate Score
  Evaluation.EvaluateBoardScore(examineBoard);
  //Invert Score to support Negamax
  return SideToMoveScore(examineBoard.Score, examineBoard.WhoseMove);
 }

 List<Position> positions = EvaluateMoves(examineBoard);

 if (examineBoard.WhiteCheck || examineBoard.BlackCheck || positions.Count == 0)
 {
  if (SearchForMate(examineBoard.WhoseMove, examineBoard, ref examineBoard.BlackMate, ref examineBoard.WhiteMate, ref examineBoard.StaleMate))
  {
   if (examineBoard.BlackMate)
   {
    if (examineBoard.WhoseMove == ChessPieceColor.Black)
     return -32767-depth;

    return 32767 + depth;
   }
   if (examineBoard.WhiteMate)
   {
    if (examineBoard.WhoseMove == ChessPieceColor.Black)
     return 32767 + depth;

    return -32767 - depth;
   }

   //If Not Mate then StaleMate
   return 0;
  }
 }

 positions.Sort(Sort);

 foreach (Position move in positions)
 {
  //Make a copy
  Board board = examineBoard.FastCopy();

  //Move Piece
  Board.MovePiece(board, move.SrcPosition, move.DstPosition, ChessPieceType.Queen);

  //We Generate Valid Moves for Board
  PieceValidMoves.GenerateValidMoves(board);

  if (board.BlackCheck)
  {
   if (examineBoard.WhoseMove == ChessPieceColor.Black)
   {
    //Invalid Move
    continue;
   }
  }

  if (board.WhiteCheck)
  {
   if (examineBoard.WhoseMove == ChessPieceColor.White)
   {
    //Invalid Move
    continue;
   }
  }

  int value = -AlphaBeta(board, (byte)(depth-1), -beta, -alpha);

  if (value >= beta)
  {
   // Beta cut-off
   return beta;
  }
  if (value > alpha)
  {
   alpha = value;
  }
 }
 
 return alpha;
}


As you see this code is almost identical to the Min-Max code above with the exception of move sorting as well as the Alpha and Beta variables.  Furthermore if we do find a cut-off (alpha > beta) then we simply return beta as the best score.

Initially the Alpha Beta method is called with Alpha being the smallest possible integer and Beta being the highest possible integer.  This ensures that we search at least one move all the way down to its last ply before performing any cut-offs.  In the next post I will discuss how to make that initial Alpha Beta call from my chess engine and some of the other modifications of Alpha Beta that will improve its speed and accuracy.

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Search for Mate

Before we can discus move searching and the Alpha Beta algorithm we need a way to check for check mates.  This method will actually be located in our static Search class.  This method will loop through all of the moves for all the chess pieces on the board and see if they actually have a valid move.  If they do then we are not in a check mate situation.  If there aren’t any valid moves for this board position that we know that this is either a check mate (if the king is in check) or a stale mate.

This method is very expensive to execute so we only call it if there is a check on any king on the board or if there are 0 possible moves.  I will explain in more detail in my Alpha Beta method.

The Search for Mate method returns true if a check mate or stale mate is found. The actual values of type of mate and side mated are stored in the three reference variables passed into the method.


internal static bool SearchForMate(ChessPieceColor movingSide, Board examineBoard, ref bool blackMate, ref bool whiteMate, ref bool staleMate)
{
 bool foundNonCheckBlack = false;
 bool foundNonCheckWhite = false;

 for (byte x = 0; x < 64; x++)
 {
  Square sqr = examineBoard.Squares[x];

  //Make sure there is a piece on the square
  if (sqr.Piece == null)
   continue;

  //Make sure the color is the same color as the one we are moving.
  if (sqr.Piece.PieceColor != movingSide)
   continue;

  //For each valid move for this piece
  foreach (byte dst in sqr.Piece.ValidMoves)
  {

   //We make copies of the board and move so we don't change the original
   Board board = examineBoard.FastCopy();

   //Make move so we can examine it
   Board.MovePiece(board, x, dst, ChessPieceType.Queen);

   //We Generate Valid Moves for Board
   PieceValidMoves.GenerateValidMoves(board);

   if (board.BlackCheck == false)
   {
    foundNonCheckBlack = true;
   }
   else if (movingSide == ChessPieceColor.Black)
   {
    continue;
   }

   if (board.WhiteCheck == false )
   {
    foundNonCheckWhite = true;
   }
   else if (movingSide == ChessPieceColor.White)
   {
    continue;
   }
  }
 }

 if (foundNonCheckBlack == false)
 {
  if (examineBoard.BlackCheck)
  {
   blackMate = true;
   return true;
  }
  if (!examineBoard.WhiteMate && movingSide != ChessPieceColor.White)
  {
   staleMate = true;
   return true;
  }
 }

 if (foundNonCheckWhite == false)
 {
  if (examineBoard.WhiteCheck)
  {
   whiteMate = true;
   return true;
  }
  if (!examineBoard.BlackMate && movingSide != ChessPieceColor.Black)
  {
   staleMate = true;
   return true;
  }
 }

 return false;
}

The Search for Mate method is also used in your Chess Engine Make Move method which will check if the last move made by the human player caused a check mate.  This will be done every time a player makes a move.

That’s it for this post.  If you have any questions feel free to email me or post a comment below.  Chances are if you have a question, other people might have it too.

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