AI game playing

8/9/2019 AI game playing

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Game Playing

CIS 479/579

Bruce R. MaximUM-Dearbrn


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Im)r'ing Searc&-Ba$e"

Prblem Sl'ing#( )!in$

. Im)r'e genera!r ! nly genera!e

g" m'e$ r )a!&$

0. Im)r'e !e$!er $ !&a! g" m'e$

recgni1e" early an" ex)lre" *ir$!


4/46

U$ing Genera!e an" #e$!

% Can be u$e" ! $l'e i"en!i*ica!in

)rblem$ in $mall $earc& $)ace$

% Can be !&ug&! * a$ being a "e)!&-*ir$!$earc& )rce$$ (i!& bac+!rac+ing

all(e"

% Den"ral 2 ex)er! $y$!em *r i"en!i*yingc&emical cm)un"$ *rm 3MR $)ec!ra


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Danger$

% Cn$i"er a $a*e crac+er !rying ! u$e

genera!e a !e$! ! crac+ a $a*e (i!& a

number cmbina!in 66-66-66% #&ere are 664 )$$ible cmbina!in$

% ,! a!!em)!$/minu!e i! (ul" !a+e 8

(ee+$ * 04/7 (r+ ! !ry eac&cmbina!in in a $y$!ema!ic manner


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Dealing (i!& ,"'er$arie$

% Game$ &a'e *a$cina!e" cm)u!er $cien!i$!$*r many year$

% Babbage 2 )laying c&e$$ n ,naly!ic :ngine

2 "e$igne" #ic-#ac-#e mac&ine

% S&ann 956 an" #uring 95

2 "e$cribe" c&e$$ )laying algri!&m$% Samuel$ 986

2 Buil! *ir$! $igni*ican! game )laying )rgramc&ec+er$


8/46

;&y game$ a!!rac!e" in!ere$! *

cm)u!er $cien!i$!$<% Seeme" ! be a g" "main *r (r+

n mac&ine in!elligence= becau$e !&ey

(ere !&ug&! !> 2 )r'i"e a $urce * a g" $!ruc!ure" !a$+

in (&ic& $ucce$$ r *ailure i$ ea$y !

mea$ure 2 n! re?uire muc& +n(le"ge !&i$ (a$ la!er

*un" ! be un!rue


9/46

C&e$$

% ,'erage branc&ing *ac!r *r eac&)$i!in i$ 5

% :ac& )layer ma+e$ 56 m'e$ in ana'erage game

% , cm)le!e game &a$ 5-66 )!en!ial

)$i!in$ ! cn$i"er % S!raig&! *r(ar" $earc& * !&i$ $)ace

(ul" n! !ermina!e "uring ei!&er)layer$ li*e!ime


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Game$

% Can! $im)ly u$e $earc& li+e in )u11le

$l'ing $ince yu &a'e an ))nen!

% 3ee" ! &a'e b!& a g" genera!r

an" an e**ec!i'e !e$!er

% @euri$!ic +n(le"ge (ill al$ be &el)*ul

! b!& !&e genera!r an" !e$!er


11/46

Ply

% Sme (ri!er$ u$e !&e !erm )ly !mean a $ingle m'e by ei!&er )layer

% Sme in$i$!$ )ly i$ ma"e u) * a m'ean" a re$)n$e

% I (ill u$e !&e *ir$! "e*ini!in= $ )ly i$

!&e $ame a$ !&e "e)!& - * !&e"eci$in !ree r!e" a! !&e curren! game$!a!e


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S!a!ic :'alua!in Aunc!in

% U$e" by !&e !e$!er

% Similar ! cl$er) *rm ur &euri$!ic

$earc& (r+ in , !y)e algri!&m$

% In general i! (ill nly be a))lie" ! !&e

lea* n"e * !&e game !ree


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S!a!ic :'alua!in Aunc!in$

% #uring C&e$$$um * (&i!e 'alue$ / $um * blac+ 'alue$

% Samuel$ C&ec+er$linear cmbina!in (i!& in!erac!in !erm$

% )iece a"'an!age

% ca)abili!y *r a"'ancemen!

% cn!rl * cen!er % !&rea! * *r+

% mbili!y


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#ic #ac #e


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#ic #ac #e

66, E 6B E C 2 66D E 6: E A

, F number * line$ (i!& $

B F number * line$ (i!& 0$

C F number * line$ (i!& $ingle

D F number * line$ (i!& H$: F number * line$ (i!& 0 H$

A F number * line$ (i!& a $ingle H


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:xam)le

H

H H

, F 6 B F 6 C F

D F 6 : F A F

66 6 E 66 E 2

66 6 E 6 E F

2 F-6


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;ea+ne$$

% ,ll $!a!ic e'alua!in *unc!in$ $u**er

*rm !( (ea+ne$$e$

2 in*rma!in l$$ a$ cm)le!e $!a!ein*rma!in ma))e" ! a $ingle number

2 Min$+y$ Cre"i! ,$$ignmen! )rblem

% i! i$ ex!remely "i**icul! ! "e!ermine (&ic& m'ein a )ar!icular $e?uence * m'e$ cau$e" a

)layer ! (in r l$$ a game r &( muc&

cre"i! ! a$$ign ! eac& *r en" re$ul!


19/46

;&a! " (e nee" *r game$<

% Plau$ible m'e genera!r

% G" $!a!ic e'alua!in *unc!in$

% Sme !y)e * $earc& !&a! !a+e$

))nen! be&a'ir in! accun! *r

nn!ri'ial game$


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-)ly Minimax

% I* !&e $!a!ic e'alua!in i$ a))lie" ! !&e lea*n"e$ (e ge!

B F C F D F -0

% S be$! m'e a))ear$ ! be B

A

CB D


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0-)ly Minimax

% ,))lying !&e $!a!ic e'alua!in *unc!in

: F 9 A F -8 G F 6 @ F 6 I F -0 J F -4 K F -

A

B C D

E F G IH J K


22/46

Pr)aga!ing !&e Lalue$

% ;ill "e)en" n !&e le'el

% ,$$uming !&a! !&e minimi1er c&$e$ *rm

!&e lea* n"e$= be (ul" ge!B F min9= -8= 6 F -8

C F min6= -0 F -0

D F min-4= - F -4

% #&e !&e maximi1er ge!$ ! c&$e *rm !&eminimi1er$ 'alue$ an" $elec!$ m'e C

, F max-8= -0= -4


23/46

Minimax ,lgri!&m

I* limi! * $earc& reac&e" !&en

cm)u!e $!a!ic 'alue * curren! )$i!in

re!urn !&e re$ul!:l$e I* le'el i$ minimi1ing le'el !&en

u$e Minimax n c&il"ren * curren! )$i!in

re)r! minimum * c&il"ren$ re$ul!$

:l$eu$e Minimax n c&il"ren * curren! )$i!in

re)r! maximum * c&il"ren$ re$ul!$


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Searc& imi!

% @a$ $mene (n !&e game<

% 3umber * )ly ex)lre" $ *ar

% @( )rmi$ing i$ !&i$ )a!&<

% @( muc& !ime i$ le*!<

% @( $!able i$ !&i$ cn*igura!in<


25/46

Cri!ici$m * Minimax

% G"ne$$ * curren! )$i!in !ran$la!e"

! a $ingle number (i!&u! +n(ing &(

!&e number (a$ *rce" n u$% Su**er$ *rm &ri1n e**ec!

2 a (in r l$$ mig&! be in !&e nex! )ly an"

(e (ul" n! +n( i!


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27/46

,l)&a-Be!a ,$$um)!in$

% ,l)&a 'alue ini!ially $e! ! -

an" ne'er

"ecrea$e$

% Be!a 'alue ini!ially $e! ! E an" ne'erincrea$e$

% ,l)&a 'alue i$ al(ay$ curren! large$! bac+e"

u) 'alue *un" by any n"e $ucce$$r

% Be!a 'alue i$ al(ay$ curren! $malle$! bac+e"

u) 'alue *un" by any n"e $ucce$$r


28/46

,l)&a-Be!a Pruning


29/46

,l)&a-Be!a Pruning


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,l)&a-Be!a

% ;i!& )er*ec! r"ering mre $!a!ic e'alua!in$are $+i))e"

% :'en (i!&u! )er*ec! r"ering many e'alua!in$can be $+i))e"

% I* (r$! )a!&$ are ex)lre" *ir$! n cu!**$ (illccur

% ;i!& )er*ec! r"ering al)&a-be!a le!$ yu exam!(ice !&e number * )ly !&a! minimax (i!&u!al)&a-be!a can examine in !&e $ame amun! *!ime


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,l)&a-Be!a ,lgri!&m

Function Value (P, ∝, β)

// P is the position in the data structure

{

// determine successors of P and call them // P(1), P(2), P(d)

if d!" then

return f(p) // call static evaluation function

// return as value to parent


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,l)&a-Be!a ,lgri!&m

else

{

m ! ∝

for i !1 to d do {

t ! # value (Pi # β, # m)

if t $ m then

m ! t

if !$ β then

e%it loop

&

&

return m

&


33/46

,l)&a-Be!a CEE

'include iostreamh$

'include timeh$

'include stdlih$

'include valuesh$

// his proram is a implementation of the lpha-eta

// alorithm found in .reuter 0 ac.enie p 2

const rue ! 13

const False ! "3

const a%4um ! 23 //node deree

const 4umPl5 ! 63 //search pl5

const 7oot ! 13 //start search at this location

const 8nde% ! 913


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,l)&a-Be!a CEE

t5pedef float ree:8nde%;3 //simulated ame tree

t5pedef int


35/46

,l)&a-Be!a CEE

void 8nit(ree 0)

// -uild dumm5 ame tree

{ int 83

for (8 ! 1>3 8 ! 13 8++)

//lan? out 6#pl5 leaf nodes :8; ! ""3 &

float @val(


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,l)&a-Be!a CEE

int erminal(


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,l)&a-Be!a CEE

int achineove(Pl5 4)

// Ahec?s to see if it is computerDs

move

// in this pl5 {

return E(4 2)3

//odd moves are computers

&


39/46

,l)&a-Be!a CEE

float lpha-eta

(


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,l)&a-Be!a CEE

if ((4 !! ") GG erminal(


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,l)&a-Be!a CEE

if (achineove(4)) //proramDs move

{

-est


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,l)&a-Be!a CEE

else

{

-est


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,l)&a-Be!a CEE

void main( )

{

randomie()3

8nit()3

cout IValue ! J

lpha-eta(Ahild(7oot, 1), 4umPl5 # 1, #B84, B84)

IKnI3

cout IValue ! J

lpha-eta(Ahild(7oot, 2), 4umPl5 # 1, #B84, B84)

IKnI3

&


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@ri1n @euri$!ic$

% Prgre$$i'e "ee)ening 2 )ly $earc& *ll(e" by 4 )ly= *ll(e" by 5 )ly=

e!c. un!il !ime run$ u!

% @euri$!ic )runing 2 r"er m'e$ ba$e" n )lau$ibili!y an" elimina!e

unli+ely )$$ibili!ie$

2 "e$ n! cme (i!& minimax guaran!ee

% @euri$!ic cn!inua!in 2 ex!en" )rmi$ing r 'la!ile )a!&$ r 0 mre

$!e)$ be*re cmmi!!ing ! c&ice


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@ri1n @euri$!ic$

% Au!ili!y cu!-**

2 $!) ex)lring (&en im)r'emen!$ are marginal

2 "e$ n! cme (i!& minimax guaran!ee% Secn"ary $earc&

2 nce yu )ic+ a )a!& u$ing a 8 )ly $earc& cn!inue

*rm lea* n"e (i!& a )ly $earc& ! cn*irm )ic+

% B+ m'e$ 2 elimina!e$ $earc& in $)eciali1e" $i!ua!in$

2 "e$ n! cme (i!& minimax guaran!ee

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