Programming AssignmenW 2: Checkers AI

Programming AssignmenW 2: Checkers AI

DXe JXl 6 b\ 10SP Points 100
Released: JXne 6, 2021
Updated on JXne 13: aXtograder.p\ and driYer.p\ modified!
TabOe Rf CRQWeQWV.
1. Critical Warning
2. IntrodXction
3. Starter Code
4. QXestion 1: Minima[
5. QXestion 2: Depth Limit
6. QXestion 3: Alpha-Beta PrXning
7. QXestion 4: State Caching
8. QXestion 5: YoXr OZn HeXristic
9. QXestion 6: Node Ordering
10. Checkers Competition
11. What To SXbmit

Fig 1. At left, the initial state and the possible
moYes for tZo of the pieces. In the middle, a
sample position Zith the possibilit\ of one
captXre. At right, a sample position Zith the
possibilit\ of tZo captXres.
>HYUPUN 7SLHZL YLHK [OPZ
AV eYeU, Ze aUe aZaUe WhaW VRlXWiRQV WR WhiV SURbleP, RU UelaWed RQeV, Pa\ e[iVW RQ Whe iQWeUQeW. Do not
Xse these solXtions as this ZoXld be plagiarism. TR eaUQ PaUkV RQ WhiV aVVigQPeQW \RX PXVW deYelRS
\RXU RZQ VRlXWiRQV. AlVR SleaVe cRQVideU Whe fRllRZiQg SRiQWV, aV \RX did ZheQ iPSlePeQWiQg SUiRU
aVVigQPeQWV:
Do not add an\ non-standard imports in the p\thon files \oX sXbmit (all iPSRUWV alUead\ iQ Whe
VWaUWeU cRde PXVW UePaiQ). All iPSRUWV WhaW aUe aYailable RQ Weach.cV aUe cRQVideUed WR be VWaQdaUd.
Do not change an\ of the sXpplied files e[cept for agenW.p\ and agenW_compeWiWion.p\ (if \oX
choose to enter the competition).
Make certain that \oXr code rXns on teach.cs Xsing p\thon3. YRX VhRXld all haYe aQ accRXQW RQ
Weach.cV aQd \RX caQ lRg iQ, dRZQlRad all Rf \RXU cRde (iQclXdiQg all Rf Whe VXSSlied cRde) WR a
VXbdiUecWRU\ Rf \RXU hRPe diUecWRU\, aQd XVe Whe cRPPaQd p\Whon3 aXWograder.p\ aQd WeVW iW WheUe
befRUe \RX VXbPiW. YRXU cRde Zill be gUaded b\ UXQQiQg iW RQ Weach.cV, VR Whe facW WhaW iW UXQV RQ \RXU
RZQ V\VWeP bXW QRW RQ Weach iV QRW a legiWiPaWe UeaVRQ fRU a UegUade.
The WeVW caVeV XVed iQ Whe aXWRgUadeU UeflecW Whe WeVW caVeV Ze Zill XVe dXUiQg PaUkiQg. The WeVW
caVeV \RX haYe aUe Rf ViPilaU difficXlW\, VR Whe gUade VhRZQ WR \RX b\ Whe aXWRgUadeU Zill be a
6/22/2021 Programming AssignmenW 2: Checkers AI
hWWps://q.XWoronWo.ca/coXrses/219334/assignmenWs/621533 2/9
UeaVRQable SUedicWRU Rf \RXU fiQal gUade RQ Whe aVVigQPeQW. We Zill alVR lRRk fRU ceUWaiQ WhiQgV iQ Whe
aVVigQPeQWV (e.g., UXQQiQg WheP WhURXgh cRde SlagiaUiVP checkeUV, lRRkiQg aW aVVigQPeQWV WhaW fail
all WeVWV, eWc.). If Ze haYe good reasons Ze Zill chaQge \RXU gUade fURP WhaW giYeQ b\ Whe aXWRgUadeU
eiWheU XS RU dRZQ.
0U[YVK\J[PVU
AcknoZledgements: ThiV SURjecW iV baVed RQ RQeV XVed iQ CRlXPbia UQiYeUViW\¶V AUWificial IQWelligeQce
CRXUVe (COMS W4701) aV Zell aV Whe UQiYeUViW\ Rf PiWWVbXUgh'V AUWificial IQWelligeQce CRXUVe (CS2710).
SSecial WhaQkV WR DU. DaQiel BaXeU aQd DU. JaQice Wiebe fRU VhaUiQg WheiU cRde aQd WheiU ideaV RQ Whe
aVVigQPeQW.
CheckeUV iV a 2-Sla\eU bRaUd gaPe WhaW iV Sla\ed ZiWh diVWiQcW SieceV WhaW aUe W\Sicall\ black RQ RQe Vide
aQd Ued RQ Whe RWheU Vide, each Vide belRQgiQg WR RQe Sla\eU. OXU YeUViRQ Rf Whe gaPe iV Sla\ed RQ aQ
8[8 cheVV bRaUd, Zhich iV VWaQdaUd. Pla\eUV (Ued aQd black) Wake WXUQV PRYiQg SieceV RQ Whe bRaUd.
MRYiQg Whe SieceV iV dicWaWed b\ Whe UXleV Rf Whe gaPe, aQd caQ UeVXlW iQ caSWXUiQg Whe RSSRQeQW'V
SieceV. AQ RYeUYieZ Rf CheckeUV iV SURYided aW https://en.Zikipedia.org/Ziki/DraXghts.
(hWWSV://en.ZikiSedia.oUg/Ziki/DUaXghWV) NRWe WhaW Whe YeUViRQ Rf CheckeUV WhaW Ze Zill be cRdiQg iV
SWaQdaUd EQgliVh DUaXghWV; the rXles are e[plained here.
(hWWSV://en.ZikiSedia.oUg/Ziki/EngliVh_dUaXghWV) EQgliVh DUaXghWV iQclXdeV PaQdaWRU\ caSWXUeV.
ObjectiYe: The Sla\eU¶V gRal iV WR haYe a PajRUiW\ Rf Whe UePaiQiQg SieceV.
Game Ending: The gaPe eQdV aV VRRQ aV RQe Rf Whe Sla\eUV haV QR SieceV UePaiQiQg RU QR legal
PRYeV lefW.
RXles: AW Whe begiQQiQg Rf Whe gaPe, each Sla\eU haV 12 SieceV Rf Ued RU black cRlRXU. The SieceV aUe
Slaced RQ Whe daUk VTXaUeV Rf Whe bRaUd acURVV Whe fiUVW WhUee URZV RQ each Vide (FigXUe 1. aW lefW). The
black Sla\eU PakeV Whe fiUVW PRYe.
Each Siece caQ RQl\ PRYe fRUZaUd diagRQall\ iQ WZR Za\V: 1) PRYiQg RQe VSace, if Whe adjaceQW VSace iV
ePSW\ (FigXUe 1, aW lefW), RU 2) PRYiQg WZR VSaceV if Whe adjaceQW VSace iV RccXSied b\ Whe RSSRQeQW, aQd
VSace be\RQd WhaW iV ePSW\ (FigXUe 1, iQ Whe Piddle). IQ Whe VecRQd caVe, Whe Sla\eU 'caSWXUeV' Whe
RSSRQeQW'V Siece WhaW ZaV jXPSed RYeU. If a PRYe leadV WR caSWXUe, aQd Whe Siece eQdV XS ViWWiQg aW a
SRViWiRQ WhaW caQ jXPS RYeU aQRWheU RSSRQeQW'V Siece, Whe Sla\eU caQ PRYe iW agaiQ aQd caSWXUe aQRWheU
Siece Rf Whe RSSRQeQW. ThiV VeTXeQce Rf PRYeV dReV QRW Qeed WR be RQ a VWUaighW liQe aQd caQ be
']ig]ag'.
WheQ RQe Rf Whe SieceV UeacheV Whe laVW URZ Rf Whe bRaUd (RU Whe fiUVW URZ fURP Whe RSSRQeQW'V Vide), iW
WXUQV iQWR a "kiQg" aQd Zill be gUaQWed a XQiTXe SRZeU: iW caQ PRYe bRWh fRUZaUd aQd backZaUd. IQ RXU
GUI a kiQg iV a Siece ZiWh a \ellRZ bRUdeU.
We recommend that \oX start this assignment b\ pla\ing some games of checkers to deYelop a
better Xnderstanding of hoZ the game Zorks and Zhat strategies can giYe \oX an adYantage. An
6/22/2021 Programming AssignmenW 2: Checkers AI
hWWps://q.XWoronWo.ca/coXrses/219334/assignmenWs/621533 3/9
online Yersion of the game that alloZs \oX to compete against an AI can be foXnd at this link.
(hWWSV://ZZZ.maWhViVfXn.com/gameV/checkeUV-2.hWml)
:[HY[LY *VKL
The VWaUWeU cRde cRQWaiQV 6 fileV. YRX caQ dRZQlRad all Whe cRde aQd VXSSRUWiQg fileV aV a Zipped file
archiYe. IQ WhaW aUchiYe \RX Zill fiQd Whe fRllRZiQg fileV:
Files \oX can Xse to test \oXr solXtion:
aXWograder.p\ A file ZiWh VRPe baVic WeVWV Rf Whe fXQcWiRQV \RX PXVW ZUiWe.
Files \oX'll edit and sXbmit on MarkXs:
agenW.p\ The file ZheUe \RX Zill iPSlePeQW \RXU gaPe ageQW; WhiV Zill be gUaded.
agenW_compeWiWion.p\ A file \RX caQ XVe if \RX chRRVe WR helS ZUiWe aQ ageQW fRU Whe
CheckeUV cRPSeWiWiRQ (Zhich iV RSWiRQal).
Files \oX might Zant to look at (look bXt don't modif\):
driYer.p\
ThiV cRQWaiQV a ViPSle gUaShical XVeU iQWeUface (GUI) fRU CheckeUV; aQd
Whe gaPe ´PaQageU´ WhaW VWRUeV Whe cXUUeQW gaPe VWaWe aQd
cRPPXQicaWeV ZiWh diffeUeQW Sla\eU AIV.
checkerV_game.p\
ThiV cRQWaiQV fXQcWiRQV fRU cRPSXWiQg legal PRYeV, caSWXUed SieceV,
aQd VXcceVVRU gaPe VWaWeV. TheVe aUe VhaUed beWZeeQ Whe gaPe
PaQageU, Whe GUI, aQd Whe AI Sla\eUV.
UaQd\.S\
A ViPSle ageQW WhaW SickV PRYeV aW UaQdRP WhaW \RX caQ XVe WR Vee Whe
gaPe iQ RSeUaWiRQ.
Game State Representation: Each gaPe VWaWe cRQWaiQV WZR SieceV Rf iQfRUPaWiRQ: The cXUUeQW Sla\eU
aQd Whe cXUUeQW SieceV RQ Whe bRaUd. ThURXghRXW RXU iPSlePeQWaWiRQ, Pla\eU 1 (black) iV UeSUeVeQWed
XViQg a 'b', aQd Pla\eU 2 (Ued) iV UeSUeVeQWed XViQg aQ 'U'.
The bRaUd iV UeSUeVeQWed aV a liVW Rf liVWV. The iQQeU liVWV UeSUeVeQWV each URZ Rf Whe bRaUd. Each eQWU\ iQ
Whe URZV iV eiWheU aQ ePSW\ VTXaUe (iQdicaWed ZiWh a '.'), a black Siece (a 'b'), RU a Ued Siece (aQ 'U'). Black
SieceV WhaW aUe kiQgV aUe iQdicaWed ZiWh a 'B' aQd Ued SieceV WhaW aUe kiQgV aUe iQdicaWed ZiWh aQ 'R'. FRU
e[aPSle, aQ 8[8 bRaUd PighW lRRk like WhiV aW Whe VWaUW Rf Whe gaPe:
[ ['b','.','b','.','b','.','b','.'],\
['.','b','.','b','.','b','.','b'],\
6/22/2021 Programming AssignmenW 2: Checkers AI
hWWps://q.XWoronWo.ca/coXrses/219334/assignmenWs/621533 4/9
['b','.','b','.','b','.','b','.'],\
['.','.','.','.','.','.','.','.'],\
['.','.','.','.','.','.','.','.'],\
['.','r','.','r','.','r','.','r'],\
['r','.','r','.','r','.','r','.'],\
['.','r','.','r','.','r','.','r'] \
]
Each PRYe iV UeSUeVeQWed aV a liVW Rf WXSleV. FRU e[aPSle, a PRYe WhaW WakeV a Siece fURP SRViWiRQ 5,1
WR SRViWiRQ 4,2 Zill be UeSUeVeQWed aV:
[(5, 1), (4, 2)]
A PRYe WhaW cRQWaiQV a jXPS aQd Zhich WakeV a Siece fURP SRViWiRQ 6,3 WR SRViWiRQ 4,5 aQd WheQ WR 2,7 Yia
jXPSV Zill be UeSUeVeQWed aV:
[(6, 3), (4, 5), (2, 7)]
NRWe WhaW \RXU VWaUWeU cRde (checkeUV_gaPe.S\) cRQWaiQV a claVV Rf W\Se BRaUd WhaW haV WZR aWWUibXWeV: a
bRaUd (Zhich iV a liVW Rf liVWV) aQd a PRYe (Zhich iV a liVW Rf WXSleV). Be PiQdfXl Rf Whe diVWiQcWiRQ beWZeeQ
aQ RbjecW WhaW iV Rf W\Se BRaUd aQd Whe bRaUd UeSUeVeQWaWiRQ iWVelf, Zhich iV a liVW Rf liVWV.
RXnning the code: YRX caQ UXQ WZR AI ageQWV agaiQVW RQe aQRWheU Yia Whe CheckeUV GUI. RXQQiQg Whe
cRde Zill bUiQg XS a gaPe ZiQdRZ. Each ageQW Zill alWeUQaWe WXUQV.
OXU GUI WakeV WZR AI SURgUaPV aV cRPPaQd liQe SaUaPeWeUV. WheQ WZR AIV aUe VSecified aW Whe
cRPPaQd liQe \RX Zill be able WR ZaWch WheP Sla\ agaiQVW each RWheU. We haYe iQclXded RQe AI QaPed
RaQd\ (aQd Zhich iV cRded iQ Whe file UaQd\.S\) WhaW Zill VelecW checkeUV PRYeV aW UaQdRP. TR Vee
RaQd\ Sla\ agaiQVW iWVelf, W\Se
$p\Whon3 driYer.p\ rand\ rand\
YRX Zill ZUiWe \RXU RZQ ageQW iQ Whe ageQW.S\ file. OQce \RX cUeaWe aQ ageQW, \RX Pa\ ZaQW WR WU\ Sla\iQg
iW agaiQVW WhRVe WhaW aUe Pade b\ \RXU fUieQdV.
The GUI iV UaWheU PiQiPaliVWic, VR \RX Qeed WR clRVe Whe ZiQdRZ aQd WheQ UeVWaUW WR Sla\ a QeZ gaPe.
Time Constraints: WheQ Ze WeVW \RXU AI Sla\eU, Ze Zill be e[SecWiQg iW WR Pake a PRYe ZiWhiQ 10
VecRQdV. If QR PRYe haV beeQ VelecWed, Whe AI Zill lRVe Whe gaPe.
4HYR )YLHRKV^U
Minima[ [30 pts]
The fiUVW WhiQg \RX Zill dR iV WR ZUiWe a fXQcWiRQ cRPSXWe XWiliW\(VWaWe, color) WhaW cRPSXWeV Whe XWiliW\
Rf a fiQal gaPe bRaUd VWaWe. NRWe WhaW VWaWe Zill be aQ RbjecW Rf W\Se BRaUd; WR acceVV Whe bRaUd aV a liVW
Rf liVWV \RX Zill ZaQW WR eYalXaWe Whe bRaUd aWWUibXWe Rf WhaW VWaWe (i.e. VWaWe.bRaUd Zhich Zill be iQ Whe
fRUPaW deVcUibed abRYe). The XWiliW\ VhRXld be baVed RQ Whe QXPbeU Rf SieceV Rf Whe Sla\eU'V cRlRXU
PiQXV Whe QXPbeU Rf SieceV Rf Whe RSSRQeQW. Make each UegXlaU Siece ZRUWh RQe SRiQW aQd each kiQg
ZRUWh 2. If \RXU ageQW haV a ViQgle kiQg aQd Vi[ UegXlaU SieceV, aVVigQ WhiV a YalXe Rf 2*1 + 6 = 8. If \RXU
ageQW'V RSSRQeQW haV WZR kiQgV aQd 3 UegXlaU SieceV, aVVigQ WhiV a YalXe Rf 2*2 + 3 = 7 SRiQWV. The
diffeUeQce iQ SRiQWV beWZeeQ ageQWV, aQd Whe UeVXlW Rf cRPSXWe_XWiliW\, Zill WheUefRUe be 8-7 = 1.
6/22/2021 Programming AssignmenW 2: Checkers AI
hWWps://q.XWoronWo.ca/coXrses/219334/assignmenWs/621533 5/9
TheQ, iPSlePeQW Whe PeWhRd VelecW_moYe_minima[(VWaWe, color, limiW = 5, caching = 0) . FRU Whe WiPe
beiQg, \RX caQ igQRUe Whe liPiW aQd cachiQg SaUaPeWeUV WhaW Whe fXQcWiRQ Zill alVR acceSW; Ze Zill UeWXUQ WR
WheVe laWeU. ThiV Zill acceSW a VWaWe (Zhich iV aQ RbjecW Rf W\Se BRaUd) aV Zell aV Whe Sla\eU'V cRlRXU ('U' RU
'b'). IW Zill UeWXUQ a ViQgle PRYe WhaW cRUUeVSRQdV ZiWh Whe PiQiPa[ VWUaWeg\. MRUe VSecificall\, \RXU
fXQcWiRQ VhRXld VelecW Whe acWiRQ WhaW leadV WR Whe VWaWe ZiWh Whe higheVW PiQiPa[ YalXe. The UeWXUQ YalXe
VhRXld be a liVW Rf WXSleV WhaW UeSUeVeQW Whe PRYe, aV abRYe. IPSlePeQW PiQiPa[ UecXUViYel\ b\ ZUiWiQg
WZR fXQcWiRQV minima[_ma[_node(VWaWe, color, limiW, caching) aQd minima[_min_node(VWaWe, color,
limiW, caching) . AgaiQ, \RX caQ jXVW igQRUe Whe liPiW aQd cachiQg SaUaPeWeUV fRU QRZ.
HiQWV: UVe Whe VXcceVVRUV(VWaWe,Sla\eU) fXQcWiRQ iQ checkerV_game.p\ , Zhich UeWXUQV all Whe Whe
VXcceVViYe VWaWeV (Zhich iQclXdeV PRYeV aQd VXcceVViYe bRaUd UeSUeVeQWaWiRQV) fRU a giYeQ Sla\eU. Pa\
aWWeQWiRQ WR Zhich Sla\eU VhRXld Pake a PRYe fRU PiQ QRdeV aQd Pa[ QRdeV.
While \RX caQ WeVW VRPe Rf Whe fXQcWiRQV iQ \RXU MINIMAX algRUiWhP XViQg Whe aXWRgUadeU, if \RX WU\ WR
UXQ iW ZiWh dUiYeU.S\ \RX Pa\ eQd XS ZiWh a VWack RYeUflRZ! ThiV iV becaXVe Whe gaPe Rf checkeUV iV
laUge. We Zill haYe WR iPSlePeQW a deSWh liPiW WR Ueali]e aQ ageQW WhaW caQ RSeUaWe iQ a WUacWable aPRXQW
Rf WiPe aQd PePRU\.
Depth Limit [10 pts]
TR Pake \RXU ageQW Ueall\ fXQcWiRQal, \RX PXVW iPSlePeQW a deSWh liPiW. YRXU VWaUWeU cRde iV VWUXcWXUed WR
dR WhiV b\ XViQg Whe '-d' flag aW Whe cRPPaQd liQe. FRU e[aPSle, if \RX W\Se
$p\Whon3 driYer agenW agenW -d 6
Whe gaPe PaQageU Zill call \RXU ageQW¶V MINIMAX URXWiQe ZiWh a deSWh liPiW Rf 6. NRWe WhaW Whe cRde
iPSlePeQWV a defaXlW deSWh liPiW Rf 5, Zhich \RX caQ RYeUUide.
ChaQge \RXU MiQiPa[ cRde WR UecXUViYel\ VeQd Whe ¶liPiW¶ SaUaPeWeU WR bRWh minima[_min_node aQd
minima[_ma[_node . IQ RUdeU WR eQfRUce Whe deSWh liPiW iQ \RXU cRde, \RX Zill ZaQW WR decUeaVe Whe liPiW
SaUaPeWeU aW each UecXUViRQ. WheQ \RX aUUiYe aW \RXU deSWh liPiW (i.e. ZheQ Whe ¶liPiW¶ SaUaPeWeU iV ]eUR),
XVe a heXUiVWic fXQcWiRQ WR defiQe Whe YalXe aQ\ QRQ-WeUPiQal VWaWe. YRX caQ call Whe cRPSXWe XWiliW\
fXQcWiRQ aV \RXU heXUiVWic WR eVWiPaWe QRQ-WeUPiQal VWaWe TXaliW\.
WhaW iV Whe laUgeVW deSWh liPiW \RX caQ Sla\ ZiWhRXW QeediQg PRUe WhaQ 10 VecRQdV SeU PRYe?
Alpha-Beta PrXning [30 pts]
The ViPSle PiQiPa[ aSSURach iV TXiWe VlRZ. TR aPeliRUaWe WhiV Ze Zill ZUiWe Whe fXQcWiRQ
VelecW_moYe_alphabeWa(VWaWe, color, limiW=5, caching=0, ordering=0) WR cRPSXWe Whe beVW PRYe XViQg
alSha-beWa SUXQiQg. The SaUaPeWeUV aQd UeWXUQ YalXeV Zill be Whe VaPe aV fRU PiQiPa[. YRX caQ igQRUe
Whe cachiQg, aQd RUdeUiQg SaUaPeWeUV WhaW Whe fXQcWiRQ Zill alVR acceSW fRU Whe WiPe beiQg; Ze Zill UeWXUQ
WR WheVe laWeU. MXch like MiQiPa[, \RXU alSha-beWa iPSlePeQWaWiRQ VhRXld UecXUViYel\ call WZR helSeU
fXQcWiRQV: alphabeWa_min_node(VWaWe, color, alpha, beWa, limiW, caching=0, ordering=0)¬ aQd
alphabeWa_ma[_node(VWaWe, color, alpha, beWa, limiW, caching=0, ordering=0). AV ZiWh MiQiPa[,
6/22/2021 Programming AssignmenW 2: Checkers AI
hWWps://q.XWoronWo.ca/coXrses/219334/assignmenWs/621533 6/9
UecXUViYel\ VeQdV Whe ¶liPiW¶ SaUaPeWeU WR alphabeWa_min_node aQd alphabeWa_ma[_node. WheQ \RX aUUiYe
aW \RXU deSWh liPiW, call cRPSXWe_XWiliW\ WR geQeUaWe a XWiliW\ YalXe fRU each giYeQ VWaWe.
Pla\iQg ZiWh SUXQiQg VhRXld VSeed XS deciViRQV fRU Whe AI, bXW \RX Pa\ VWill Qeed WR XVe a faiUl\ VhallRZ
deSWh. UVe Whe cRPPaQd
$driYer agenW agenW -d 6 -a
WR Sla\ agaiQVW \RXU ageQW XViQg Whe ALPHA-BETA algRUiWhP ZiWh a deSWh liPiW Rf 6.
WhaW iV Whe laUgeVW deSWh liPiW \RX caQ Sla\ ZiWhRXW QeediQg PRUe WhaQ 10 VecRQdV SeU PRYe?
Caching States [10 pts]
We caQ WU\ WR VSeed XS Whe AI eYeQ PRUe b\ cachiQg VWaWeV Ze¶Ye VeeQ befRUe. TR dR WhiV, Ze Zill ZaQW
WR alWeU \RXU SURgUaP VR WhaW iW UeVSRQdV WR Whe -c flag aW Whe cRPPaQd liQe. TR iPSlePeQW VWaWe cachiQg
\RX Zill Qeed WR cUeaWe a dicWiRQaU\ iQ \RXU AI Sla\eU (WhiV caQ jXVW be VWRUed iQ a glRbal YaUiable RQ Whe
WRS leYel Rf Whe file) WhaW PaSV bRaUd VWaWeV WR WheiU MiQiPa[ YalXe, RU WhaW checkV YalXeV agaiQVW VWRUed
alSha aQd beWa SaUaPeWeUV. MRdif\ \RXU MiQiPa[ aQd alSha-beWa SUXQiQg fXQcWiRQV WR VWRUe VWaWeV iQ WhaW
dicWiRQaU\ afWeU WheiU YalXe iV kQRZQ. TheQ check Whe dicWiRQaU\ aW Whe begiQQiQg Rf each fXQcWiRQ. If a
VWaWe iV alUead\ iQ Whe dicWiRQaU\ aQd dR QRW e[SlRUe iW agaiQ. The VWaUWeU cRde iV VWUXcWXUed VR WhaW if \RX
W\Se
$driYer agenW agenW -d 6 -c
Whe gaPe PaQageU Zill call \RXU ageQW¶V MiQiPa[ URXWiQeV ZiWh Whe ¶cachiQg¶ flag RQ. If iQVWead \RX W\Se
$driYer agenW agenW -d 6 -a -c
Whe gaPe PaQageU Zill call \RXU ageQW¶V ALPHA-BETA URXWiQeV ZiWh Whe ¶cachiQg¶ flag RQ.
YoXr OZn HeXristic [10 pts]
The SUiRU VWeSV VhRXld giYe \RX a gRRd AI Sla\eU, bXW Ze haYe RQl\ VcUaWched Whe VXUface. TheUe aUe
PaQ\ SRVVible iPSURYePeQWV WhaW ZRXld cUeaWe aQ eYeQ beWWeU AI. TR iPSURYe \RXU AI, cUeaWe \RXU RZQ
gaPe heXUiVWic. YRX caQ XVe WhiV iQ Slace Rf cRPSXWiQg XWiliW\ iQ \RXU alSha-beWa RU MiQiPa[ URXWiQeV.
WheQ \RX VXbPiW \RXU cRde, hRZeYeU, SleaVe XVe cRPSXWe_XWiliW\ aV Whe heXUiVWic \RX XVe ZheQ \RX hiW
Whe deSWh liPiW iQ \RXU gaPe ageQW. ThiV Zill faciliWaWe PaUkiQg! YRX caQ XVe \RXU RZQ heXUiVWic iQ \RXU
ageQW_cRPSeWiWiRQ.S\ file, hRZeYeU.
Some Ideas for HeXristic FXnctions for Checkers Game
1. CRQVideU bRaUd lRcaWiRQV ZheUe SieceV aUe VWable, i.e. ZheUe Whe\ caQQRW be caSWXUed aQ\PRUe.
2. CRQVideU Whe QXPbeU Rf PRYeV \RX aQd \RXU RSSRQeQW caQ Pake giYeQ Whe cXUUeQW bRaUd
cRQfigXUaWiRQ.
3. UVe a diffeUeQW VWUaWeg\ iQ Whe RSeQiQg, Pid-gaPe, aQd eQd-gaPe.
6/22/2021 Programming AssignmenW 2: Checkers AI
hWWps://q.XWoronWo.ca/coXrses/219334/assignmenWs/621533 7/9
YRX caQ alVR dR \RXU RZQ UeVeaUch WR fiQd a Zide UaQge Rf RWheU gRRd heXUiVWicV (fRU e[aPSle, heUe iV a
gRRd VWaUW: hWWSV://ZZZ.XlWUabRaUdgaPeV.cRP/checkeUV/WiSV.ShS).
IQ addiWiRQ WR eQgiQeeUiQg \RXU RZQ heXUiVWic, please inclXde a (short) description that details \oXr
heXristic as a comment at the start of \oXr solXtion file.
Node Ordering HeXristic [10 pts]
FiQall\, QRWe WhaW alSha-beWa SUXQiQg ZRUkV beWWeU if QRdeV WhaW lead WR a beWWeU XWiliW\ aUe e[SlRUed fiUVW. TR
dR WhiV, iQ Whe AlSha-beWa SUXQiQg fXQcWiRQV, WU\ XViQg \RXU heXUiVWic WR RUdeU Whe QRdeV WhaW \RX e[SlRUe.
If \RXU heXUiVWic PakeV UeaVRQabl\ gRRd eVWiPaWeV Rf QRQ-WeUPiQal VWaWe YalXeV, WhiV VhRXld lead WR a liWWle
biW Rf a VSeed XS becaXVe a gRRd RUdeUiQg Zill lead WR PRUe SUXQiQg. NRWe WhaW \RX caQ XVe \RXU RZQ
heXUiVWic WR RUdeU QRdeV ZheQ \RX VXbPiW \RXU cRde. UVe cRPSXWe_XWiliW\ WR aVVeVV YalXeV Rf QRdeV
ZheQ \RX hiW Whe deSWh liPiW, hRZeYeU.
TR UXQ \RXU cRde ZiWh QRde RUdeUiQg, XVe Whe -R flag. MRUe VSecificall\ if \RX W\Se:
$dUiYeU ageQW ageQW -d 6 -a -c -R
YRX Zill UXQ \RXU ageQW agaiQVW iWVelf XViQg alSha-beWa ZiWh a deSWh liPiW Rf 6 aQd bRWh cachiQg aQd QRde
RUdeUiQg ON.
*OLJRLYZ*VTWL[P[PVU 6W[PVUHS
If \RX ZaQW, \RX caQ eQWeU \RXU ageQW iQ Whe CSC384 CheckeUV cRPSeWiWiRQ. The fiQaliVWV aQd Whe
ZiQQeUV Rf Whe cRPSeWiWiRQ Zill UeceiYe a VhRXW-RXW RQ Whe cRXUVe ZebViWe. We aUe SlaQQiQg WR UXQ PRVW Rf
Whe cRPSeWiWiRQ afWeU Whe laVW da\ Rf claVV. A WeQWaWiYe SlaQ iV WR UXQ Whe cRPSeWiWiRQ iQ a leagXe fRUPaW RQ
aQ 8[8 bRaUd aQd a WiPe cRQVWUaiQW Rf 10 VecRQdV.
TR VXbPiW aQ AI WR Whe cRPSeWiWiRQ, ViPSl\ iQclXde Whe file ageQW_cRPSeWiWiRQ.S\ ZiWh \RXU hRPeZRUk
VXbPiVViRQ. YRX caQ UeVWUXcWXUe Whe cRde iQ \RXU VXbPiVViRQ aV \RX SleaVe aV WhiV file Zill QRW be
PaUked.
If \RX like, \RX caQ e[SlRUe RWheU gaPiQg algRUiWhPV like MRQWe CaUlR TUee SeaUch (MCTS) aV \RX
deYelRS \RXU gaPe ageQW fRU cRPSeWiWiRQ. MCTS ZaV iQiWiall\ cUeaWed fRU GR iQ 2006. MaQ\ WRRlV aQd
aSSlicaWiRQV haYe beeQ baVed RQ WhiV algRUiWhP, iQclXdiQg AlShaGR. ThiV iV Whe PRVW adYaQced GR AI WR
daWe aQd iW ZaV deYelRSed b\ DeeSPiQd. MCTS SURYided a fRXQdaWiRQ fRU AlShaGR, Zhich ZaV
aXgPeQWed b\ cRPSle[ QeXUal QeWZRUkV. IQ WhiV cRPSeWiWiRQ, \RX caQ iPSlePeQW a baVic MRQWe CaUlR
TUee SeaUch algRUiWhP aQd aWWePSW WR iPSURYe RQ iW.
TR helS \RX, Ze SURYide aQ RYeUYieZ Rf MCTS. TheUe aUe fRXU VWageV iQ each iWeUaWiRQ Rf Whe algRUiWhP
WhaW aUe deWailed belRZ. MCTS Zill iWeUaWe WhURXgh each Rf WheVe fRXU VWageV Zhile WiPe allRZV:
1. Selection: ThiV VWeS bXildV a gaPe WUee ZiWh Whe cXUUeQW bRaUd aV Whe iQiWial VWaWe S0. The child ZiWh
Whe higheVW SURbabiliW\ Rf ZiQQiQg iV WheQ VelecWed. We VXggeVW WhaW b\ defaXlW \RX XVe Whe USSeU
6/22/2021 Programming AssignmenW 2: Checkers AI
hWWps://q.XWoronWo.ca/coXrses/219334/assignmenWs/621533 8/9
CRQfideQce BRXQd (UCB) VWaWiVWic WR VelecW Whe child ZiWh Whe higheVW SURbabiliW\ Rf ZiQQiQg.
2. E[pansion: AfWeU VelecWiQg a child VWaWe, S1, Ze PXVW deWeUPiQe if iW iV a WeUPiQal VWaWe. (Whe geW
SRVVible PRYeV(bRaUd, cRlRU) fXQcWiRQ UeWXUQV aQ ePSW\ UeVXlW aW a WeUPiQal VWaWe). If Whe VWaWe iV a
QRQ-WeUPiQal VWaWe, iW Zill be e[SaQded.
3. SimXlation: We dRQ¶W kQRZ Whe cRQVeTXeQce Rf VelecWiQg WhiV VWaWe. TR eVWiPaWe Whe SRWeQWial beQefiW
WR be deUiYed fURP Whe VWaWe, Ze Zill ViPXlaWe gaPeSla\ fURP WhaW VWaWe. TR dR WhaW, UaQdRPl\ aVVigQ
Whe PRYeV WR geQeUaWe VXbVeTXeQW VWaWeV XQWil a WeUPiQal VWaWe iV Ueached. (FRU iQVWaQce, begiQQiQg
fURP S1, UaQdRPl\ Pake PRYeV fRU bRWh Sla\eUV XQWil Whe gaPe eQdV. If Ze ZiQ, Pake QRWe Rf Whe facW
WhaW Ze haYe deUiYed a UeZaUd Rf 1; RWheUZiVe, Ze haYe deUiYed a UeZaUd Rf 0.
4. Backpropagation: OQce Ze fiQiVh aQ\ ViPXlaWiRQ, Ze Qeed WR XSdaWe Whe ViPXlaWiRQ UeVXlWV ZiWh
iQfRUPaWiRQ abRXW Whe UeZaUd WhaW ZaV deUiYed fURP Whe ViPXlaWiRQ. TR dR WhiV, UeZaUdV fRXQd aW
WeUPiQalV Zill be back-SURSagaWed WhURXgh SaUeQW QRdeV. The iQfRUPaWiRQ PXVW be XSdaWed aW eYeU\
aQceVWRU Rf Whe WeUPiQal, RQe b\ RQe, XQWil UeachiQg Whe URRW (i.e Whe iQiWial VWaWe, S0 ).
OQce WiPe UXQV RXW, MCTS caQ VelecW Whe PRYe aVVRciaWed ZiWh Whe PRVW ViPXlaWiRQV RU higheVW aYeUage
Sa\Rff.
The ageQW_cRPSeWiWiRQ.S\ file alVR iQclXdeV VRPe MCTS fXQcWiRQ VWXbV WR geW \RX VWaUWed, iQ caVe \RX
ZRXld like WR XVe WheVe (\RX dRQ'W haYe WR)!
The MCTS Ze iQWURdXced iQ WhiV claVV iV a ¶YaQilla¶ YeUViRQ WhaW PakeV XVe Rf UCB. HRZeYeU, WheUe aUe
PaQ\ iPSURYePeQWV \RX caQ add WR Pake WhiV algRUiWhP SeUfRUP beWWeU. FRU e[aPSle, Whe ViPXlaWiRQ
VWage deWailed abRYe iV SXUel\ UaQdRP. ThiV PakeV MCTS geQeUali]e WR RWheU gaPeV bXW aW Whe cRVW Rf
high YaUiaQce. IW caQ Wake a YeU\ lRQg WiPe WR cRPSXWe a Ueliable UeVXlW.
TR addUeVV WhiV iVVXe diUecWl\, \RX caQ geQeUaWe QRQ-UaQdRP PRYeV dXUiQg \RXU ViPXlaWiRQV XViQg
heXUiVWic fXQcWiRQV. MRUe VSecificall\, \RX caQ cUeaWe a heXUiVWic fXQcWiRQ XViQg e[SeUW kQRZledge, RU
\RX caQ e[SlRUe WUaiQiQg a heXUiVWic baVed RQ SUeYiRXV gaPeV.
B\ iPSURYiQg Whe efficieQc\ Rf ViPXlaWiRQ, Whe algRUiWhP VhRXld \ield a beWWeU eVWiPaWiRQ Rf VWaWeV
PRUe TXickl\. See WhiV SaSeU fRU PRUe iQfRUPaWiRQ: https://doi.org/10.1145/1273496.1273531
(hWWSV://doi.oUg/10.1145/1273496.1273531)
UCB Sla\V aQ iPSRUWaQW URle iQ Whe VelecWiRQ VWage. YRX Pa\ ZaQW WR e[SlRUe eQhaQced YeUViRQV Rf
UCB WR fXUWheU iPSURYe SeUfRUPaQce.
PUXQiQg VXb-RSWiPal PRYeV fURP Whe VeaUch WUee iV alVR a feaVible Za\ WR UedXce cRPSle[iW\. The
eaVieVW Za\ iV WR XVe e[SeUW kQRZledge WR ideQWif\ aQd e[clXde XQaWWUacWiYe bUaQcheV.
YRX aUe ZelcRPe WR chRRVe aQ\ Rf Whe abRYe diUecWiRQV WR e[SlRUe RU \RX aUe fUee WR cRPe XS ZiWh
\RXU RZQ ideaV. YRX caQ XVe e[WeUQal libUaUieV iQ WhiV SaUW Rf Whe aVVigQPeQW, aVVXPiQg Whe\ aUe
iQVWalled RQ Weach.cV. HRZeYeU, dR QRW iQclXde aQ\ QXPbeU Rf VeaUch WUeeV diUecWl\ iQ \RXU
VXbPiVViRQ. PaUallel SURceVViQg aQd GPU acceleUaWiRQ aUe alVR SURhibiWed.
>OH[ [V :\ITP[
6/22/2021 Programming AssignmenW 2: Checkers AI
hWWps://q.XWoronWo.ca/coXrses/219334/assignmenWs/621533 9/9
YRX Zill be XViQg MaUkUV WR VXbPiW \RXU aVVigQPeQW. YRX Zill VXbPiW WZR fileV (RQe Rf Zhich iV RSWiRQal):
1. YRXU PRdified agenW.p\
2. YRXU PRdified agenW_compeWiWion.p\ (RSWiRQal)
NRWe WhaW Zhile Whe aVVigQPeQW iV dXe RQ JXl\ 6, Ze Zill cRQWiQXe WR acceSW ageQWV fRU cRPSeWiWiRQ XQWil
AXgXst 10 at Midnight!
GOOD LUCK!