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PYIWIT'02 1
Threat Analysis to Reduce the Effects of
the Horizon Problem in Shogi
Reijer Grimbergen
Department of Information Science
Saga University
PYIWIT'02 2
Presentation Outline
Game programming
Time limits and the horizon effect
Pruning and extension techniques
Threat analysis in two-player games
Application to shogi
Implementation issues
Preliminary results
Conclusions and future work
PYIWIT'02 3
Game ProgrammingDefinitions
Two-player perfect information gamesOnly two players involved
Game state is fully accessible to both players
Goal: win the game against all the possible replies of the opponent
PYIWIT'02 4
Game ProgrammingSearch vs. knowledge
Two basic approaches for game programmingSearch
Knowledge
Problem of search: impossible to search to the end of the game
Search space of chess is
Problem of knowledge: expert knowledge is hard to capture
12380 1035
PYIWIT'02 5
Time Limits and the Horizon EffectSearch in games
Search in games:Most successful methodDecisions have to be made under strict time constraints
Basic search method is iterative deepeningSearch with increasing nominal search depthUse an evaluation function to estimate the probability of winning
Horizon effect: no way of knowing what will happen beyond the nominal search depth
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Pruning and Extension TechniquesExample
Starting position
Nominal
search depth
Pruning
Extensions
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Pruning and Extension TechniquesResearch objective
Merits of pruning and extensionsPruning saves timeExtensions improve reliability
Risks of pruning and extensionsImportant moves are discardedMeaningless extensions can be costly
For each game, careful tuning is vital
PYIWIT'02 8
Doesn’t carry over to other games
Pruning and Extension TechniquesPractical use
Pruning and extensions in chessFutility pruning: search is terminated when it is unlikely to recover from a material lossQuiescence search: play out captures beyond the nominal search depth
Research Objective
Construct a general framework for
pruning and extension decisions
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Threat AnalysisGeneral idea
IdeaPruning and extension decisions
should be based on threats
The problems that the search is facing
PYIWIT'02 10
Threat AnalysisDefinitions
Assume two players B and W (B to move first)
A set of threats
A partial order on the set of threatsIf (Ti) > (Tj) then Ti has a higher priority than Tj
Two sets of unresolved threats
nTTT ,,, 21
w1
v1
yry2y11r1211
xqx2x11q1211
μ,,μ,μ,,μ,,μ,μ
andδ,,δ,δ,,δ,,δ,δ
where,
W
B
WB
PYIWIT'02 11
Threat AnalysisDefinitions
: the set of threats against B at search depth i
: the set of threats against W at search depth i
Maximum operator Γ
: initial threat sets against B and W
iB
iW
11 and WB
UiiB BU
PYIWIT'02 12
Threat AnalysisGeneral goals
Safety
All threats against player B are resolved
Control
There is a stronger threat against W than any of the threats against B
Problem: how to judge that a threat is resolved?Search is still needed to resolve threats
0B
UTBW UT
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Pruning rule 1
Prune all moves at search depth N-1 (N is the nominal search depth) that do not resolve any threats
Pruning rule 2
Prune all moves at depth i that introduce threats against W with a lower priority than the highest priority threat against B
Threat AnalysisPruning rules
UTNBNBNN UTBB 11
iiW BT T
PYIWIT'02 14
Extension rule 1
Extend the search if the highest priority threat of the initial set is still unresolved
Extension rule 2
Extend the search if the highest priority threat extends a certain threshold
Threat AnalysisExtension rules
NBB 1
βNB
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Empty the threat stack
IF
THEN execute
ELSE defend against
Threat AnalysisExtensions
NN WB
NB
NW
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Threat Analysis in ShogiFeatures of shogi
The assumptions behind futility pruning and
quiescence search do not apply in shogi
Pieces captured from the opponent can be re-used
Evaluation is a combination of
material, attack and defense
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Threat Analysis in ShogiThreat set
Tmin : no threatM1,…M7: material threats
Capture of a pawn, lance, knight, silver, gold, bishop or rook
K1,…,K4: threats against the king. Based on the attack and defense of the eight squares around the king
Tmax: maximum threat, i.e. threat to capture the king
max4171min ,,,,,,, TKKMMT
PYIWIT'02 18
Threat Analysis in ShogiPartial order of threats
Tmax
Tmin
M6 M7
M4 M5
M2 M3
M1
K4
K3
K2
K1
PYIWIT'02 19
Threat Analysis in ShogiImplementation issues
Partial implementation in the shogi program SPEAR
Both of the pruning rules
Neither of the extension rules
A static search extension to empty and NB
NW
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ResultsTactical problem test
300 tactical problems from Shukan ShogiCompare the performance of a program without threat analysis (NTA) to a program with threat analysis (TA)60 seconds per problem on an Athlon 1.2GHz standard PC
Version Solved % Total Time
NTA 100 34% 2:52:00
TA 107 36% 2:54:16
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Conclusions and Future Work
Preliminary results indicate that threat analysis might improve the tactical ability of a shogi program
A full implementation of the method is needed to further investigate the merits of the method
Self-play experiments are needed to establish whether the improved tactical ability is actually leading to an improvement in playing strength