Threat Analysis to Reduce the Effects of the Horizon Problem in Shogi

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Threat Analysis to Reduce the Effects of the
Horizon Problem in Shogi

• Reijer Grimbergen
• Department of Information Science
• Saga University

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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

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Game ProgrammingDefinitions

• Two-player perfect information games
• Only two players involved
• Game state is fully accessible to both players
• Goal win the game against all the possible
  replies of the opponent

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Game ProgrammingSearch vs. knowledge

• Two basic approaches for game programming
• Search
• 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

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Time Limits and the Horizon EffectSearch in games

• Search in games
• Most successful method
• Decisions have to be made under strict time
  constraints
• Basic search method is iterative deepening
• Search with increasing nominal search depth
• Use 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
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Pruning and Extension TechniquesResearch
objective

• Merits of pruning and extensions
• Pruning saves time
• Extensions improve reliability
• Risks of pruning and extensions
• Important moves are discarded
• Meaningless extensions can be costly
• For each game, careful tuning is vital

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Pruning and Extension TechniquesPractical use

• Pruning and extensions in chess
• Futility pruning search is terminated when it is
  unlikely to recover from a material loss
• Quiescence search play out captures beyond the
  nominal search depth

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Threat AnalysisGeneral idea
Idea Pruning and extension decisions should be
based on threats
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Threat AnalysisDefinitions

• Assume two players B and W (B to move first)
• A set of threats
• A partial order ? on the set of threats
• If ?(Ti) gt ?(Tj) then Ti has a higher priority
  than Tj
• Two sets of unresolved threats

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Threat AnalysisDefinitions

• the set of threats against B at search
  depth i
• the set of threats against W at search
  depth i
• Maximum operator G
• initial threat sets against B
  and W

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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

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Threat AnalysisPruning rules

• 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

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Threat AnalysisExtension rules

• 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

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Threat AnalysisExtensions
Empty the threat stack IF THEN execute ELSE
defend against
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Threat Analysis in ShogiFeatures of shogi
Pieces captured from the opponent can be re-used
Evaluation is a combination of material, attack
and defense
The assumptions behind futility pruning and
quiescence search do not apply in shogi
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Threat Analysis in ShogiThreat set

• Tmin no threat
• M1,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

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Threat Analysis in ShogiPartial order of threats
Tmax
M6
M7
K4
M4
M5
K3
M2
M3
K2
M1
K1
Tmin
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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

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ResultsTactical problem test

• 300 tactical problems from Shukan Shogi
• Compare 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 25200
TA 107 36 25416
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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