Analysis and Implementation of the game Gipf

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Analysis and Implementation of the game Gipf

• Diederik Wentink
• Institute of Knowledge and Agent Technology
• Universiteit Maastricht

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Overview

• Explanation of the game Gipf
• Basic strategies
• Complexity
• Search- and evaluation heuristics used in the
  program Gipfted

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Explanation of the game Gipf

• The board
• Basic game
• Gipf-stones

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The board
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The basic game

• 18 pieces for each player in his reserve
• Start with an empty board

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Moving a piece

• One piece at a time
• From a point to a spot
• Stones cannot be pushed off the board

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Example
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Example
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Example
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Goal 1

• Try to exhaust the opponents reserve, so that he
  is not able to move anymore because he has run
  out of stones

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Four in a row

• Four in a row
• All connected pieces at the row are removed from
  the board
• The player who had four pieces in a row adds his
  own stones to his reserve
• Other stones are captured
• It does not matter who causes the four in a row

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Example 1
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Example 2
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Example 3
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Gipf-stones

• Two pieces from the reserve
• Only played at the first moves
• Minimal one, no maximum
• When a player has to take off four stones in a
  row, he decides whether to keep the Gipf-stones
  at the board or to take them

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Example
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Example
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Goal 2

• If a player captures the last Gipf-stone from
  his opponent, he has won

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Summary of Gipf

• Players move one piece on turn, starting with
  Gipf-stones
• Game is won
• Opponent cannot move because he has run out of
  stones
• Opponent has lost all his Gipf-stones

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Basic strategy

• Have as much stones at the board as possible
• Keep a save number of stones in reserve

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Number of Gipf stones

• Usually three or four Gipf-stones
• Few Gipf-stones aggressive play
• Many Gipf-stones conservative play

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Complexity

• State-space complexity is about 1025
• Game tree complexity is about 10140
• Branching factor 46 on average

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Search heuristics

• Minimal window a-ß search with
• PVS
• Killer heuristic
• History heuristic
• Domain specific ordering
• Transposition table
• Quiescence search on capture moves

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Evaluation heuristics used

• Number of stones at the board and in reserve
• Centre stones
• Cluster Gipf-stones
• Trade stones when leading in number of captured
  stones

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Example
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Further properties Gipted

• Opening book
• Timed game using estimation of total moves
  according to evaluation function

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Performance

• About 12K nodes for a 4-ply search and 50K nodes
  for a 5-ply search
• Using a Pentium III, the program investigates
  about 4K positions per second

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Conclusion

• Interesting new game for further research
• The first of a project of games
• More information at www.gipf.com