Mini Chess Resolution

Standard chess remains way too big to be solved but the game-theoretic value of smaller variants can be found. Previous results by Kyril Kryovich gave strong resolution for 3x3, 3x4 and up to 9 pieces in 4x4 by giving the Distance To Mate (dtm) of all legal positions.

In this page we study bigger variants (but smaller than regular 8x8 chess). We mainly use adapted versions of Stockfish as a basic resolution engine. In our analyses we consider only games where at least one player plays perfectly. It allows to considerably reduce the number of positions to analyze and is sufficient to caracterize the game (we do not consider games in which both players make bad moves).

5 X 5 : Gardner Chess, Mallet Chess

Tools:

• A 5x5 minichess engine based on Stockfish.
• A 5x5 graphical user interface has been built based on ScidvsPC. It is particularly useful to use this GUI when promotions occur in the game.

Proofs:

• The Gardner minichess variant has been proved to be a draw. The paper can be found on here.
• The White oracle with the four interesting Black oracles which prove the draw for Gardner can be viewed and dowloaded in pgn format:
  • White oracle: pgn file, browsable version of the White oracle
  • Black oracle for White plays 1.b4: pgn file, browsable version of the Black oracle for White plays 1.b4
  • Black oracle for White plays 1.d4: pgn file, browsable version of the Black oracle for White plays 1.d4
  • Black oracle for White plays 1.e4: pgn file, browsable version of the Black oracle for White plays 1.e4
  • Black oracle for White plays 1.f4: pgn file, browsable version of the Black oracle for White plays 1.f4
• We have also proved that Mallett Chess is a forced win for White: checkmate in 25 moves from the start position. In Mallett chess White's pieces are, from left to right : Rook, Knight, King, Queen, Knight whereas Black's pieces are from left to right : Rook, Bishop, King, Queen, Bishop. It appears that the theoretical value is draw if White has the Bishops. We provide justification lines:
  • pgn downloadable file
  • browsable here

Gardner Minichess analysis

• We have done a detailed analysis of the sound games in Gardner chess. It means that we collect the perfect games and their direct variations (up to one blunder). Justifying lines are given by at least one possible variation. We provide:
  • a pdf document, included are the list of all four valid openings together with some difficult checkmates.
  • a pgn downloadable file. Note that this is a not a usual pgn file, it is much larger, as it contains all correct moves up to depth 5 (together with many variations to help to understand the positions).
  • a browsable version of the pgn file.

  Here follows two screenshots of the engine and the graphical user interface. These screenshots show that the engine is not sufficient for the complete analysis of Gardner Minichess positions. The justifications are given in the pgn file.

  

  

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  Los Alamos Chess

  • Los Alamos minichess variant engine

  If you have any questions feel free to contact either Frederic dot Prost at imag.fr or Mehdi dot Mhalla at imag.fr.