The Anti-Pattern Game
14 days ago
- #modal logic
- #combinatorics
- #game theory
- The anti-pattern game is a two-player game using black and white pebbles, where players lose if they create a sequence with a pattern repeated three times.
- Player 1 has a winning strategy, confirmed by a Haskell program, and can win in less than twenty-two moves.
- An open question is whether an infinite binary sequence without any contiguous subsequence repeated three times exists.
- A sample game with 1,000 moves demonstrates the game can continue for a long time without a losing pattern.
- The game's dynamics change with more colors or players, and winning strategies become less clear in multi-player variants.
- Different winning conditions in multi-player games affect cooperation and strategy.
- The game's sequence is highly compressible, showing interesting data compression properties.