Monday, March 14, 2005

Suicide checkers: is it a draw?

Two player games such as checkers have a so-called game-theoretic value. The game-theoretic value is the outcome of the game when it is played perfectly. A game is said to be weakly solved when the game-theoretic value is known. For checkers, it is rather obvious that the game-theoretic value is a draw, but it is not proven (yet, see a previous post on the end of checkers). Most interesting games, such as checkers or chess, are very likely drawn with perfect play. Games which are a win or a loss for the first player can be considered to be flawed - somehow, it's not right that one side has a winning advantage right from the start of the game. An example for this is Connect 4: It is a win for the player who starts the game. A computer solution of that game was already given about a decade ago. How about the checkers variants? As I already mentioned, Kingscourt (the checkers variant where the first side to get a king wins) cannot be a draw and is therefore flawed. But how about suicide checkers? Is it a flawed game or not? I do not have a real proof, but I believe the game is a draw. My suicide checkers book now has 62'000 positions, and it comes to the conclusion that the game is drawn.
Among human players, suicide checkers mostly leads to decisive games, unlike regular checkers where the draw is a very common result. Therefore, Suicidal Cake's verdict may seem surprising, but there are in fact some things about suicide checkers that make it more drawish than one might think at first - I will return to this subject in another post!

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