L Game - Analysis

Analysis

All possible final positions, blue has won

In a game with two perfect players, neither will ever win or lose. The L game is small enough to be completely solvable. There are 2296 different possible valid ways the pieces can be arranged, not counting a rotation or mirror of an arrangement as a new arrangement, and considering the two neutral pieces to be identical. Any arrangement can be reached during the game, with it being any player's turn. Each player has lost in 15 of these arrangements, if it is that player's turn. The losing arrangements involve the losing player's L-piece touching a corner. Each player will also soon lose to a perfect player in an additional 14 arrangements. A player will be able to at least force a draw (by playing forever without losing) from the remaining 2267 positions.

Even if neither player plays perfectly, defensive play can continue indefinitely if the players are too cautious to move a neutral piece to the killer positions. If both players are at this level, a sudden-death variant of the rules permits one to move both neutral pieces after moving. A player who can look three moves ahead can defeat defensive play using the standard rules.

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