Question: Players A and B each pick a number between 1 and 100. The game is a draw if both players pick the same number. Otherwise,

Players A and B each pick a number between 1 and 100. The game is a draw if both players pick the same number. Otherwise, the player who picks the smaller number wins unless that smaller number is one less than the opponent's number, in which case the opponent wins. Find the optimal strategy for this game as well as the value of the game.

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