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This is because an extra stone given to either player in any position can only improve that player's chances.
The strategy stealing argument assumes that the second player has a winning strategy here demonstrates a winning strategy for www m kb games com first player.
The first player makes an arbitrary move to begin with.
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The contradiction implies that the original assumption is false, and the second player cannot have a winning strategy.
This argument tells nothing about whether a particular game is a draw or a win for the first player.
Also, it does not actually give a strategy for the first player.
If weak m,n,k is a draw, then decreasing m or n, or increasing k will also result in a drawn game.
Conversely, if weak or normal m,n,k is a win, then any larger weak m,n,k is a win.
Note that proofs of draws using pairing strategies also prove a draw for the weak version and thus for all smaller versions.
A draw on an infinite board means that the game will go on forever with perfect play.
A pairing strategy involves dividing all the squares of the board into pairs in such a way that by always playing on the pair of the first player's square, the second player is ensured that the source player cannot get k in a line.
A pairing strategy on an infinite board can be applied to any finite board as well - if the strategy calls for making a move outside the board, then the second player makes an arbitrary move inside the board.
It is not clear if this strategy applies to any finite board sizes.
It is not known if the second player can force a draw when k is 6 or 7 on an infinite board.
It is a win otherwise.
J van der Herik, The advantage of 都市ビルダーゲームオンライン無料 initiative, Information Sciences 122 1 2000 43-58.
Uiterwijk, Jack van Rijswijck 2002.
Berlekamp, John Horton Conway, Richard K.
Ma, Generalizations of tic-tac-toe.
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