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An m,n,k-game is an abstract board game in which two players take turns in placing a stone of their color on an m-by-n board, the winner being the player who first gets k stones of their own color in a row, horizontally, vertically, or diagonally. Thus, tic-tac-toe is the 3,3,3-game and free-style … Pogledajte više A standard strategy stealing argument from combinatorial game theory shows that in no m,n,k-game can there be a strategy that assures that the second player will win (a second-player winning strategy). This is … Pogledajte više A useful notion is a "weak (m,n,k) game", where k-in-a-row by the second player does not end the game with a second player win. Pogledajte više • k = 1 and k = 2 are trivial wins, except for (1,1,2) and (2,1,2) • (3,3,3) is a draw (see Tic-tac-toe), and (m,n,3) is a draw if m < 3 or n < 3. … Pogledajte više • Connect Four • Connect6 • Gomoku • Harary's generalized tictactoe Pogledajte više The following statements refer to the first player in the weak game, assuming that both players use an optimal strategy. • If a particular (m0, n0, k0) is a draw, then (m0, n0, k) … Pogledajte više It is possible to consider variants played on a multidimensional board instead of a bidimensional board. For the case of k-in-a-row where the board is an n-dimensional hypercube with all edges with length k, Hales and Jewett proved that … Pogledajte više WebPosted by u/AutoModerator - No votes and no comments blueberry cheesecake recipe philippines
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