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Math Help - Chameleon Tic-Tac-Toe

  1. #1
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    Chameleon Tic-Tac-Toe

    Chameleon Tic-Tac-Toe
    It is well known that in classic Tic-Tac-Toe neither player has a guaranteed winning strategy. However in Chameleon Tic-Tac-Toe each player may choose to place either a X or a O as their move, and they may complete a row/column/diagonal of either three O's or three X's to win (but not both).
    Which player, if any, has a winning strategy?
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  2. #2
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    Quote Originally Posted by b0mb3rz View Post
    Chameleon Tic-Tac-Toe
    It is well known that in classic Tic-Tac-Toe neither player has a guaranteed winning strategy. However in Chameleon Tic-Tac-Toe each player may choose to place either a X or a O as their move, and they may complete a row/column/diagonal of either three O's or three X's to win (but not both).
    Which player, if any, has a winning strategy?
    First person. You put thee 'x' or 'o' in the corner. Then for the next move put it the other corner. After that put it in the other corner closest to it so you can have an up and down, left and right, and across row of your letter. So you win in 4 moves.
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  3. #3
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    Quote Originally Posted by Barthayn View Post
    First person. You put thee 'x' or 'o' in the corner. Then for the next move put it the other corner. After that put it in the other corner closest to it so you can have an up and down, left and right, and across row of your letter. So you win in 4 moves.
    What if opponent used up 2 corners before your 3rd move?

    Anyway, if you use 2 corners as your 1st 2 moves, opponent wins,
    as he'll simply go in between.
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  4. #4
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    Quote Originally Posted by b0mb3rz View Post
    Chameleon Tic-Tac-Toe
    It is well known that in classic Tic-Tac-Toe neither player has a guaranteed winning strategy. However in Chameleon Tic-Tac-Toe each player may choose to place either a X or a O as their move, and they may complete a row/column/diagonal of either three O's or three X's to win (but not both).
    Which player, if any, has a winning strategy?
    Player 1 places an X somewhere.
    Player 2 places an X somewhere that CANNOT result in three in a row on the next turn.
    Player 1 is forced to use an O on his next turn.
    Player 2 places an O where three-in-a row cannot result on the next turn.
    Player 1 ? (cannot get 3-in-row, on this move, but may be in a position to block a loss)
    Player 2 most likely wins.
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  5. #5
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    "Player 1 places an X somewhere.
    Player 2 places an X somewhere that CANNOT result in three in a row on the next turn."

    Not possible if Player 1 places X at center;
    if so, Player 2 forced to use an O.

    "Player 1 places an X somewhere.
    Player 2 places an X somewhere that CANNOT result in three in a row on the next turn.
    Player 1 is forced to use an O on his next turn."

    Disagree; label the positions this way:
    123
    456
    789
    Player1 places X in p1
    Player2 places X in p6
    Player1 places X in p8
    Then it's Player 2 that's forced to use an O.
    And both forced to use O's during next 3 moves.
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  6. #6
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    Got it: 1st player ALWAYS wins by starting at center.
    Label them:
    1 2 3
    4 5 6
    7 8 9

    Ok; I pick center, enter X; opponent has 2 choices: corner or non-corner:

    Case 1 : opponent takes a corner
    opponent can only enter a O, since entering a X anywhere means I win;
    so enters O say in position 3;
    I then enter O in position 7 (complete diagonal 3-5-7);
    opponent loses , since entering a O anywhere means I win
    (works same way regardless of which corner opponent starts in)

    Case 2 : opponent takes a non-corner
    this still applies, of course:
    opponent can only enter a O, since entering a X anywhere means I win;

    so enters O say in position 2;
    I then enter O in position 8 (complete column 2-5-8);
    now opponent has only 2 choices: positions 4 or 6
    (going to a corner means he'll lose);
    say oppnent picks position 4;
    I then enter O in posiion 6 (complete row 4-5-6);
    so opponent now forced to a corner; means I win
    (works same way regardless of which non-corner opponent starts in)

    RECAP:
    start at center
    complete diagonal if opponent starts in a corner
    complete row/column or column/row if opponent starts in a non-corner
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