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.
"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.
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