Wild Tic Tac Toe
Wild tic-tac-toe is like traditional tic-tac-toe except that on each turn, a player may place an X or an O. The first person to get a row, column, or diagonal of three Xs or Os wins the game.
If Wild tic-tac-toe is played optimally, who should win?
This particular game ends on victory for player 2. The moves (and which player made them) are marked.
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1 solution
That was the strategy I came up with also.
I wonder if there is any other winning strategy for the first player?
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From what I can tell if Player 1 starts anywhere other than the center, and if both players play optimally, the game will end in a tie, but there are a lot of variations to consider so I may have missed something.
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David - see my updated reply on a different comment. According to a program I developed to exhaustively search the game state space, a win can be forced only when player 1 starts in the center. If player 1 starts in a corner or an edge, and both players play optimally, a draw is always forced.
Player 1 playing a "X" instead of a "O" in his third move (same place) is the only variation i found.
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ok my 1st move x top left, yours?
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@Brad Shad – The result is "player 1 " wins. the strategy is detailled is David post. at least take the time to read it... this is not traditionnal tic-tac-toe. the strategy starts with "X" in the center by player 1.
The first player is not forced to play "O" at every turn. In the last case (where player 2 prolong the game), the third move by player 1 (in total the Fifth move) could be an "X" or "O". it would still ensure a win for player 1. Player 2 would have to play with the following situation :
Player 1 is still sure to win
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an x on the bottom middle instead of the o, ensures a tie
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the bottom middle is taken... when whould you do that move? i was speaking only on the first player third move, leading to the situation in picture;
Good observation
This is smart
i only guessed first player because the example showed player 2 and examples don't usually show the correct answer And in the normal tic tac toe the first player can also always win so i thought it might be similar here
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Actually, in normal Tic Tac Toe if both players are playing optimally the game will end in a tie.
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Can't player 1 do the trick where you start at a corner and make a fork where he will have 2 winning opportunities and player 2 can't block both of them?
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@Laura Gao – If Player 2 is playing optimally then he or she will prevent a "fork" from happening in the first place. Check out this website for more details.
always a tie.
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Let's play a game and see. I'll start by placing an X in the middle. Your turn.
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o top left
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@Brad Shad – O bottom right
I do not agree with the solution given. If played optimally ends up in a ties. The only times where someone wins is when there is a mistake. So I kindly disagree
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If everyone plays optimally, then by definition, no one will make a mistake.
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Agree, so the solution should be "Always a tie"
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@Paolo Chiarlone – Please read David's solution again, he clearly demonstrates that the first player has a winning position, even if the second player plays optimally.
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@Pi Han Goh – I read it and I can assure you that you will never beat me at this game even if you play optimally... Again, unless I do make a mistake, it will always end in a tie.
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@Paolo Chiarlone – Let's play a game and see. I'll start by placing an X in the middle. Your turn.
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@David Vreken – Upper left
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@Paolo Chiarlone – You have to specify whether you play an O or X. If you played an X, I would play an X in the bottom right and win, so I'll assume you played an O in the upper left. Then I would play an O in the bottom right. Your turn.
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@David Vreken – So you can switch the symbols?
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@Paolo Chiarlone – Yes, the question states, "Wild tic-tac-toe is like traditional tic-tac-toe except that on each turn, a player may place an X or an O"
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@David Vreken – This has been a very amusing thread!
@David Vreken – Oppps missed that then! AH AH
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@Paolo Chiarlone – No problem! I'm glad you understand now.
I disagree, there's a difference between Wild Tic-Tac-Toe and Tic-Tac-Toe. Player One has the advantage since their turn comes first, so they can place an X or O in the middle which -- as demonstrated by David Vreken -- will always let Player One win. Since it will always let Player 1 win, definitionally that is the optimal choice for Player 1. From that point on, no matter what Player 2 does, Player 1 can still force a win by choosing the optimal choice of placing an O or X in the middle.
I thought people on this site were smarter than disagreeing with facts. Do you realize how stupid that makes you sound?
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Calling other people stupid makes you very smart instead, good job Vilim
Exactly how I went about it!
Wrong. If both players play perfectly, it is always a tie.
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Let's play a game and see. I'll start by placing an X in the middle. Your turn.
without mistakes, it is always a tie.
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no it is not. if first player plays an "X" center first move, and then follows the strategy details in David Vreken post, player 1 always win. This is not traditionnal tic-tac-toe. Happy to show it to you. i can start with "X" center. your move.
This strategy always results in player 1 winning - player 2 cannot force a draw (or win) if player 1 uses this strategy. I think the skeptics out there may be getting the point of the puzzle confused. David is not claiming that player 1 always wins no matter what the starting move is. David is claiming that player 1 always wins if player 1 uses the strategy described. I wrote a small program to search the entire game state space and there are definitely ways that player 1 can lose or draw - but then, by definition, player 1 did not play optimally. The puzzle question asked who should win if the game is played optimally and the answer is player 1. Unfortunately, the game state space is quite large and resisted my attempts to infer if there are any alternate winning strategies. I will need to extend my program to figure that out - maybe some day.... Cheers.
Update: There is a "trivially different" alternate solution. If you exchange the X and O tokens in David's solution (i.e., player 1 starts with O in the center with Xs and Os reversed in the strategy description), you end up with an equivalent winning strategy that is only trivially different than David's strategy. I mention this for completeness, but do not believe this constitutes a different solution than David's.
Update: Expanded my program. Unless my program has a bug, based on exhaustive search of the game state space, this solution is the ONLY solution that can force a win when both players play optimally. By symmetry, there are 3 basic starting moves for player 1: (1) center, (2) corner, and (3) edge. Player 1 can force a win by starting in the center as David has pointed out. A draw is forced when player 1 starts in the corner or on an edge and both players play optimally.
The key here is that it is NOT standard Tic-Tac-Toe. Either player can write X or O. Almost all the comments below seem to assume a standard game of Tic-Tac-Toe, but the example shows a different sequence. Good puzzle - I'd recommend emphasizing the difference immediately rather than saying "is like traditional tic-tac-toe except....". Try "Wild tic-tac-toe is a variant of Tic-Tac-Toe where either player can ..."
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The first player always wins, so there's no fun in playing it
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It might be a fun game if it was extended to a 4x4 grid. (extending to 3 dimensions has the same solution of 1st player always winning). I wonder if that results in a more interesting game.
Unless you're player #1 and player #2 hasn't caught on yet... :)
You are right. This is not the standard TicTacToe. The question was wrong.
You need to improve your instructions on this game.
I wonder about 4x4...I also thought of a possible variant. What if each player can either place a letter or erase and change a letter? There would probably have to be a rule preventing repetitive loops, like you can't change the same square twice in a row, or even you can't change the same letter twice in a row.
Relevant wiki: Combinatorial Games - Winning Positions
Player 1 can always win by starting in the center and then always playing the same letter directly opposite of Player 2 until a winning move presents itself.
Let's say Player 1 places an X in the center. If any player places another X anywhere, the other player can place a 3rd X and win. So now both players must only use Os for optimal play.
If Player 2 places an O in any of the corners, Player 1 can place an O in the opposite corner, and then no matter where Player 2 places an X or O Player 1 can place a 3rd X or O and win.
Player 2 can prolong the game by placing Os in the sides, but as long as Player 1 matches Os in the opposite sides, eventually all the sides will be used up and Player 2 will be forced to place an X or O in one of the corners, in which case Player 1 can place a 3rd X or O and win.
No matter how Player 2 plays, Player 1 can force a win.