Can a Player Always Win in Double Move Tic-Tac-Toe?

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In summary: This is exactly the kind of reasoning you need to use to prove that player 1 always has a winning strategy in this game. So, here's another question: Suppose player 1 lets player 2 place 3 marks in a row before making his first move. Does player 1 still have a winning strategy?In summary, the conversation discusses the game of double move tic-tac-toe and the question of whether there exists a winning strategy for the first player. It is suggested that the first player can always win by placing their first two marks in the corner and center, and then forcing the second player to block all possible winning combinations. It is also proposed that even if the second player is allowed to make the first move for
  • #1
hammonjj
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Homework Statement


Consider the game of `double move tic-tac-toe' played by the usual rules of tic-
tac-toe, except that each player makes two marks in succession before relinquishing
his turn to the other player (you may know tic-tac-toe by the name `noughts and
crosses'). Prove that there exists a strategy by which the first player always wins.

Homework Equations


None that I can think of.

The Attempt at a Solution


I have no clue how to prove this. The obvious strategy is that player one places an X at one of the corners of the board and then one in the center. Player two can't block all the winning strategies with their two moves.

The question is, how do I show this in "math speak"?

Thanks! Sorry for all the posting lately, I'm just terrible at Discrete Math.
 
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  • #2
After the first turn the board looks like


+-+-+-+
|X| | |
+-+-+-+
| |X| |
+-+-+-+
| | | |
+-+-+-+


Where do player 2 need to place O's for you not to be able to win in your turn? Can this be done with just 2 O's? If you can find three disjoint sets of spots that must each be blocked, then you are finished.

In other words, can you partition the last 7 empty spaces into 3 disjoint subsets such that if any of the 3 disjoint subsets are left untouched by player 2, then you can win in your turn?
 
  • #3
obviously, player 2 cannot win in 1 move (he only can place two marks).

since player 2 cannot win on their first move, their best strategy is to prevent player 1 from winning on player 1's second move.

player 2 must place a mark at (3,3), or else player 1 will on the next move, and then win.

there are 4 possible ways player 1 might place two marks and win on their next move, given that (3,3) is taken: complete the center row, complete the center column, or complete the left column, or the top row. player 2 must block all 4 of these possibilities with a single move.

show that player 2 can at most only block 2 of these.

a slightly more challenging question is: suppose player 1 allows player 2 to make his first move for him (still using X's for player 1, and O's for player 2. player 2 does NOT get to place 4 O's). does player 1 still always have a winning strategy?
 
  • #4
+-+-+-+
|x| | |
+-+-+-+
| | | |
+-+-+-+
| | |x|
+-+-+-+

In this case player two can never win because you have three rows to win, right?
 

FAQ: Can a Player Always Win in Double Move Tic-Tac-Toe?

1. What is Double Tic-Tac-Toe Strategy?

Double Tic-Tac-Toe Strategy is an advanced version of the classic tic-tac-toe game, where two players compete on two separate tic-tac-toe boards at the same time. The goal is to get three in a row on both boards to win the game.

2. What is the best strategy for winning at Double Tic-Tac-Toe?

The best strategy for winning at Double Tic-Tac-Toe is to focus on controlling the center spaces on both boards, as this will give you the most options for creating a winning pattern. It is also important to pay attention to your opponent's moves and block their attempts to create a winning pattern.

3. Is there a specific opening move that is more effective in Double Tic-Tac-Toe?

There is no one specific opening move that guarantees a win in Double Tic-Tac-Toe. However, starting in the center space of one of the boards is generally a good strategy, as it allows you to control both boards at the same time.

4. Can Double Tic-Tac-Toe be played with more than two players?

Yes, Double Tic-Tac-Toe can be played with more than two players, but it becomes more complex and challenging. Each player would typically have their own separate board, and the goal would be to get three in a row on all boards simultaneously.

5. Are there any variations to the Double Tic-Tac-Toe game?

There are various variations of Double Tic-Tac-Toe, such as playing on a larger grid with more spaces, or using different symbols or shapes instead of X's and O's. These variations can add an extra level of complexity to the game and make it more challenging.

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