5

Ultimate Tic Tac Toe is played on nine tic-tac-toe boards arranged in a 3 × 3 grid.

Rules: Playing on a spot inside a board, determines the next board in which the opponent must play their next move. The goal is to win a three in a row boards. You can play your next move at any board if you are directed to play in a full board or a board that has been won.

Example:

enter image description here

If the last rule is excluded then the game has been solved and has a winning strategy for the first player (paper, implementation). That is to say, if a player is directed to play at a board that has been won but is not full yet, she does not get a wildcard move, instead she must play at that already-won board.

With the rule that directing to a won board allows the opponent to play at any board, the game is currently unsolved. This was mentioned on the site some years ago.

I known of computer implementations of the game that use Monte Carlo or similar methods. Are there known strategies that a human can apply and use? Something like favorable or recommended openings for 1st player, and responses for 2nd player?

Cohensius
  • 4,220
  • 18
  • 48
Vepir
  • 151
  • 1
  • 1
  • 7

3 Answers3

1

The following ai-agents evaluate game-states using the following features. It is a reasonable assumption that an expert human player should consider those features as well.

AI Approaches to Ultimate Tic-Tac-Toe [paper]

  • heuristic#2 takes into consideration the following features:
  1. Small board wins add 5 points,
  2. Winning the center board adds 10,
  3. Winning a corner board adds 3,
  4. Getting a center square in any small board is worth 3,
  5. Getting a square in the center board is worth 3.
  6. Two board wins which can be continued for a winning sequence (i.e. they are in a row, column or diagonal without an interfering win for the other player in the third board of the sequence) are worth 4 points,
  7. And a similar sequence inside a small board is worth 2 points.
  8. A symmetric negative score is given if the other player has these features
  • heuristic#4 builds upon the previous heuristic, but adds:

if you are sent to a small board that is full or won you can play anywhere, so that add 2 points to the heuristic (and -2 for the other player)

ULTIMATE TIC-TAC-TOE by Powell & Merrill [paper]

  1. Winning the game is worth infinity points. Losing the game is worth negative infinity points.
  2. Winning or losing a board results in a gain or loss of 100 points.
  3. If a board is won and it results in two won boards in a row (i.e. winning one more board would result in a won game), then an additional 200 points are added (this may occur multiple times if there are multiple paths to victory).
  4. Winning a board that results in blocking three in a row for the opponent results in 150 points.
  5. Winning a board that is already blocked by the opponent’s boards results in -150 points.
  6. Making two marks in a row on a small board adds 5 points
  7. Blocking an opponent win on a small board adds 20 points
  8. Making a move in a board that has no benefit to the player subtracts 20 points

They report that alpha-beta pruning that explores 7 moves a head and evaluates states with using this heuristic won 100% of the games vs a random agent and vs a greedy agent.

Cohensius
  • 4,220
  • 18
  • 48
  • Why would you care about winning the center board when it isn't that critical of a square in normal tick tack toe? – Joe W Jul 04 '21 at 15:50
  • 1
    The middle board is the strongest since it involves in the most "winning lines". The middle square is part of 4 winning possibilities, Corners are part of 3, and edges are only part of 2. – Cohensius Jul 04 '21 at 15:59
  • But it is also one of the easiest to block a corner spot gives your opponent more opportunity to make a mistake. – Joe W Jul 04 '21 at 16:13
  • Honestly when you play in a corner there is only 1 out of the 8 possible moves that will prevent you from controlling the board and winning. This also applies to a game of ultimate tick tack toe as well. – Joe W Jul 04 '21 at 17:34
0

I would treat the larger board like a single game of tic-tac-toe and play like you are trying to win a single game.

https://www.wikihow.com/Win-at-Tic-Tac-Toe

Most experienced tic tac toe players put the first "X" in a corner when they get to play first. This gives the opponent the most opportunities to make a mistake. If your opponent responds by putting an O anywhere besides the center, you can guarantee a win.[1]

For me I would start by trying to win one of the corners and after that react based on what my opponent does as if you win a corner you should at worst be able to force a draw.

Joe W
  • 14,098
  • 2
  • 46
  • 71
  • Doesn't that ignore the rule that the position your opponent played in the smaller board determines which of the smaller boards you have to play with your next move? So if you play in the top right corner of the top right board as X, your opponent plays in the centre of that board (since you just forced them to play top right board), forcing you to play your next move on the centre board. Your opponent needs to let you move back to the top right board by playing top right on a sub-board. – Andrew Oct 06 '20 at 18:57
  • @Andrew I am not saying to completely ignore the smaller boards but you if you get a corner and your opponent gets the center you are still better off as you will have more options at getting a win overall if you have a corner than if you have the center. In truth if that situation happens the game should end in a draw. – Joe W Oct 06 '20 at 18:59
  • This is very weak strategy. Have you got much experience in this game? – Cohensius Jul 04 '21 at 11:05
  • @Cohensius Please explain why you think this is a weak strategy, I have not had any bad experience with this as that. – Joe W Jul 04 '21 at 15:49
  • @JoeW, please try to play few games using your advice, you will see it is a losing strategy. Can try it here: https://ultimate-t3.herokuapp.com/ – Cohensius Jul 05 '21 at 05:56
  • Please, explain to me why you think it is such a bad strategy instead of just telling me it is one. – Joe W Jul 05 '21 at 15:42
  • You also haven't explained why the center is better than the corner when the corner only has 1 of 8 possible responses that won't lead you to winning the game. – Joe W Jul 05 '21 at 18:22
  • "The corner only has 1 of 8 possible responses" - this would be meaningful if you play Vs a player that makes random moves. Assume strong opponent, if there is a single good response, she will play it. – Cohensius Jul 06 '21 at 06:26
  • This doesn't explain why the middle is as good as you claim it is. If you are playing against a strong player you are likely to get a draw every game anyway. – Joe W Jul 06 '21 at 12:16
  • @JoeW, are you talking about regular TTT? Ultimate-TTT is unsolved yet. My conjunction is that the game is a first-player win, not a draw. – Cohensius Jul 06 '21 at 13:25
  • @Cohensius So you are making a guess about it being a first player win? You don't have any evidence that supports my advice being wrong? – Joe W Jul 06 '21 at 13:31
  • @JoeW, an educated guess. from https://www.cs.huji.ac.il/~ai/projects/2013/UlitmateTic-Tac-Toe/files/report.pdf "We ran two identical alpha-beta time-bounded agents (0.1 seconds), and tested which player has a better chance of winning. The first player won 56.17% of games (n=300, p-value<0.05), meaning he has a statistically significant advantage. – Cohensius Jul 06 '21 at 18:28
  • Your still making guesses and not explaining what you think is wrong with my answer. It sounds like you think it is wrong but lack evidence to prove it. – Joe W Jul 06 '21 at 18:29
  • @JoeW, Hey Joe, I really love to read your answers and comments on this site! Except maybe on this question :) . The thing is you are right, I am lucking of evidence to prove you are wrong. It's not trivial to prove you are wrong, however, it is easy for you to play few games and see that you are wrong (without proving it). I will be happy to try proving it after you said you played 10 games and still thinks that the center square isn't better than the corner. – Cohensius Dec 05 '21 at 14:16
  • @JoeW, I found a strong evidence (not a proof) that might convince you: the strong ai-agent of www.uttt.ai always start with first move at middle of the middle board. – Cohensius Apr 02 '22 at 20:48
-1

Found several tips that @Arkadiusz Nowaczyński learned from playing vs his super-human AI agent that he wrote:

  1. Start in the center square of the center subgame.
  1. The 'O' response is to push to the corner subgame, so then let the next 8 moves be played in the corner subgames.
  1. When the 'O' breaks out of the corner subgames, jump between the side subgames (these are the least useful to take, but still, one has to be careful not to mess up here).
  1. Maintain the overall balance on the board and wait for the opponent's mistake (the game is a marathon, not a sprint).
  1. Think twice before sending your opponent to the finished subgame (being able to choose any move from the unfinished subgames is very powerful).

My less important tips:

  1. don't let your opponent play in the middle board. Do it by completing 3-in-a-row without the middle in the non-middle boards.

  2. focus on the boards that matter: it is common to see a player that won 5 mini-boards losing the game.

Cohensius
  • 4,220
  • 18
  • 48