Strategy for Ultimate Tic Tac Toe

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:

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?

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.

• Why would you care about winning the center board when it isn't that critical of a square in normal tick tack toe? Commented Jul 4, 2021 at 15:50
• 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. Commented Jul 4, 2021 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. Commented Jul 4, 2021 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. Commented Jul 4, 2021 at 17:34

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.

• 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. Commented Oct 6, 2020 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. Commented Oct 6, 2020 at 18:59
• This is very weak strategy. Have you got much experience in this game? Commented Jul 4, 2021 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. Commented Jul 4, 2021 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: ultimate-t3.herokuapp.com Commented Jul 5, 2021 at 5:56

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.