# At Most 43 Moves, At Least 29: Optimal Strategies and Bounds for Ultimate Tic-Tac-Toe

arXiv: https://arxiv.org/abs/2006.02353 · HTML: https://mlsanity.com/paper/2006.02353/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2020.

## Built on by (most cited first, 1 of 1)

- [Explain yourself! Effects of Explanations in Human-Robot Interaction](https://mlsanity.com/paper/2204.04501/) (2022)

## Abstract (arXiv)

Ultimate Tic-Tac-Toe is a variant of the well known tic-tac-toe (noughts and crosses) board game. Two players compete to win three aligned "fields", each of them being a tic-tac-toe game. Each move determines which field the next player must play in. We show that there exist a winning strategy for the first player, and therefore that there exist an optimal winning strategy taking at most 43 moves; that the second player can hold on at least 29 rounds; and identify any optimal strategy's first two moves.