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

TL;DR

This paper analyzes Ultimate Tic-Tac-Toe, proving the existence of a winning strategy for the first player within 43 moves, and establishing bounds on the second player's resilience, while identifying initial optimal moves.

Contribution

It establishes the existence of an optimal winning strategy for the first player and bounds on the game length, providing new strategic insights for Ultimate Tic-Tac-Toe.

Findings

First player has a winning strategy within 43 moves.

Second player can survive at least 29 rounds.

Identified initial moves for optimal strategies.

Abstract

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.