11 x 11 Domineering is Solved: The first player wins

TL;DR

This paper introduces MUDoS, a highly efficient solver that conclusively determines the first player wins in the 11 x 11 Domineering game, solving previously intractable board sizes through extensive computation.

Contribution

The development of MUDoS enables solving large Domineering boards, including the 11 x 11, and provides definitive winning strategies for various board sizes.

Findings

First player wins the 11 x 11 Domineering game.

Solved multiple previously unsolved boards.

Demonstrated the effectiveness of MUDoS in large-scale game solving.

Abstract

We have developed a program called MUDoS (Maastricht University Domineering Solver) that solves Domineering positions in a very efficient way. This enables the solution of known positions so far (up to the 10 x 10 board) much quicker (measured in number of investigated nodes). More importantly, it enables the solution of the 11 x 11 Domineering board, a board up till now far out of reach of previous Domineering solvers. The solution needed the investigation of 259,689,994,008 nodes, using almost half a year of computation time on a single simple desktop computer. The results show that under optimal play the first player wins the 11 x 11 Domineering game, irrespective if Vertical or Horizontal starts the game. In addition, several other boards hitherto unsolved were solved. Using the convention that Vertical starts, the 8 x 15, 11 x 9, 12 x 8, 12 x 15, 14 x 8, and 17 x 6 boards are all won by Vertical, whereas the 6 x 17, 8 x 12, 9 x 11, and 11 x 10 boards are all won by Horizontal.