Abstract
We have developed a program called MUDoS (Maastricht University Domineering Solver) that solves Domineering positions in a very efficient way. It enables the solution of known positions (up to the \(10\times 10\) board) to be much quicker.
More importantly, it enables the solution of \(11\times 11\) Domineering, a board size that up till now was far out of the 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 \(11\times 11\) Domineering, irrespective whether Vertical or Horizontal starts.
In addition, several other new boards were solved. Using the convention that Vertical starts, the \(8\times 15\), \(11\times 9\), \(12\times 8\), \(12\times 15\), \(14\times 8\), and \(17\times 6\) boards are all won by Vertical, whereas the \(6\times 17\), \(8\times 12\), \(9\times 11\), and \(11\times 10\) boards are all won by Horizontal.
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Notes
- 1.
We note that solving a board investigating a single node is not exactly the same as perfectly solving a board, since in the latter the board is solved using characteristics of the board solely, without generating the possible moves, whereas in the former the possible moves are generated, but immediately proven to contain at least one winning move or only losing moves.
- 2.
Although Drummond-Cole determined the outcome classes for \(8\times 26\) and \(26\times 8\) (H and V), these results were not included in his table of known outcome classes for Domineering [11].
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Uiterwijk, J.W.H.M. (2016). 11 \(\times \) 11 Domineering Is Solved: The First Player Wins. In: Plaat, A., Kosters, W., van den Herik, J. (eds) Computers and Games. CG 2016. Lecture Notes in Computer Science(), vol 10068. Springer, Cham. https://doi.org/10.1007/978-3-319-50935-8_12
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