Domineering

With our program DOMI we have solved many Domineering games. All data are summarized in the following table.

m\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 1 1 1 2 1 1 1 2 1 1 1 2 2 1 1 2 2 1 1 2 2 2 1 2 2 2 1 2 2 2
3 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
4 1 1 1 1 1 1 1 2 1 2 1 2 2 2 2 2 2 2
5 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
6 1 1 1 1 1 1 1 2 1 1 1 2
7 1 1 1 2 1 2 1 2 2 2 2
8 1 1 1 1 1 1 1 1 1
9 1 2 1 2 1 2 1 2 1
10 1 1 1 1 1 1 1 1
11 1 1 1 2 1 1 1
12 1 1 1 1 1 1
13 1 2 1 2 1
14 1 1 1 1 1
15 1 1 1 1 1
16 1 1 1 1 1
17 1 1 1 1
18 1 1 1 1
19 1 1 1
20 1 1 1
21 1 1 1
22 1 1 1
23 1 1 1
24 1 1 1
25 1 1 1
26 1 1 1
27 1 1 1
28 1 1 1
29 1 1 1
30 1 1 1


Table 1: Game-theoretic values of many mn Domineering games, with m denoting the number of rows and n the number of columns. In all games, Vertical plays first. Of course the result for an mn board with Horizontal to move equals the result of the nm board with Vertical to move. A '1' indicates a first-player win, a '2' a second-player win.


m\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
1 2 H H H H H H H H H H H H H H H H H H H H H H H H H H H H H
2 V 1 1 H V 1 1 H V 1 1 H 2 1 1 H H 1 1 H H H 1 H H H 1 H H H
3 V 1 1 H H H H H H H H H H H H H H H H H H H H H H H H H H H
4 V V V 1 V 1 V H V H V H 2 H H H H H
5 V H V H 2 H H H H H H H H H H H
6 V 1 V 1 V 1 V H V 1 1 H
7 V 1 V H V H 1 H H H H
8 V V V V V V V 1 V H or 1
9 V H V H V H V H 1
10 V 1 V V V 1 V V or 1
11 V 1 V H V 1 V
12 V V V V V V
13 V 2 V 2 V
14 V 1 V V V
15 V 1 V V V
16 V V V V V
17 V V V V
18 V 1 V V
19 V 1 V
20 V V V
21 V V V
22 V V V
23 V 1 V
24 V V V
25 V V V
26 V V V
27 V 1 V
28 V V V
29 V V V
30 V V V


Table 2: Game-theoretic values of many mn Domineering games, with m denoting the number of rows and n the number of columns. A '1' indicates a first-player win, a '2' a second-player win, a 'V' means a win for Vertical (irrespective of who begins) and a 'H' means a win for Horizontal (irrespective of who begins). In the latter two cases the result of 'V' for an mn board is equivalent with the result 'H' for the nm board, and vice versa.

The main results have been published in the following two publications:

  • Breuker, D.M., Uiterwijk, J.W.H.M., and Herik, H.J. van den (2000). Solving 88 Domineering. Theoretical Computer Science, Vol. 230, pp. 195-206.
  • Uiterwijk, J.W.H.M. and Herik, H.J. van den (2000). The Advantage of the Initiative. Information Sciences, Vol. 122, No. 1, pp. 43-58.

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