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 m×n 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 m×n board with Horizontal to move equals the result of the n×m 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 m×n 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 m×n board is equivalent with the result 'H' for the n×m 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 8×8 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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