A Principled Method for Exploiting Opening Books

In the past we used a great deal of computational power and human expertise for storing a rather big dataset of good 9×9 Go games, in order to build an opening book. We improved the algorithm used for generating and storing these games considerably. However, the results were not very robust, as (i) opening books are definitely not transitive, making the non-regression testing extremely difficult, (ii) different time settings lead to opposite conclusions, because a good opening for a game with 10s per move on a single core is quite different from a good opening for a game with 30s per move on a 32-cores machine, and (iii) some very bad moves sometimes still occur. In this paper, we formalize the optimization of an opening book as a matrix game, compute the Nash equilibrium, and conclude that a naturally randomized opening book provides optimal performance (in the sense of Nash equilibria). Moreover, our research showed that from a finite set of opening books, we can choose a distribution on these opening books so that the resultant randomly constructed opening book has a significantly better performance than each of the deterministic opening books.