Heuristic sampling: a method for predicting the performance of tree searching programs
SIAM Journal on Computing
Journal of the ACM (JACM)
EvoWorkshops '09 Proceedings of the EvoWorkshops 2009 on Applications of Evolutionary Computing: EvoCOMNET, EvoENVIRONMENT, EvoFIN, EvoGAMES, EvoHOT, EvoIASP, EvoINTERACTION, EvoMUSART, EvoNUM, EvoSTOC, EvoTRANSLOG
Efficient selectivity and backup operators in Monte-Carlo tree search
CG'06 Proceedings of the 5th international conference on Computers and games
The Development of Human Expertise in a Complex Environment
Minds and Machines
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We present several results concerning the number of positions and games of Go. We derive recurrences for L(m, n), the number of legal positions on an m × n board, and develop a dynamic programming algorithm which computes L(m, n) in time O(m3n2λm) and space O(mλm), for some constant λ L(n, n) for n ≤ 17. For larger boards, we prove the existence of a base of liberties lim mn√L(m,n) ∼2.9757341920433572493. Based on a conjecture about vanishing error terms, we derive an asymptotic formula for L(m, n), which is shown to be highly accurate. We also study the Game Tree complexity of Go, proving an upper bound on the number of possible games of (mn)L(m,n) and a lower bound of 22n2/2-O(n) on n × n boards and 22n-1 on 1 × n boards, in addition to exact counts for mn ≤ 4 and estimates up to mn = 9. Most proofs and some additional results had to be left out to observe the page limit. They may be found in the full version available at [8].