Mean and temperature search for Go endgames

Incentive Learning in Monte Carlo Tree Search

“…Games in are the left's options and games in are the right's options. The simplest game is game 0, defined as (2) The negation of a game is defined as (3) The sum of two games is a game There is a partial order relation defined on the classes of games (5) where no in (6) The partial order relation introduces an equivalence relation and (7) Equations (1)-(7) define a commutative group of games. We also use the notation when is neither greater than nor equal to .…”

“…A constructive algorithm, thermograph, for the mean and the temperature was due to [1] and [2]. Another approach for calculating the mean and the temperature with partial information of a single option game was proposed in [5]. In this paper, we use the notation and to denote the mean and the temperature of a game .…”

Maximizing the chance of winning in searching Go game trees

“…In Go, after decomposition [12,13] or soft-decomposition [8,9], each battle and other local component game can be represented by a component PCG, G i , and the whole game is represented by G ¼ P n i¼1 G i assuming that there are n sub-games. If, for each outcome distribution D = {(S i , p i )jS i 2 I, 0 < p i < = 1, and P n i¼1 p i ¼ 1g, we use e ¼ P n i¼1 p i à S i to replace D in G, then we get an ordinary combinatorial game model.…”

TDS+: Improving Temperature Discovery Search

“…Two forward search approaches for computing means and temperatures are known. Mean and Temperature Search (MTS) (Kao 2000;Kao et al 2012) searches a subgame in alternating-first order and refines bounds on means and temperatures up to convergence. The main limitation of MTS is the requirement that all game positions of temperature zero and below can be statically recognized and evaluated.…”