Maximizing the Chance of
Winning in Searching Go
Game Trees
Author: Keh-Hsun Chen
Accepted by Information Sciences
Presenter: Ling Zhao
March 16, 2005
Motivation
Traditional approach in Go:
maximize territory
 Should it better to maximize the
probability of winning?

Expected territory vs. chance of
winning

k groups, prob pi to be value Ai, and prob 1–
pi to be –Ai

(qi, A’i) either (pi, Ai) or (1-pi, -Ai)
2^n combinations
Case study: All groups are safe
Territory score is a good predication of the
outcome of the game in end games.
 Less reliable in opening or middle game.
 Major difficulty: measuring no man’s lands

Frontier space points of a block
1.
2.
3.
Must be adjacent empty points of the block
Must have an adjacent point which is not the
same color of the block
Can be used to measure
openness of the boundary.
Frontier space points

Usually the total number of frontier space points
(F) is 0 at the beginning, increases until to its peak
(about 60) in the middle game, then decreases to 0
in the end. M is the move number.

if (M < 100)
if (EA > 60+(100-M)/4) EW = 1;
else if (EA < -60-(100-M)/4) EW = 0;
else EW = 0.5+ 0.5 * EA/(60+(100-M)/4);
else
if (EA > F) EW = 1;
else if (EA < -F) EW = 0;
else EW = 0.5+0.5*EA/F;
Case study: Existence of unsafe
groups
k groups, the first k1 groups are safe, and the
rest are unsafe.
 Pessimistic evaluation:


Optimistic evaluation:
Battles
An unsafe group’s transitive closure of
adjacent unsafe groups forms a battle.
 Evaluation of one battle
Probability p1, p2,……pn with sum of 1.
EW =

Multi-battle situation


Combinatorial game model:
G1 = {A | B}
G = G1 + G2 + …+ Gn
Probabilistic combinatorial game (PCG) model:
G1 = {A1 , p1 , A2 , p2 | B1 , q1 , B2 , q2 }
G = G1 + G2 + …+ Gn
Solution
Mini-max based on winning percentage
 Terminal nodes: no branching in the game

Experimental results
Experimental Go intellect is slightly inferior
to the regular version.
 Reasons:
Probability and the correspondent outcome
score are difficult to estimate when there are
one or more battles.
 Solutions: more thorough knowledge
engineering and implementation.

Lessons learned



Dynamic modification of weights on some move
generators. For example, reduce weight for
attacking moves when far ahead.
Adjust territory evaluation by the probability of
winning. For example, if the winning percentage
is 99%, add 10 points to territory score.
Incremental increase of performance found from
experiments from the above two techniques.
Conclusions
Right direction for Go.
 More concrete experimental results.
 Interesting problem in itself and possible
applications in other games like Amazon.
 Need better implementation for computing
winning probability.
