Strategies Based On Threats Ling Zhao University of Alberta March 10, 2003 Comparative evaluation of strategies based on the values of direct threats by Tristan Cazenave in Board Games in Academia V, Barcelona, 2002.

Outline Motivations Direct threats Thermograph Threat strategies Experimental results

Motivations Apply combinatorial game theory to Go - independent subgames - approach the best stategy

Direct threats Each subgame has at most two moves

Root of the tree Black: 22 points White: 15 points Value: 7 points for black

Sequence after two black moves Black: 25 points White: 14 points Value: 11 points for black

Direct threat: 4 values A, B, C, D with A >= B >= C >= D Denoted as (A, B, C, D) After one black move => (A,B) After one white move => (C,D)

Problem model Given a set of independent subgames with direct threats, how to compute good moves fast and accurately. (A1,B1,C1,D1) (A2,B2,C2,D2)... (An, Bn, Cn, Dn) Choose which subgame to play a move?

Thermograph Temperature: 6.5 Mean value: -4.5 Thermograph for direct threat (4,0,-6,-16)

Strategies Optimal stategy: brute force (NP-hard?) BMove: compare the best Left move (A,B,C,D) => value B (A,B) => value A MaxMove: (A,B,C,D) => value B-C (A,B) => value A-B

Stategies Sente Strategy A – B > MaxV => Sente C – D > MaxV => Reverse Sente Sente or Reverse Sente => MaxV *= 2 both => MaxV *= 4 SenteQ Strategy Always choose sente or reverse sente moves first. Use MaxV to break ties.

MaxThreat stategy

Stategies HotStrat: compare temperature ThermoStrat: adding all the thermographs of all the subgame to choose the best subgame to play in.

Experimental results Randomly choose 5 subgames (A>=B>=C>=D) 8 Strategies playing against each other (56 games one round) 100 rounds

Conclusions Simple strategy is good enough! Hotstrat strategy is easy to implement and can get 12% improvement. Problems (my thoughts) Impact of imprecise evaluation? How to generalize to more than 2 plies?