## Associating shallow and selective global tree search with monte carlo for 9x9 go (2004)

Venue: | In Proceedings of the 4th Computer and Games Conference (CG04 |

Citations: | 10 - 2 self |

### BibTeX

@INPROCEEDINGS{Bouzy04associatingshallow,

author = {Bruno Bouzy},

title = {Associating shallow and selective global tree search with monte carlo for 9x9 go},

booktitle = {In Proceedings of the 4th Computer and Games Conference (CG04},

year = {2004},

pages = {67--80}

}

### OpenURL

### Abstract

This paper explores the association of shallow and selective global tree search with Monte Carlo in 9x9 go. This exploration is based on Olga and Indigo, two experimental Monte Carlo programs. We provide a min-max algorithm that iteratively deepens the tree until one move at the root is proved to be superior to the other ones. At each iteration, random games are started at leaf nodes to compute mean values. The progressive pruning rule and the min-max rule are applied to non terminal nodes. We set up experiments demonstrating the relevance of this approach. Indigo used this algorithm at the 8th Computer Olympiad held in Graz. 1

### Citations

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Citation Context ...ery broad meaning, using the random function of the computer and averaging outcomes [14]. Simulated annealing is a refinement that includes a temperature which decreases during the simulation process =-=[17]-=-. Monte Carlo simulations have already been used in other games than go. Abramson has proposed the expected-outcome model, in which the proper evaluation of a game-tree node is the expected value of t... |

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Citation Context ...used in the Baum and Smith work about the Bayesian player [2], and applied to Othello. Berliner proposed the B* algorithm [3]. And Korf and Chickering described a general best-first min-max algorithm =-=[18]-=- that also inspired our work. Buro’s probCut algorithm uses the results of shallow tree searches to prune moves [12]. Junghanns surveyed all the alfa-beta works [15]. Rivest studied a back-up rule usi... |

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Citation Context ...imable, efficiently calculable, and domain-independent” [1]. In games containing either randomness or hidden information, the use of simulations has nothing surprising. Poki uses simulations at Poker =-=[4]-=-, and Maven at Scrabble [22]. Tesauro and Galperin have tried “truncated rollouts” in Back-gammon by using a parallel approach [23]. In Go, the information is not hidden and randomness is absent, appa... |

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Citation Context ...demonstrating the relevance of this approach. Indigo used this algorithm at the 8th Computer Olympiad held in Graz. 1 Introduction Knowledge and tree search are the two main approaches to computer go =-=[8]-=-. However, other approaches are worth considering. The Monte Carlo approach has been developed by Brügmann [10], and recently by Bouzy and Helmstetter [9]. While using very little go knowledge, Monte ... |

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Citation Context ...k-up rule when the evaluation is a probability distribution [19]. It has been used in the Baum and Smith work about the Bayesian player [2], and applied to Othello. Berliner proposed the B* algorithm =-=[3]-=-. And Korf and Chickering described a general best-first min-max algorithm [18] that also inspired our work. Buro’s probCut algorithm uses the results of shallow tree searches to prune moves [12]. Jun... |

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Citation Context ...ble, and domain-independent” [1]. In games containing either randomness or hidden information, the use of simulations has nothing surprising. Poki uses simulations at Poker [4], and Maven at Scrabble =-=[22]-=-. Tesauro and Galperin have tried “truncated rollouts” in Back-gammon by using a parallel approach [23]. In Go, the information is not hidden and randomness is absent, apparently yielding very little ... |

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Citation Context ... evaluation is not a value but a set of values, such as a probability distribution or a sample of values. 2sPalay suggested the use of a back-up rule when the evaluation is a probability distribution =-=[19]-=-. It has been used in the Baum and Smith work about the Bayesian player [2], and applied to Othello. Berliner proposed the B* algorithm [3]. And Korf and Chickering described a general best-first min-... |

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Citation Context ...the expected outcome is a powerful heuristic. He concluded that the expected-outcome model of two-player games is “precise, accurate, easily estimable, efficiently calculable, and domain-independent” =-=[1]-=-. In games containing either randomness or hidden information, the use of simulations has nothing surprising. Poki uses simulations at Poker [4], and Maven at Scrabble [22]. Tesauro and Galperin have ... |

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Citation Context ...bution or a sample of values. 2sPalay suggested the use of a back-up rule when the evaluation is a probability distribution [19]. It has been used in the Baum and Smith work about the Bayesian player =-=[2]-=-, and applied to Othello. Berliner proposed the B* algorithm [3]. And Korf and Chickering described a general best-first min-max algorithm [18] that also inspired our work. Buro’s probCut algorithm us... |

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Citation Context ...rithm [3]. And Korf and Chickering described a general best-first min-max algorithm [18] that also inspired our work. Buro’s probCut algorithm uses the results of shallow tree searches to prune moves =-=[12]-=-. Junghanns surveyed all the alfa-beta works [15]. Rivest studied a back-up rule using a complex formula [20], using an exponent p. When p = 0, the formula yields the classical min-max back-up rule an... |

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Citation Context ...of simulations has nothing surprising. Poki uses simulations at Poker [4], and Maven at Scrabble [22]. Tesauro and Galperin have tried “truncated rollouts” in Back-gammon by using a parallel approach =-=[23]-=-. In Go, the information is not hidden and randomness is absent, apparently yielding very little interest for simulations. However, ten years ago, Brügmann showed the adequacy of simulated annealing i... |

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Citation Context ...ch are the two main approaches to computer go [8]. However, other approaches are worth considering. The Monte Carlo approach has been developed by Brügmann [10], and recently by Bouzy and Helmstetter =-=[9]-=-. While using very little go knowledge, Monte Carlo go programs have performed well on 9x9 boards. Furthermore, associating domain-dependent knowledge with Monte Carlo has been very effective too [6].... |

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Citation Context ...en the tree search works that have inspired our present work. 2.1 Monte Carlo and games The term Monte Carlo has a very broad meaning, using the random function of the computer and averaging outcomes =-=[14]-=-. Simulated annealing is a refinement that includes a temperature which decreases during the simulation process [17]. Monte Carlo simulations have already been used in other games than go. Abramson ha... |

18 |
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Citation Context ...neral best-first min-max algorithm [18] that also inspired our work. Buro’s probCut algorithm uses the results of shallow tree searches to prune moves [12]. Junghanns surveyed all the alfa-beta works =-=[15]-=-. Rivest studied a back-up rule using a complex formula [20], using an exponent p. When p = 0, the formula yields the classical min-max back-up rule and when p = ∞, it gives the average back-up, that ... |

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Citation Context ...f Amazons may be a relevant choice. Besides, since most of the thinking time of the program is spent at the beginning of the game, we want to develop an opening book. Finally, as 5x5 Go was solved by =-=[24]-=-, we also plan to apply this algorithm on small boards ranging from 5x5 up to 9x9. To sum up, we have issued the algorithm that Indigo used during the 9x9 Go competition at the last Computer Olympiad ... |

9 |
Indigo home
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(Show Context)
Citation Context ...iments about go playing programs, let us start by clearly defining the programs’ names used in this paper. First, Indigo is the generic name of the program we have been developing over the past years =-=[5]-=-. It regularly attends computer go competitions. Each year, we set up a new release of this program, and Indigo2002 corresponds to Indigo’s release at the end of 2002. Indigo2002 was mainly based on k... |

8 | The move decision process of Indigo - Bouzy - 2003 |

6 |
Associating knowledge and Monte Carlo approaches within a go program
- Bouzy
- 2003
(Show Context)
Citation Context ... [9]. While using very little go knowledge, Monte Carlo go programs have performed well on 9x9 boards. Furthermore, associating domain-dependent knowledge with Monte Carlo has been very effective too =-=[6]-=-. Therefore, the remaining question is to study the association of tree search with Monte Carlo. Because a strength of Monte Carlo consists in avoiding the breaking down of the whole game into sub-gam... |

6 |
Gnugo home
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- 2003
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Citation Context ...s of programs using different depths. Subsection 4.2 underlines the relative strengths of programs using different widths. Then, subsection 4.3 shows the relative strengths of Olga against GNU Go 3.2 =-=[11]-=-. Finally, subsection 4.4 mentions the result of Indigo at the last 9x9 go competition held during the 8th Computer Olympiad. 4.1 Making the depth vary This subsection contains the results of the expe... |

6 |
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Citation Context ...ur work. Buro’s probCut algorithm uses the results of shallow tree searches to prune moves [12]. Junghanns surveyed all the alfa-beta works [15]. Rivest studied a back-up rule using a complex formula =-=[20]-=-, using an exponent p. When p = 0, the formula yields the classical min-max back-up rule and when p = ∞, it gives the average back-up, that is a feature of Monte Carlo. Sadikov, Kononenko and Bratko h... |

5 |
Vegos home
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Citation Context ...s. However, ten years ago, Brügmann showed the adequacy of simulated annealing in Go, with his program Gobble [10]. Recently, Kaminski has performed Brügmann’s experiment again with his program Vegos =-=[16]-=-. Last year, Bouzy and Helmstetter studied Monte Carlo Go programs, experimentally demonstrating their effectiveness on 9x9 boards [9]. Since then, Bouzy has successfully associated Monte Carlo and kn... |

4 | A study of decision error in selective game tree search
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- 2001
(Show Context)
Citation Context ... [21]. This would explain the success of tree search in practice, although, in theory, pathologies exist in game tree. Chen has experimentally shown the effect of selectivity during tree search in Go =-=[13]-=-. 3 Our Work This section describes our work based on go playing programs. First, it defines the names of the programs mentioned along the paper. Second, it gives an intuitive view of the requirements... |

2 | Search versus knowledge: an empirical study of minimax on krk
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- 2003
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Citation Context ... Kononenko and Bratko have shown that evaluations containing errors introduce a bias in the min-max values of the tree. The bias varies in the search depth, but remains constant for two sibling nodes =-=[21]-=-. This would explain the success of tree search in practice, although, in theory, pathologies exist in game tree. Chen has experimentally shown the effect of selectivity during tree search in Go [13].... |