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研究生:張瓈文
論文名稱:「德州撲克」不完全資訊賽局之研究
論文名稱(外文):On Study of An Imperfect Information Game: Texas Hold'em Poker
指導教授:林順喜林順喜引用關係
學位類別:碩士
校院名稱:國立臺灣師範大學
系所名稱:資訊工程研究所
學門:工程學門
學類:電資工程學類
論文出版年:2006
畢業學年度:94
語文別:中文
論文頁數:79
中文關鍵詞:德州撲克不完全資訊賽局賽局理論撲克
外文關鍵詞:Texas Hold'em PokerImperfect Information GameGame TheoryPoker
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賽局是指兩人以上的競賽,交通路線選擇、益智遊戲的出招方式、股市投資、人際關係、公司經營、商場或政局中激烈的競爭、甚至國際情勢間的戰與和,都屬於賽局的一種,為了求得勝利而產生了各種策略、智謀,也就是賽局理論。
  撲克屬於不完全資訊賽局的一種,由於有機率因素而使複雜度大幅提高,在所有撲克變形中,德州撲克又是複雜度最高的類型之一,若視牌桌為一個小型的經濟社會,撲克投注策略即為簡化過的投資策略,對於不完全資訊賽局是良好的研究目標。
  本篇研究以德州撲克的下注策略為主題,進行不完全資訊賽局之研究,從雙人德州撲克賽局開始著手,以多人德州撲克之應用為目標。首先,在每次輪詢下注時,利用賽局理論中的策略矩陣求最佳策略分佈,並使用取樣及近似方法以加速計算複雜的勝率,以便利用於策略矩陣中;再將單次輪詢之策略矩陣以樹狀結構組織,形成矩陣迭代樹的模型,以簡化運算複雜度,並可在合理時間內得到德州撲克賽局之非確定性策略;最後嘗試將此結構擴張為多人賽局模型,以驗證此模型之通用性。
實驗結果顯示,使用矩陣迭代樹模型確實能得出快速而符合理論的最佳解,隨著賽局局數的增加,獲利逐漸累積上升,且同樣的模型可以輕易轉換至多人賽局中使用,也能在相差不多的短時間內得到最佳解,對於不完全資訊賽局分析而言,矩陣迭代樹的確是一個具擴張性的良好模型。
A game is a competition among people. It includes choosing traffic routes, deciding strategies in a casino, stock market investment, interpersonal relationship skills, company managing, market competitions and political strife. Even war and peace in the international situation are a kind of games. In order to win the games, a variety of ideas and strategies are proposed, which are called Game Theory.
Poker is one of the imperfect information games. Its complexity rises substantially because of the probability factor. Among all poker games, Texas Hold’em is one of the poker games with the highest complexity. If we treat the table as a little economical society, poker-betting strategy is just a simplified investment strategy, so it is a good target for studying the imperfect information games.
This thesis focuses on the study of imperfect information games with the topic of Texas Hold’em betting strategy. We start from two-players Texas Hold’em Poker and aim to k-players Texas Hold’em Poker. First, we use the strategy matrix mentioned in Game Theory to derive the optimal strategy distribution in each betting round and speed up the calculation of winning probability, which will be used in the strategy matrix, with sampling and approximation. Then we organize the matrix into a tree, form an iterated matrix tree model to simplify the computation, and get a mixed strategy of Texas Hold’em in reasonable time. Finally, we extend this structure to form a k-players game model.
The experiment results show that we can certainly get a theoretically optimal solution with iterated matrix tree model in a short time. Since more games are played, the profit has been increasing cumulatively. In addition, the same model can be easily converted to k-players mode and will also generate an optimal solution in almost the same moment. Iterated matrix tree is indeed an appropriate extendable model for analyzing imperfect information games.
附表目錄                         vii
附圖目錄                         viii
第一章 簡介                      1
第一節 研究背景與動機………………………………………1
第二節 問題敘述………………………………………………2
第三節 研究方向及目的………………………………………4
第四節 論文架構………………………………………………6
  
  第二章 德州撲克賽局                  7
第一節  德州撲克簡介…………………………………………7
第二節  遊戲進行方式…………………………………………8
第三節  複雜度分析……………………………………………13

  第三章 相關研究探討                  15
第一節  三重機率………………………………………………16
第二節  經驗法則………………………………………………17
第三節  賽局樹與搜尋…………………………………………18
第四節  對手行為模擬…………………………………………21
第五節  賽局理論………………………………………………22

  第四章 雙人德州撲克                  26
第一節  賽局特性分析…………………………………………27
第二節  策略矩陣………………………………………………31
第三節  矩陣迭代樹狀結構……………………………………37
第四節  勝率計算………………………………………………40

  第五章 實驗及結果                   46
第一節  取樣測試………………………………………………46
第二節  兩人撲克測試結果……………………………………48
第三節 雛形系統之研發………………………………………54


  第六章 多人德州撲克模型                59
第一節  策略矩陣修訂…………………………………………59
第二節 勝率計算修訂…………………………………………61
第三節  多人模式賽局之結構…………………………………64

  第七章 結論與未來發展                 66

附錄A 牌型分數對應表及說明                67
附錄B 公開牌取樣法與分別取樣平均法所有底牌牌型之
    勝率計算對照                    68

參考文獻                         69
[1] D. Billings, N. Burch, A. Davidson, R. Holte, J. Schaeffer, T. Schauenberg, D. Szafron, “Approximating Game-Theoretic Optimal Strategies for Full-scale Poker”, IJCAI, 2003, pp.661-668.
[2] D. Billings, D. Papp, J. Schaeffer, D. Szafron, “Opponent Modeling in Poker”, AAAI, 1998, pp.493-999.
[3] D. Billings, D. Papp, L. Peña, J. Schaeffer, D. Szafron, “Using Selective- Sampling Simulations in Poker”, AAAI Spring Symposium on Search Techniques for Problem Solving under Uncertainty and Incomplete Information, AAAI Press. Technical Report SS-99-06, 1999, pp. 13-18.
[4] D. Billings, L. Peña, J. Schaeffer, D. Szafron, “Using probabilistic knowledge and simulation to play poker”, AAAI, 1999, pp. 697-703.
[5] E. Borel, “La théorie du jeux et les équations intégrales à noyau symétriques”, C. R. Math. Acad. Sci. Paris, 1921, Vol.173, pp.1304-1308.
[6] E. Borel, “Le jeu de poker”, Applications aux Jeux des Hazard, Chapter 5, 1938.
[7] A.M Brandenburger, B. J. Nalebuff, “The Right Game: Use Game Theory to Shape Strategy,” Journal of Harvard Business Review, 1995, Vol.73, No.4, pp.57-71.
[8] T. S. Ferguson, Game Theory, Part II, Class notes for Math 167, Fall 2000.
[9] G. Kendall, M. Willdig, “An Investigation of an Adaptive Poker Player”, In Proc. 14th Australian J.Conf. Artificial Intelligence, Adelaide, Australia, 2001, pp.189-200.
[10] D. Koller, N. Megiddo, “The Complexity of Two-Person Zero-Sum Games in Extensive Form”, Games and Economic Behavior, 1992, Vol.4, pp.528-552.
[11] D. Koller, N. Megiddo, B. v. Stengel, “Efficient solutions of extensive two-person games”, Games and Economic Behavior, 1996, Vol.14, pp.247-259.
[12] D. Koller, N. Megiddo, B. v. Stengel, “Fast algorithms for finding randomized strategies in game trees”, In Proceedings of the 26th Annual ACM Symposium on the Theory of Computing, 1994, pp.750-759.
[13] D. Koller, A. Pfeffer, “Representations and solutions for game-theoretic problems”, Artificial Intelligence, 1997, Vol.94, No.1, pp.167-215.
[14] K. B. Korb, A. E. Nicholson, N. Jitnah, “Bayesian poker”, In proceedings of 15th Conference on Uncertainty in Articial Intelligence, 1999, pp. 343-350.
[15] H. W. Kuhn, “A simplified two-person poker”, Contributions to the Theory of Games I, Princeton University Press, 1950, pp.97-103.
[16] H. W. Kuhn, “Extensive games and the problem of information”, in Contributions to the Theory of games II, Princeton Univ. Press, 1953, pp.193-216.
[17] J. F. Nash, “Equilibrium points in N-person Games”, Proc. Nat. Acad. Sc. 36, 1950, pp.48-49.
[18] J. v. Neumann, “Zur Theorie der Gesellschaftsspiele”, Math. Ann., 1928, Vol.100, pp.295-320.
[19] J. v. Neumann, O. Morgenstern, The Theory of Games and Economic Behavior. Princeton University Press, 1944.
[20] J. -P. Ponssard, S. Sylvain, “The LP formulation of finite zero sum games with incomplete information”, International Journal of Game Theory, 1980, Vol. 9, pp. 99-105.
[21] M. Salim, P. Rohwer, “Poker Opponent Modeling”,
http://www.cs.indiana.edu/~msalim/research/
[22] Terence Conrad Schauenberg, “Opponent Modelling and Search in Poker”, M.Sc. thesis, 2006.
[23] D. Sklansky, “The Theory of Poker”, Two Plus Two Publishing, fourth edith, 1989.
[24] D. Sklansky, M. Malmuth, “Hold'Em Poker for Advanced Players”, Two Plus Two Publishing, 3rd edition, 1999.
[25] D. Snidal, “Game Theory of International Politics,” in Kenneth Oye, eds. Cooperation under Anarchy, 1986, pp. 25-57.
[26] F. Southey, M. Bowling, B. Larson, C. Piccione, N. Burch, D. Billings, C. Rayner, “Bayes' Bluff: Opponent Modelling in Poker”, in 21st Conference on Uncertainty in Artificial Intelligence (UAI-2005), 2005, pp.550-558.
[27] E. Zermelo, “Uber eine Anwendung der Mengenlehre auf die Theorie des Schachspiels”, In Proceedings of the Fifth InternationalCongress of Mathe- maticians II, Cambridge University Press, 1913, pp.501–504.
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