This thesis investigates the use of Bayesian analysis upon an opponent's behaviour in order to determine the desired goals or strategy used by a given adversary. A terrain analysis approach utilising the A* algorithm is investigated, where a probability distribution between discrete behaviours of an opponent relative to a set of possible goals is generated. The Bayesian analysis of agent behaviour accurately determines the intended goal of an opponent agent, even when the opponent's actions are altered randomly. The environment of Poker is introduced and abstracted for ease of analysis. Bayes' theorem is used to generate an effective opponent model, categorizing behaviour according to its similarity with known styles of opponent. The accuracy of Bayes' rule yields a notable improvement in the performance of an agent once an opponent's style is understood. A hybrid of the Bayesian style predictor and a neuroevolutionary approach is shown to lead to effective dynamic play, in comparison to agents that do not use an opponent model. The use of recurrence in evolved networks is also shown to improve the performance and generalizability of an agent in a multiplayer environment. These strategies are then employed in the full-scale environment of Texas Hold'em, where a betting round-based approach proves useful in determining and counteracting an opponent's play. It is shown that the use of opponent models, with the adaptive benefits of neuroevolution aid the performance of an agent, even when the behaviour of an opponent does not necessarily fit within the strict definitions of opponent 'style'.

This thesis investigates the use of Bayesian analysis upon an opponent¿s behaviour in order to determine the desired goals or strategy used by a given adversary. A terrain analysis approach utilising the A* algorithm is investigated, where a probability distribution between discrete behaviours of an opponent relative to a set of possible goals is generated. The Bayesian analysis of agent behaviour accurately determines the intended goal of an opponent agent, even when the opponent¿s actions are altered randomly. The environment of Poker is introduced and abstracted for ease of analysis. Bayes¿ theorem is used to generate an effective opponent model, categorizing behaviour according to its similarity with known styles of opponent. The accuracy of Bayes¿ rule yields a notable improvement in the performance of an agent once an opponent¿s style is understood. A hybrid of the Bayesian style predictor and a neuroevolutionary approach is shown to lead to effective dynamic play, in comparison to agents that do not use an opponent model. The use of recurrence in evolved networks is also shown to improve the performance and generalizability of an agent in a multiplayer environment. These strategies are then employed in the full-scale environment of Texas Hold¿em, where a betting round-based approach proves useful in determining and counteracting an opponent¿s play. It is shown that the use of opponent models, with the adaptive benefits of neuroevolution aid the performance of an agent, even when the behaviour of an opponent does not necessarily fit within the strict definitions of opponent ¿style¿. / Engineering and Physical Sciences Research Council (EPSRC)

General game playing is an area of artificial intelligence which focuses on creating agents capable of playing many games from some class. The agents receive the rules just before the match and therefore cannot be specialized for each game. Deepstack is the first artificial intelligence to beat professional human players in heads-up no-limit Texas hold'em poker. While it is specialized for poker, at its core is a general algorithm for playing two-player zero-sum games with imperfect information - continual resolving. In this thesis we introduce a general version of continual resolving and compare its performance against Online Outcome Sampling Monte Carlo Counterfactual Regret Minimization in several games.

Title: Solving Endgames in Large Imperfect-Information Games such as Poker Author: Bc. Karel Ha Department: Department of Applied Mathematics Supervisor: doc. Mgr. Milan Hladík, Ph.D., Department of Applied Mathematics Abstract: Endgames have a distinctive role for players. At the late stage of games, many aspects are finally clearly defined, deeming exhaustive analysis tractable. Specialised endgame handling is rewarding for games with perfect information (e.g., Chess databases pre-computed for entire classes of endings, or dividing Go board into separate independent subgames). An appealing idea would be to extend this approach to imperfect-information games such as the famous Poker: play the early parts of the game, and once the subgame becomes feasible, calculate an ending solution. However, the problem is much more complex for imperfect information. Subgames need to be generalized to account for information sets. Unfortunately, such a generalization cannot be solved straightaway, as it does not generally preserve optimality. As a consequence, we may end up with a far more exploitable strategy. There are currently three techniques to deal with this challenge: (a) disregard the problem entirely; (b) use a decomposition technique, which sadly retains only the same quality; (c) or formalize improvements of...