CS 427 Research Paper: Artificial Intelligence Applications to Texas Hold em Poker

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1 CS 427 Research Paper: Artificial Intelligence Applications to Texas Hold em Poker By: Introduction Attempting to build agents that simulate human players for games that rely on hidden information and are nondeterministic in nature is an active area in Artificial Intelligence research. Texas Hold em poker provides a context in which to study the effectiveness of various implementation techniques and theories because [t]he game of poker has been identified as a beneficial domain for current AI research because of the properties it possesses such as the need to deal with hidden information and stochasticity (Rubin and Watson 958). Texas Hold em poker is targeted specifically because it is a popular variant of the game and contains many human experts that are still able to outperform modern AI implementations. Attempting to solve complicated games like Texas Hold em is important for the field of artificial intelligence because successfully achieving high computer performance in a non-trivial game can be a stepping stone toward solving more challenging real-world problems (Rubin and Watson 958). Problem Complexity: The Complexity of Texas Hold em Poker Poker is a complex game because it is a game of imperfect information, where multiple competing agents must deal with probabilistic knowledge, risk assessment, and possible deception, not unlike decisions made in the real world (Billings et al. 201). Billings et al explains that one way to reduce the complexity of the game is to look at a subset of the game. A common method for simplifying the analysis of Texas Hold em is having only scenarios that involve two-players, since complexity normally increases exponentially for each player added. Nicolai and Hilderman explain what makes the game challenging by stating, the game is difficult for a computer agent to play well, as it has a very large state space, some information is hidden from the players, there is an element of chance due to the order in which the cards are dealt, and opponents often provide false information (125). Their approximation for the tree for Texas Hold em limit poker is about nodes, which is far too large to analyze completely (222). The state space is large because the deck contains 52 unique cards, each player has 2 cards facedown, and there are different rounds of betting per hand. A complete hand involves the flop, which is three cards dealt face up, the turn which is an additional card dealt face up, and the river which is the last card dealt face up. Each player must build the best standard 5-card poker hand with the community cards dealt on the flop, turn, and river and any number of their starting 2 cards. There is also a round of betting between each phase of cards being dealt. The complexity of the game is increased by betting as well, there are variable rounds of betting and these amounts may be fixed or not depending on whether it is a limit or no-limit game that is being played. For a no-limit game, betting complicates things dramatically, because for each round of betting there may be a bet of 0 (called a Check) to a bet of all 1

2 available chips that a player may have (called an All-In ) and any number in between. This means that for no limit games, an agent must be able to analyze the bet being made in addition to the board state. A way that this complexity is handled is by taking a subset of the game and determining strategies for these problem states instead of a general solution for the entire game of Texas Hold em. Miltersen and Sorensen consider in their study a limited Texas Hold em tournament where only heads-up play (2 players) is considered with a fixed small and big blind (1168). This allowed them to apply minimax with unique jam/fold actions to determine near-optimal play (1170). This near-optimal strategy only considers bets where the current posted bet is an all-in for one of the players, they explain the difference in calculating this by stating the reason computing optimal jam/fold strategies turns out to be feasible is that they make analysis of the post-flop game irrelevant, (1170). This is because the expected payoff is collapsed into a singular model that doesn t expand when considering additional betting rounds (1171). Stochastic Methods: How Randomness Affects the Game Texas Hold em Poker is a nondeterministic game, meaning that different outcomes are entirely possible given the same board states. It s something that must be considered when designing and implementing an agent. This is because some outcomes will be very unlikely, such as having a royal flush on the board and other events will be substantially more likely, such as having only a high card hand among the community cards. Although there are many events left to chance, it is possible to have some idea of how good a starting hand is, disregarding the other players hands which are unknown. A very good measurement (feature) of a player s hand before the community cards are shown or any of the opponents actions observed, is the strength of cards in one s possession. Equity Value (EV) of a hand provides a quality description of its strength. Each card pair is associated with a numerical value calculated from the sample of 115 million hands using data mining methods (Bosilj et al. 1629). With games where much of the information is unknown and left to chance, some methods emphasize the information that is known and making decisions based off of that. Bosilj et al go on to explain that as the game progresses, both human and mathematical factors play an equally important role in making decisions about the next move (1629). It has already been mentioned just how complex Texas Hold em poker is, but it is important to note that since the game is nondeterministic, it is also very computationally intensive to determine the probability of other players having certain hands. It must be considered what the probability of each player having a certain hand and the odds that they will fold a hand of that type. This overlaps with opponent modeling, but there is also a mathematical foundation for which hands are generally considered good. Teofilo and Reis mention that usually, the Hand Rank Evaluator takes a poker hand and maps it to a unique integer which is the score of the hand (2). They later go on to state that this normally involves calculating the relative value of a 2 card hand (Chen Formula), Hand Strength, Hand Potential, and Effective Hand Strength (2-3). Randomness and stochasticity must be considered when building high-performing artificial poker agents, given that the nature of the game stems from this analysis of chance. 2

3 Opponent Theory: Human Opponent Modeling Human opponent modeling is a very large research subject for many different Artificial Intelligence applications. Texas Hold em provides interesting insights into how one might model human players by defining traits of players and using various techniques that emulate the ways that humans themselves learn and adapt to uncertainty and changing levels of success and failure. These attempts are not always successful, and, as mentioned below, there are many challenges that have still not been solved. Difficulties and Traits of Human Opponent Models The difficulty of opponent modeling in Texas Hold em Poker comes from the fact that poker is a game of imperfect information and an optimal strategy for an opponent may often involve bluffing that is, betting like they have a better hand than they actually do. Onisawa and Takahashi underline the techniques in calculating relative hand strengths and how these can only be calculated using only probability information (2348). They also state that expected hand strengths change due to the stage of the game hands that are weaker in the beginning may end up being stronger, more playable hands toward the end of the game when there are fewer players in the game (2348). They also go into what makes human opponent modeling both difficult and exciting by explaining, [a]lthough bluff is a useful and an essential strategy in a poker game, it is difficult to incorporate this strategy in a computer poker game since bluff is a kind of strategy that deceives opponent players purposefully and should not be detected by them. In this sense the incorporation of bluff strategy in a playing system is one of exciting problems. Modeling a realistic opponent often involves modeling human opponents mistakes as well as their successes. There has been much effort in simulating different player s temperaments, Teofilo and Reis describe this as an aggressiveness factor. A player s aggression factor is equal to the ratio of the number of raises that player makes to the number of calls that same player makes (2). Depending on the implementation, there may be various other characteristics that players have. Rubin and Watson define something called the exploitability factor. This is defined as a measure that determines how well a poker agent can perform against unknown competition (961). Poker Agent Simulation Techniques Bosilj et al mention some of the methods used for constructing pokerbots, including expertly defined rules, Monte Carlo methods, Case-Based reasoning, and Machine Learning based on modeling of Bayesian networks ( ). It is apparent from this that poker is a very complex game and many different methods of artificial intelligence have been applied to the game to try and simulate a master player. A rule-based expert system is defined as a collection of if-then rules for various scenarios that are likely to occur (Rubin and Watson 961). This can be particularly useful if these scenarios are encountered, but as mentioned before, the inherent complexity of the game will make the number of states that can be encountered in a single game quite large. Luckily there have been many other attempts at player simulation using different methods. Since the state space of this problem is so large it may be necessary to implement many heuristics and evolve these over time, some researchers argue that [e]volutionary methods have been shown to find relatively good results in large state spaces, and neural networks have been shown to be able to find 3

4 solutions to non-linear search problems such as Poker (Nicolai and Hilderman 125). Nicolai and Hilderman used an evolutionary approach by allowing agents to be mutated and have successful traits be selected from multiple agents, who in turn are combined as parents and then these child agents are tested for their viability (126). They used the metric that reinforces learning as the ranking of particular agents during tournament play (127). They describe how tournament ranking is not the sole way that surviving agents are determined by their co-evolution approach where: Co-evolution uses multiple, genetically distinct populations in direct competition in an effort to increase the genetic diversity of the overall playing population. Competing populations play games against each other, but are evolved separately. In this way, agents that perform at a level that would be deemed poor at the global level may still survive within their respective population. Furthermore, as the generations progress, agents enter a so-called arms race, where each population orients itself towards evolving a strategy that can defeat opponents from the other population. As these opposing strategies meet and pass each other, the overall skill level of the entire population increases (127). In their suggestion where the work should progress from here, they suggest the possibility of using a strategy using an infinite pool of their best agents (called the hall of fame) with random natural selection (130). Conclusion After analyzing the complexity, stochasticity, and the various implementation methods of Texas Hold em poker agents it is safe to say that it is still provides a domain of Artificial Intelligence that is applicable to many other problems through the techniques and the analysis applied. The derivation of a single cohesive solution seems to be far from being actualized due to the inherent complexity of the game, but the given implementations offer various benefits and disadvantages to consider for varying application scenarios. This means that although many of these agents may fail to defeat the top players in the world, there is progress being made on the methods that may allow future, more powerful hardware to have a better chance at emulating and outperforming human players. There is a great deal of uncertainty whether or not artificial pokerbots will be able to match human players. Billings et al summarizes the differences in human players to their computer counterparts by saying: Human poker players are very good at understanding their opponent, often forming an accurate model based on a single data point (and occasionally before the first hand is dealt!). Programs may never be able to match the best players in this area, but they must at least try to reduce the gap, since they can clearly be superior in other aspects of the game (235). In many ways this represents Artificial Intelligence research as a whole, where there are inherent aspects of problems that humans excel at and computers have difficulty at and many scenarios where the opposite is true. 4

5 Bibliography Billings, D., Davidson, A., Schaeffer, J., & Szafron, D. (2002). The challenge of poker. Artificial Intelligence, 32, 12, Bosilj, P., Palasek, P., Popvic, B., & Stefic, D. (2011). Simulation of a texas hold'em poker player. MIPRO 2011, 11, Gilpin, A., Sandholm, T., & Sorensen, T. B. (2008). A heads-up no-limit texas hold em poker player: Discretized betting models and automatically generated equilibrium-finding programs. Carnegie Mellon University computer science periodical, Koller, D., & Pfeffer, A. (1997). Representations and solutions for game-theoretic problems. Artificial intelligence, 94, Miltersen, P. B., & Sorensen, T. B. (2007). Near-optimal strategy for a heads-up no-limit texas hold'em poker tournament. The sixth intl. joint conf. on autonomous agents and multi-agent systems, Nicolai, G., & Hilderman, R. J. (2009). No-limit texas hold em poker agents created with evolutionary neural networks IEEE symposium on computational intelligence and games, Onisawa, T., & Takahashi, C. (2004). Poker playing system considering opponent player's strategy. SICE annual conference in Sapporo, Rubin, J., & Watson, I. (2011). Computer poker: A review. Artificial intelligence, 175, 74, Teofilo, L., & Reis, L. (2010). Universidade do Porto, Portugal. PHD Dissertation

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