Collaborating Authors

BeeMo, a Monte Carlo Simulation Agent for Playing Parameterized Poker Squares

AAAI Conferences

We investigated Parameterized Poker Squares to approximate an optimal game playing agent. We organized our inquiry along three dimensions: partial hand representation, search algorithms, and partial hand utility learning. For each dimension we implemented and evaluated several designs, among which we selected the best strategies to use for BeeMo, our final product. BeeMo uses a parallel flat Monte-Carlo search. The search is guided by a heuristic based on hand patterns utilities, which are learned through an iterative improvement method involving Monte-Carlo simulations and optimized greedy search.

Approximating Poker Probabilities with Deep Learning Artificial Intelligence

Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate it. Monte Carlo simulation is an effective technique that can be used to approximate the probability that a player will win and/or tie a hand. However, without the use of a memory-intensive lookup table or a supercomputer, it becomes infeasible to run millions of times when training an agent with self-play. To combat the space-time tradeoff, we use deep learning to approximate the probabilities obtained from the Monte Carlo simulation with high accuracy. The learned model proves to be a lightweight alternative to Monte Carlo simulation, which ultimately allows us to use the probabilities as inputs during self-play efficiently. The source code and optimized neural network can be found at

Integrating Opponent Models with Monte-Carlo Tree Search in Poker

AAAI Conferences

In this paper we apply a Monte-Carlo Tree Search implementation that is boosted with domain knowledge to the game of poker. More specifically, we integrate an opponent model in the Monte-Carlo Tree Search algorithm to produce a strong poker playing program. Opponent models allow the search algorithm to focus on relevant parts of the game-tree. We use an opponent modelling approach that starts from a (learned) prior, i.e., general expectations about opponent behavior, and then learns a relational regression tree-function that adapts these priors to specific opponents. Our modelling approach can generate detailed game features or relations on-the-fly. Additionally, using a prior we can already make reasonable predictions even when limited experience is available for a particular player. We show that Monte-Carlo Tree Search with integrated opponent models performs well against state-of-the-art poker programs.

Learning and Using Hand Abstraction Values for Parameterized Poker Squares

AAAI Conferences

We describe the experimental development of an AI player that adapts to different point systems for Parameterized Poker Squares. After introducing the game and research competition challenge, we describe our static board evaluation utilizing learned evaluations of abstract partial Poker hands. Next, we evaluate various time management strategies and search algorithms. Finally, we show experimentally which of our design decisions most signicantly accounted for observed performance.