In trick-taking card games, a two-step process of state sampling and evaluation is widely used to approximate move values. While the evaluation component is vital, the accuracy of move value estimates is also fundamentally linked to how well the sampling distribution corresponds the true distribution. Despite this, recent work in trick-taking card game AI has mainly focused on improving evaluation algorithms with limited work on improving sampling. In this paper, we focus on the effect of sampling on the strength of a player and propose a novel method of sampling more realistic states given move history. In particular, we use predictions about locations of individual cards made by a deep neural network --- trained on data from human gameplay - in order to sample likely worlds for evaluation. This technique, used in conjunction with Perfect Information Monte Carlo (PIMC) search, provides a substantial increase in cardplay strength in the popular trick-taking card game of Skat.
Perfect Information Monte Carlo (PIMC) search @cite_10 has been successfully applied to popular trick-taking card games like Contract Bridge @cite_5 , Skat @cite_11 , Hearts and Spades @cite_3 . PIMC has been heavily criticized over the years, starting with Frank and Basin because it naively evades the imperfect information elements of the game tree. However, it has remained relevant because it is still among the state-of-the-art algorithms for these games. In the authors attempt to understand this success and conclude that for classes of games with certain properties, including trick-taking card games, PIMC will not suffer large losses in comparison to a game-theoretic solution.''
@cite_5 @cite_10 @cite_3 @cite_11
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Perfect information Monte Carlo (PIMC) search is the method of choice for constructing strong Al systems for trick-taking card games. PIMC search evaluates moves in imperfect information games by repeatedly sampling worlds based on state inference and estimating move values by solving the corresponding perfect information scenarios. PIMC search performs well in trick-taking card games despite the fact that it suffers from the strategy fusion problem, whereby the game's information set structure is ignored because moves are evaluated opportunistically in each world. In this paper we describe imperfect information Monte Carlo (IIMC) search, which aims at mitigating this problem by basing move evaluation on more realistic playout sequences rather than perfect information move values. We show that RecPIMC - a recursive IIMC search variant based on perfect information evaluation - performs considerably better than PIMC search in a large class of synthetic imperfect information games and the popular card game of Skat, for which PIMC search is the state-of-the-art cardplay algorithm. Perfect Information Monte Carlo (PIMC) search is a practical technique for playing imperfect information games that are too large to be optimally solved. Although PIMC search has been criticized in the past for its theoretical deficiencies, in practice it has often produced strong results in a variety of domains. In this paper, we set out to resolve this discrepancy. The contributions of the paper are twofold. First, we use synthetic game trees to identify game properties that result in strong or weak performance for PIMC search as compared to an optimal player. Second, we show how these properties can be detected in real games, and demonstrate that they do indeed appear to be good predictors of the strength of PIMC search. Thus, using the tools established in this paper, it should be possible to decide a priori whether PIMC search will be an effective approach to new and unexplored games. Monte Carlo tree search (MCTS) is an AI technique that has been successfully applied to many deterministic games of perfect information. This paper investigates the application of MCTS methods to games with hidden information and uncertainty. In particular, three new information set MCTS (ISMCTS) algorithms are presented which handle different sources of hidden information and uncertainty in games. Instead of searching minimax trees of game states, the ISMCTS algorithms search trees of information sets, more directly analyzing the true structure of the game. These algorithms are tested in three domains with different characteristics, and it is demonstrated that our new algorithms outperform existing approaches to handling hidden information and uncertainty in games. In this paper, we examine the use of Monte Carlo tree search (MCTS) for a variant of one of the most popular and profitable games in the world: the card game Magic: The Gathering (M:TG). The game tree for M:TG has a range of distinctive features, which we discuss here; it has incomplete information through the opponent's hidden cards and randomness through card drawing from a shuffled deck. We investigate a wide range of approaches that use determinization, where all hidden and random information is assumed known to all players, alongside MCTS. We consider a number of variations to the rollout strategy using a range of levels of sophistication and expert knowledge, and decaying reward to encourage play urgency. We examine the effect of utilizing various pruning strategies in order to increase the information gained from each determinization, alongside methods that increase the relevance of random choices. Additionally, we deconstruct the move generation procedure into a binary yes no decision tree and apply MCTS to this finer grained decision process. We compare our modifications to a basic MCTS approach for M:TG using fixed decks, and show that significant improvements in playing strength can be obtained.