We present a method for encoding game logs as numeric features in the card game Dominion. We then run the manifold learning algorithm t-SNE on these encodings to visualize the landscape of player strategies. By quantifying game states as the relative prevalence of cards in a player's deck, we create visualizations that capture qualitative differences in player strategies. Different ways of deviating from the starting game state appear as different rays in the visualization, giving it an intuitive explanation. This is a promising new direction for understanding player strategies across games that vary in length.
Gold's paper proposed two specific models for predicting card buys: a trigram model based on two previous buys, and a naive Bayes model, based on all cards currently in the player's deck. The author notes that the natural follow-up experiment should be to determine whether EM can assign players to one model structure or other based on how well the models capture player behavior" @cite_0 . Thus Gold proposed clustering players on which factors inform their decision making.
@cite_0
2210286836 2139774323 1574482857 2099873701
Probabilistic models were fit to logs of player actions in the card game Dominion in an attempt to find evidence of personality types that could be used to classify player behavior as well as generate probabilistic bot behavior. Expectation Maximization seeded with players' self-assessments for their motivations was run for two different model types - Naive Bayes and a trigram model - to uncover three clusters each. For both model structures, most players were classified as belonging to a single large cluster that combined the goals of splashy plays, clever combos, and effective play, cross-cutting the original categories - a cautionary tale for research that assumes players can be classified into one category or another. However, subjects qualitatively report that the different model structures play very differently, with the Naive Bayes model more creatively combining cards. (This article originally appeared in Management Science, November 1967, Volume 14, Number 3, pp. 159-182, published by The Institute of Management Sciences.) The paper develops a new theory for the analysis of games with incomplete information where the players are uncertain about some important parameters of the game situation, such as the payoff functions, the strategies available to various players, the information other players have about the game, etc. However, each player has a subjective probability distribution over the alternative possibilities. In most of the paper it is assumed that these probability distributions entertained by the different players are mutually "consistent," in the sense that they can be regarded as conditional probability distributions derived from a certain "basic probability distribution" over the parameters unknown to the various players. But later the theory is extended also to cases where the different players' subjective probability distributions fail to satisfy this consistency assumption. In cases where the consistency assumption holds, the original game can be replaced by a game where nature first conducts a lottery in accordance with the basic probability distribution, and the outcome of this lottery will decide which particular subgame will be played, i.e., what the actual values of the relevant parameters will be in the game. Yet, each player will receive only partial information about the outcome of the lottery, and about the values of these parameters. However, every player will know the "basic probability distribution" governing the lottery. Thus, technically, the resulting game will be a game with complete information. It is called the Bayes-equivalent of the original game. Part I of the paper describes the basic model and discusses various intuitive interpretations for the latter. Part II shows that the Nash equilibrium points of the Bayes-equivalent game yield "Bayesian equilibrium points" for the original game. Finally, Part III considers the main properties of the "basic probability distribution." We present Open Trumps, a version of the popular card game Top Trumps with decks that are procedurally generated based on open data. The game is played among multiple players through drawing cards and selecting the feature that is most likely to trump the same feature on the other players’ cards. Players can generate their own decks through choosing a suitable dataset and setting certain attributes; the generator then generates a balanced and playable deck using evolutionary computation. In the example dataset, each card represents a country and the features represent such entities as GDP per capita, mortality rate or tomato production, but in principle any dataset organised as instances with numerical features could be used. We also report the results of an evaluation intended to investigate both player experience and the hypothesis that players learn about the data underlying the deck they play with, since understanding the data is key to playing well. The results show that players enjoy playing the game, are enthusiastic about its potential and answer questions related to decks they have played significantly better than questions related to decks they have not played. Unsupervised learning of linguistic structure is a difficult problem. A common approach is to define a generative model and maximize the probability of the hidden structure given the observed data. Typically, this is done using maximum-likelihood estimation (MLE) of the model parameters. We show using part-of-speech tagging that a fully Bayesian approach can greatly improve performance. Rather than estimating a single set of parameters, the Bayesian approach integrates over all possible parameter values. This difference ensures that the learned structure will have high probability over a range of possible parameters, and permits the use of priors favoring the sparse distributions that are typical of natural language. Our model has the structure of a standard trigram HMM, yet its accuracy is closer to that of a state-of-the-art discriminative model (Smith and Eisner, 2005), up to 14 percentage points better than MLE. We find improvements both when training from data alone, and using a tagging dictionary.