21,906 research outputs found
Optimal Play of the Dice Game Pig
The object of the jeopardy dice game Pig is to be the first player to reach 100 points. Each player\u27s turn consists of repeatedly rolling a die. After each roll, the player is faced with two choices: roll again, or hold (decline to roll again). If the player rolls a 1, the player scores nothing and it becomes the opponent\u27s turn. If the player rolls a number other than 1, the number is added to the player\u27s turn total and the player\u27s turn continues. If the player holds, the turn total, the sum of the rolls during the turn, is added to the player\u27s score, and it becomes the opponent\u27s turn.
For such a simple dice game, one might expect a simple optimal strategy, such as in Blackjack (e.g., stand on 17 under certain circumstances, etc.). As we shall see, this simple dice game yields a much more complex and intriguing optimal policy, described here for the first time. The reader should be familiar with basic concepts and notation of probability and linear algebra
Biasing MCTS with Features for General Games
This paper proposes using a linear function approximator, rather than a deep
neural network (DNN), to bias a Monte Carlo tree search (MCTS) player for
general games. This is unlikely to match the potential raw playing strength of
DNNs, but has advantages in terms of generality, interpretability and resources
(time and hardware) required for training. Features describing local patterns
are used as inputs. The features are formulated in such a way that they are
easily interpretable and applicable to a wide range of general games, and might
encode simple local strategies. We gradually create new features during the
same self-play training process used to learn feature weights. We evaluate the
playing strength of an MCTS player biased by learnt features against a standard
upper confidence bounds for trees (UCT) player in multiple different board
games, and demonstrate significantly improved playing strength in the majority
of them after a small number of self-play training games.Comment: Accepted at IEEE CEC 2019, Special Session on Games. Copyright of
final version held by IEE
A Versatile Stochastic Duel Game
This paper deals with a standard stochastic game model with a continuum of
states under the duel-type setup. It newly proposes a hybrid model of game
theory and the fluctuation process, which could be applied for various
practical decision making situations. The unique theoretical stochastic game
model is targeted to analyze a two-person duel-type game in the time domain.
The parameters for strategic decisions including the moments of crossings,
prior crossings, and the optimal number of iterations to get the highest
winning chance are obtained by the compact closed joint functional. This paper
also demonstrates the usage of a new time based stochastic game model by
analyzing a conventional duel game model in the distance domain and briefly
explains how to build strategies for an atypical business case to show how this
theoretical model works.Comment: This paper is the condensed version of the original paper titled "A
Versatile Stochastic Duel Game" which has been published in the Mathematic
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