In this project we set out to analyze an adapted version of the Thirty-One game where checking your hand instantly ends the game. We used a BDI (Belief-Desire-Intention) logic to model the game for multiple players playing the game. We analyzed the actions a player can make within the game by categorizing them in groups. For each group we analyzed which strategies they could have based on the action the player took. In most cases a single action was not enough to conclude a conclusive strategy for a player. Based on several of these action over the course of the game the players are able to reason about the true intention of the player based on combination of the set of possible strategies from each individual action.
To simulate the game we made a program, using Java language, that demonstrates how players' Knowledge and Intention update given different actions. Once the number of players (between 2 and 7) is selected the match begins. At every stage of the game , you can see the knowledge of all players, the current state of the game, player's knowledge of other's intention and the game log. You can choose to make a move for specific player or follow the game routine by clicking on "Next Move" button that automatically updates player turn. At each round a player would decide on what is the best action to take (deciding its intention) and takes an action (swaps a card with widow) accordingly.
From experimentation with the program we can make some conclusions about the game. Firstly most games are too short and have only a small amount of knowledge to go on. For example, someone going for a Three of a Kind will likely start with one of the cards in his hand. This means it will never enter the widow and become public knowledge. In practice there are barely any situations where blocking comes into account, which is the strategy that relies on knowledge of player intentions.
For future work it might be interesting to look at strategies which more aggressively try to hinder their opponents. Trying to hinder other even if you are not sure what their true intention is to force them to make sub-optimal moves. Using this strategy against the strategy we used in different amount of players might result in big differences in win percentages.