Introduction

Sleuth is a card game. There are 2 types of cards. The first type are the diamond playing cards. Each diamond card has 3 parameters: one of three possible colours(red, green, blue) and 1..4 diamonds and 1 of 3 diamond type. Each card is unique so in total there are 3*4*3 = 36 different diamond cards. But for our implementation we choose to use just colours(red, green, blue) and number of diamonds(1..3), so we we will have 3*3=9 different cards.

In the initial state of the game one random diamond card is removed from the deck and the other cards are evenly distributed between players. If it is the case that the cards cannot be evenly distributed the excess cards are shown to all players.

The goal of each player is to find out which card is hidden from the deck. The way to do that is to ask other players about the type of diamond cards they have. Questions are asked using question cards, from which each players gets 4 at the start of the game. There are a different kind of questions like for example “how many blue cards you have”. When a question card is played it is removed and a new question card is drawn from the stack. In the original game asking there are questions where the person being asked only shows the answer to the person asking the question. Since we only use public announcements in our implementation we presume that the person being asked the question will just show the cards to all the players.

Simplification

Because the purpose of this project is the understanding of a game from a epistemic logic point of view, we have simplified the game so it is straightforward to follow the logic.

We decided changing from 36 cards to 9 cards, due to the original game with 3 players will lead approximately (equation 1) to 6*10^(19) worlds in our Kripke model. This model also is too complex for a programming implementation and a regular computer will have problems to keep it in memory. So we decided to simplify the game in the way we explained above with only 9 cards(3 colours, and 1,2,3 diamond on the card) and 3 players. This simplified version of the game lead us to (equation 2) 22680 worlds in our Kripke model.

Due to this simplification now the cards only have 2 parameters instead of 3, and the different kind of questions are 2 instead of 3.