Distributed Cribbage Computation

A Distributed Computing Screen Saver

Overview

Cribbage is one of the oldest card games in existence. The game is played to a score of 121 points, and the score is tracked on a cribbage board. People who have played enough cribbage note that their optimal play changes depending on where they and their opponent are located on the board. This project generates information to improve play at different board positions.

Conditions

The Distributed Cribbage Computation Program calculates a value for each board position for several conditions. The expected pay-off for each board position is computed using game theory and Monte Carlo simulation. Four different conditions are examined:

Percent Chance of Winning
It is assumed that both players are playing to maximize the likelihood of winning.
Expected Number of Game Points
In tournaments and games using the American Cribbage Congress rules, the winner of the game gets 2 game points if the game did not end in a skunk, and 3 game points if the game did end in a skunk. The loser gets 0 game points. It is assumed that both players are playing to maximize the different between their game points and their opponent's game points.
Expected 1 and 2 Payoff
Many people bet on cribbage, where, if the game does not end in a skunk, the loser pays the winner one dollar. If the game ends in a skunk, the loser pays the winner two dollars. This is known as 1 and 2. It is assumed that both players are trying to maximize their earnings.
Spread Points
It is assumed that both players are trying to maximize the number of points by which they beat their opponent.

The Distributed Program

In Cribbage, a player can be at any of 121*121 different board positions. The player can be dealt any of 20,358,520 hands, while his opponent can have any of 9,366,819 hands (the player knows his opponent doesn't have any of the cards he holds). After considering his opponent's hand, there are any of 40 possible up-cards. The player can either be the dealer or the eldest hand, but this is incorporated into the way the board positions are specified. There are 4 different conditions that are being analyzed.

To deterministically compute the values for the board positions of cribbage, a total of 446,713,476,462,225,772,800 conditions would need to be analyzed. Using Monte Carlo techniques, a good approximation can be reached by analyzing only several billion cases. This would still take a few decades on a single computer, however.

By distributing the program, multiple computers can work on the problem at the same time. This reduces the total computation time to something manageable, such as a few years.

The method is discussed further on the details page. The results, as they are currently known, are shown on the results page, with full details on the page devoted to each specific condition.

Download

Please download the distributed cribbage computation and give your spare computer time to this process.