# Carte Primus

## Cribbage Statistics

The stars, I see, will kiss the valleys first. The odds for high and low's alike.

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More statistics are available. See the Distributed Cribbage Computation project.

The following question was posed in the newsgroup rec.games.playing-cards: Does anyone have a statistical analysis of crib tosses in the 2-player game? The following table answers this question.

In order to calculate the probability of any given crib toss, I have assumed that the player's are logical. Game theory is used to determine the strategy of each player, which may either be a mixed or pure strategy. The dealer and the eldest hand (the non-dealer) are both trying to maximize their points.

There are many possible combinations of hands (1.9e14), each of which could have any of 40 turn-up cards. This number is too big to calculate every possible outcome. As such, a Monte Carlo method is used to determine the odds. This picks two hands random, determines the average pay-off (score) for each possible crib throw, and then determines the logical strategy for each player. The results are shown below:

Percent Chance of Cribbage Discard, 2 Player Game
A2345678910JQK
1.0961.7931.8462.3570.4720.9571.1171.0030.7220.6930.7140.8821.034A
A0.4061.2903.5561.6570.4730.8901.0080.8860.8690.6340.6550.8290.9842
21.8350.3771.2041.7550.6790.7840.7050.8170.8270.6080.6260.8040.9523
31.5560.4740.2490.9621.1150.5820.7880.6940.6350.6060.6450.8000.9464
40.7941.2140.7370.2080.8621.1740.8580.5580.5261.4321.6301.8021.8975
50.2270.2410.1490.1190.0301.0892.3392.2532.2990.5080.3820.4080.5246
61.2021.1561.1920.5270.0920.1981.3813.7121.7940.5360.4290.5020.6397
71.6921.5111.0701.2100.1030.8860.3141.2702.2451.0750.4290.4620.5338
81.7431.5831.2761.0050.1941.4520.5750.5081.0701.5740.9420.4660.5129
91.5731.5331.3571.0160.2340.6671.9221.5290.4520.8641.9761.3480.78310
101.5641.3931.2031.0610.1281.2541.5511.0540.8580.3000.8442.5001.811J
J1.2451.0911.0070.9140.1110.7950.8671.0850.8741.1630.2340.9541.799Q
Q1.8871.7421.5891.3480.1251.2951.5461.6851.8962.2321.3550.4271.057K
K2.2412.1151.9071.6040.1271.6602.0402.1492.0843.2531.7803.2750.501
A2345678910JQK