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
		Dealer's Discard
		A	2	3	4	5	6	7	8	9	10	J	Q	K
		1.096	1.793	1.846	2.357	0.472	0.957	1.117	1.003	0.722	0.693	0.714	0.882	1.034	A
A	0.406		1.290	3.556	1.657	0.473	0.890	1.008	0.886	0.869	0.634	0.655	0.829	0.984	2
2	1.835	0.377		1.204	1.755	0.679	0.784	0.705	0.817	0.827	0.608	0.626	0.804	0.952	3
3	1.556	0.474	0.249		0.962	1.115	0.582	0.788	0.694	0.635	0.606	0.645	0.800	0.946	4
4	0.794	1.214	0.737	0.208		0.862	1.174	0.858	0.558	0.526	1.432	1.630	1.802	1.897	5
5	0.227	0.241	0.149	0.119	0.030		1.089	2.339	2.253	2.299	0.508	0.382	0.408	0.524	6
6	1.202	1.156	1.192	0.527	0.092	0.198		1.381	3.712	1.794	0.536	0.429	0.502	0.639	7
7	1.692	1.511	1.070	1.210	0.103	0.886	0.314		1.270	2.245	1.075	0.429	0.462	0.533	8
8	1.743	1.583	1.276	1.005	0.194	1.452	0.575	0.508		1.070	1.574	0.942	0.466	0.512	9
9	1.573	1.533	1.357	1.016	0.234	0.667	1.922	1.529	0.452		0.864	1.976	1.348	0.783	10
10	1.564	1.393	1.203	1.061	0.128	1.254	1.551	1.054	0.858	0.300		0.844	2.500	1.811	J
J	1.245	1.091	1.007	0.914	0.111	0.795	0.867	1.085	0.874	1.163	0.234		0.954	1.799	Q
Q	1.887	1.742	1.589	1.348	0.125	1.295	1.546	1.685	1.896	2.232	1.355	0.427		1.057	K
K	2.241	2.115	1.907	1.604	0.127	1.660	2.040	2.149	2.084	3.253	1.780	3.275	0.501
	A	2	3	4	5	6	7	8	9	10	J	Q	K
	Eldest Hand's Discard

6987132 random samples were used to compute this table. Because a Monte Carlo method was used, these values are not exact.

Note that this table is the expected probability of any given crib throw. The upper-righthand part of the table is for the dealer, while the lower-lefthand part is for the eldest hand (non-dealer). Since you know what is in your hand, the odds of your opponent are different than those listed here.

Also, on average, the dealer will score 4.727 points more than the other player because of the crib.

If you have any questions or suggestions for other statistical analyses, please email me.