Probability of being dealt a 7-card flush in Rummy
What are the odds of being dealt all 7 cards in the same suit?


The odds of pulling 7 spades in 7 cards the number of ways to pull 7 spades (from among the 13 spades) divided by the number of ways to pull 7 cards (from among the 52 cards).

13c7 = 1716

52c7 = 133784560

1716 / 133784560 = 0.0000128 = 0.00128 %

For general suit (not just spades), multiply that by four:

= 0.0000513 = 0.00513 %

If you want to continue to the eighth card:

The odds of pulling 8 spades in 8 cards the number of ways to pull 8 spades (from 13) divided by the number of ways to pull 8 cards (from 52).

13c8 = 1287

52c8 = 752538150

1287 / 752538150 = 0.00000171 = 0.000171 %

And again multiply by four for general suit:

= 0.00000684 = 0.000684 %

(subtract the number of ways to get a straight if you want to exclude straights from "all cards in the same suit".)

Notation explanation:

13c8 is read as "13 choose 8" and means "the number of ways to choose 8 things from a set of 13 things". It is computed as 13!/((13-8)! * 8!).

In general, NcM = N! / ( (N-M)! * M! )