Next consider straight flushes in different suits. We have to multiply 39,015,600 by two, because either player can have the higher straight flush, so the chance of two straight flushes in the same suit is about 1 / 77,803,398. In the other 40 cases, the high straight hand can be filled with any two cards of the remaining 42, but the lower straight hand can be filled with only 41 cards (it cannot have the immediately higher suited card). In 20 of those, the card immediately above the high card of the lower straight is in the higher straight, so the remaining four cards can be any of the 42 remaining cards in the deck. So there are 4*(5+4+3+2+1) = 60 ways to pick two high cards in the same suit. If it's A there are 5 other possible straights in the suit (high card 5 to 9), K allows 4 and so on down to T allows 1. The high card of the higher straight can be anything from A to T.

First consider two straight flushes in the same suit. There are C(52,7) = 133,784,560 hands, so the chance for one player to get a straight flush is (4,324 + 37,260) / 133,784,560 or about 1 / 3,217.įor two players, it's a bit more complicated. So there are 36*C(46,2) = 37,260 non-royal straight flushes. If the high card is any of the 36 cards from 5 to K, the remaining two cards cannot include the next higher card of the suit, because we have already counted that straight flush under the higher card. So there are 4*C(47,2) = 4,324 royal flushes in seven card stud. If the high card is any of the four Aces, then the next four cards are determined (KQJT of the same suit), and the remaining two cards can be any of the other 47.

To do this, we label all straight flushes by the highest card (meaning the 5 in A2345).

The one trick to counting straights and straight flushes in seven card games is avoiding double-counting.

Straight flush high card