Seven Card Stud: Probabilities

Examples of probability distribution in Seven Card Stud

Preliminary remark

The probabilities of winning the hands listed below have not been calculated using a mathematical formula but in each case result from the simulation of 500,000 hands with a showdown after Seventh Street. Of course, in Seven Card Stud there is also a point in always knowing one's outs as precisely as possible. But we mustn't forget that knowing the outs as a variable for calculating the odds in Stud is of much less importance than in Texas Hold'em or other flop games. 

A board with community cards always provides an absolute value for calculating the probability of winning. For example, if there is no pair on the board, no player can have a full house.

By contrast, in Seven Card Stud everyone plays his or her individual hand consisting of seven cards. Even if there is no pair among the four open cards, a player may have four of a kind after Seventh Street. If two cards of a possible royal flush are open in front of a player, that player may theoretically have made it if none of the other cards needed for the royal flush is among the rest of the upcards of the other players. In this respect, the stated probabilities can only offer some aid to orientation. Basing our game strategy mainly on calculating the odds, as in flop games, is the wrong approach in Seven Card Stud.

However, it can be useful to develop a sense for the probabilities, so here are a few classic situations.

Starting hand selection (percentages in brackets)

Three of a kind         vs.            3 card straight flush
  (76)                           (24)

Three of a kind         vs.             1 pair of aces
  (84)                            (16)

High pair                   vs.             Small pair 
  (63)                           (37)

Middle pair                vs.             3 flush cards
(55)                             (45)

Small pair                   vs.              3 high cards
(58)                             (42)

Middle pair               vs.              open-ended straight draw with 2 high cards
(52)                             (48)

Fourth Street (percentages in brackets)

Three of a kind                 vs.          2 high pairs

(75)                          (25)

Three of a kind              vs.             4 card flush draw
(62)                          (38)

Three of a kind              vs.             4 card open-ended straight draw
(68)                          (32)

2 low pairs                    vs.              1 high pair with 2 high kickers
(56)                          (44)

Small pair (high kicker)   vs.             High pair (low kicker)
(44)                         (56)

2 pairs                            vs.            4 card flush draw
(55)                         (45)

2 pairs                            vs.           4 card open-ended straight draw
(54)                         (46)

Small pair                        vs.           4 high cards
(59)                         (41)