Seven Card Stud: Probabilities
Examples of probability distribution in Seven Card Stud
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
Three of a kind vs. 1 pair of aces
High pair vs. Small pair
Middle pair vs. 3 flush cards
Small pair vs. 3 high cards
Middle pair vs. open-ended straight draw with 2 high cards
Fourth Street (percentages in brackets)
Three of a kind vs. 2 high pairs
Three of a kind vs. 4 card flush draw
Three of a kind vs. 4 card open-ended straight draw
2 low pairs vs. 1 high pair with 2 high kickers
Small pair (high kicker) vs. High pair (low kicker)
2 pairs vs. 4 card flush draw
2 pairs vs. 4 card open-ended straight draw
Small pair vs. 4 high cards