Starting Hands Probabilities for:

Seven-Card Stud and Seven-Card Stud High-Low Eight or Better (Stud-Eight) Poker

There are 22,100 combinations possible for 3 cards dealt from a 52-card deck. Because in the ranking of hands the rules of poker do not rank suits, 3Club, 4Club, 5Club, is not distinguishable from 3Diamond, 4Diamond, 5Diamond, and AClub, AHeart, 2Club is not distinguishable from AClub, ADiamond, 2Heart. After subtracting all duplicate hands the number of unique three-card starting hands is reduced to 1755. These starting cards can be sorted into six broad categories: suited-connected, trips, connected, suited, paired, and none of the above (unsuited, unconnected, unpaired). The table below lists the categories, along with descriptions and examples.

Description and Examples for Three-Card Starting Hands in Seven-Card Stud Poker
Starting Hand Description Example
Suited-Connected Three sequential cards of the same suit JDiamond QDiamond KDiamond
Trips Three cards of the same rank 8Club 8Diamond 8Heart
Connected Three sequential cards 6Club 7Diamond 8Spade
Suited Three cards of the same suit ASpade JSpade 3Spade
Pair Two cards of the same rank with a third card of a different rank 8Club 8Diamond 7Heart
Not connected, suited or paired Three cards not meeting any of the descriptions above 9Club 8Club 2Heart

The next table lists the number of unique hands possible for each category along with the number of three-card combinations that result in the hand. Also listed are the probabilities and odds for each category’s occurrence. The probabilities (or frequencies) are computed by dividing the number of combinations for each category by the total number of three-card combinations possible (22,100) and then multiplying by 100 to convert to a percentage. This table is true for Stud-Eight and high-only Seven-Card Stud.

Probabilities and odds for occurrence of starting hands in Seven-Card Stud
Starting Hand No. Possible No. Combinations Probability (%) Odds
Suited-Connected 12 48 0.22 459:1
Trips 13 52 0.24 424:1
Connected 48 720 3.26 30:1
Suited 274 1096 4.96 19:1
Pair 312 3744 16.94 4.9:1
Not connected, suited or paired 1096 16,440 74.39 1:3
Totals 1755 22,100 100

As a general rule starting cards in the last category are unplayable in both Stud-Eight and Seven-Card Stud. Notice that this category includes 75% of all hands dealt. Stud-Eight does have an exception to this general rule because an Ace unconnected to two other wheel cards (2, 3, 4, or 5) has value as a starting hand. However, only 20 of the 1096 hands in the last category meet that definition and these hands will only occur 1.36% of the time.

The most important decision a player makes is the choice of starting cards. Automatically folding the approximately 75% of hands in this un-connected, unsuited, unpaired category is a necessary discipline for success. The exceptions are when a bet has a reasonable chance of stealing antes or winning uncontested.