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, 3
, 4, 5, is not distinguishable from 3
, 4, 5, and A, A
, 2 is not distinguishable from A, A, 2. 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.
| Starting Hand | Description | Example |
|---|---|---|
| Suited-Connected | Three sequential cards of the same suit | J Q K |
| Trips | Three cards of the same rank | 8 8 8 |
| Connected | Three sequential cards | 6 7 8 |
| Suited | Three cards of the same suit | A J 3 |
| Pair | Two cards of the same rank with a third card of a different rank | 8 8 7 |
| Not connected, suited or paired | Three cards not meeting any of the descriptions above | 9 8 2 |
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.
| 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.