Mississippi Stud odds and probabilities
These figures are exact, not simulated. The engine enumerates all 2,598,960 possible five-card hands and every optimal decision, so the counts below are counts, not estimates.
Short answer
At showdown you make a paying hand (a pair of Jacks or better, up through a royal flush) about 33.6% of the time, push with a medium pair about 16.3% of the time, and lose the rest. Under optimal play you fold roughly 31.07% of hands on the first street, so you only carry a fraction of deals to the end.
Five-card hand frequencies
Every possible five-card hand, counted once. Probabilities are out of 2,598,960 combinations.
| Final hand | Combinations | Probability | About 1 in |
|---|---|---|---|
| Royal flush | 4 | 0.00015% | 649,740 |
| Straight flush | 36 | 0.00139% | 72,193 |
| Four of a kind | 624 | 0.02401% | 4,165 |
| Full house | 3,744 | 0.14406% | 694 |
| Flush | 5,108 | 0.19654% | 509 |
| Straight | 10,200 | 0.39246% | 255 |
| Three of a kind | 54,912 | 2.11285% | 47 |
| Two pair | 123,552 | 4.75390% | 21 |
| Pair, Jacks or better | 337,920 | 13.00212% | 7.7 |
| Pair, 6s through 10s | 422,400 | 16.25265% | 6.2 |
| Pair, 2s through 5s | 337,920 | 13.00212% | 7.7 |
| Less than a pair | 1,302,540 | 50.11774% | 2.0 |
Add the paying rows, pair of Jacks or better and up, and you reach about 33.6%. The push band, pairs of 6s through 10s, adds another 16.3%. Everything below that loses, which is why folding weak starts early is the backbone of the strategy.
How often optimal play folds
Because you fold weak hands before betting more, most deals end early. Across all starting hands, optimal play resolves like this:
| Outcome of the hand | Probability |
|---|---|
| Fold on 3rd street | 31.07% |
| Fold on 4th street | 7.67% |
| Fold on 5th street | 15.48% |
| Reach showdown | 45.78% |
First-street decision mix
Of the 1,326 possible two-card starts, optimal play splits them as follows:
| First-street action | Share of starting hands |
|---|---|
| Fold | 31.07% |
| Bet 1x | 63.05% |
| Bet 3x | 5.88% |
The 3x share is small because it is exactly the pocket pairs, 78 of the 1,326 starts. Everything else is a 1x bet or a fold.
Common questions
Are these numbers exact or simulated?
Exact. They come from a full enumeration of the 52-card deck, not a Monte Carlo sample, so they do not change from run to run.
How often do I make a flush or better?
About 0.36% of showdowns are a flush or stronger. Straights and trips are far more common and do more of the heavy lifting on the paytable.
Why do I fold so many hands?
More than half of all five-card hands finish below a pair. Folding weak two-card starts keeps you out of the deals most likely to end in a loss.