Mississippi Stud house edge
The headline cost of Mississippi Stud, and the arithmetic behind it. Both figures below come from the exact engine, and they cross-check against each other.
Short answer
With exact optimal play the house edge is 4.9149% per ante. Measured against every unit you actually wager, which averages about 3.4836 antes per hand, the edge is 1.4109% per unit, the figure often called the element of risk. The per-ante number is the one that describes what the game costs your bankroll.
Two ways to measure the same game
There are two honest ways to state the cost, and they answer different questions.
| Measure | Value | What it means |
|---|---|---|
| House edge per ante | 4.9149% | Average loss per hand, as a share of your opening ante. |
| Element of risk | 1.4109% | Average loss as a share of every unit you put at risk. |
| Average total wager | 3.4836 antes | How much you bet per hand on average, ante plus streets. |
The element of risk looks smaller because it divides the same loss across a larger denominator. It is useful for comparing games, but the per-ante figure is what you feel at the table, since the ante is the unit you choose.
Where the number comes from
The engine works backward from the showdown. For every four-card hand it averages the paytable result over all remaining fifth cards, which gives the exact value of that spot. It then steps back through the fifth, fourth, and third streets, at each point choosing the action, fold, 1x, or 3x, with the highest value. Averaging the value of the best first-street action over all 1,326 starting hands gives an expected result of 4.9149% lost per ante.
As a check, a separate forward pass replays those same optimal decisions across the full deck and reproduces the identical figure, and it confirms the average wager of about 3.4836 antes. The two methods agreeing to the last digit is how we know the strategy and the edge are exact rather than approximate.
How it compares
At 4.9149% per ante, Mississippi Stud costs more per hand than blackjack or Ultimate Texas Hold’em, and sits in the same range as many carnival poker games. The wide paytable, topped by the 500 to 1 royal, is what pays for those long-shot jackpots, and it is funded by the frequent small losses on weak hands.
Common questions
Is 4.91% the per-hand or per-bet figure?
Per ante, meaning per hand relative to your opening bet. The per-unit-wagered figure is 1.4109%, lower only because it spreads the same loss over a bigger base.
Can good strategy get the edge lower?
4.9149% already assumes perfect play. You cannot beat it, only match it. Every deviation raises the edge, so the goal is to avoid mistakes rather than to find a trick.
Why is the element of risk quoted so often?
Because Mississippi Stud lets you multiply your bet mid-hand, total action is much larger than the ante. The element of risk captures that, which is why it reads lower than the per-ante edge.