Mississippi Stud Odds

Every number on this page was produced by enumerating the game rather than simulating it. There are 1,326 possible pairs of hole cards and 117,600 ordered ways the three community cards can follow, which is 155,937,600 deals in total, small enough to walk through every one of them. Nothing here is sampled, so nothing here has a margin of error.

The house edge, and the two numbers behind it

The 4.915% figure assumes the highest-value choice at every one of the three decisions. The chart most players carry (raise 3x with a pair, 1x with two points, and so on) comes to 4.929%, a gap of 0.014% of an ante per hand. That is a rounding error over a session, and it is why the chart is worth using: almost all the benefit of perfect play, from nine lines you can remember.

Why the ante is a misleading yardstick

Both of those percentages are quoted against the ante, and the ante is the smallest bet you make. By the time a hand is settled you have an average of 3.590 antes on the table: the ante itself, plus whatever you raised on 3rd, 4th and 5th Street. Measured against the money you actually put at risk, the edge is 1.373%, the figure usually called the element of risk.

At a $5 table that is an expected loss of 24.6 cents a hand on an average of $17.95 of action. Both figures are true and they answer different questions: use the ante figure to work out what a session costs, and the element of risk to compare Mississippi Stud with a game where you bet once and it is settled.

How often each hand turns up

The middle columns below are simply the five-card frequencies: your two hole cards and the three community cards are five cards off a fresh deck, so a royal flush arrives once in 649,740 deals whatever you do about it. The showdown column is different. Because you fold the worst starting hands, the deals that survive to the end are better than average, and every paying line gets more common.

Percentages are of all 155,937,600 deals and of the 87,949,056 that reach a showdown. The return column is for the published chart and sums to −0.049287 antes a hand, which is the 4.929% edge.

How often you fold

Folding is not a failure state in Mississippi Stud, it is most of the strategy. Under the chart you get out of 43.60% of hands, and the pattern of where you get out matters as much as the total.

• 31.07% are folded on 3rd Street, before you have raised anything. That costs one ante.
• 7.67% are folded on 4th Street, after a 1x raise. That costs two antes, every time.
• 4.85% are folded on 5th Street, one card from the end. That costs three antes, or five on the eight thousandths of one percent of hands that got there through a 3x raise.

That is not an accident. You raise 3x on 3rd Street only with a pair, and across all 155,937,600 deals the chart never folds a hand on 4th Street that raised 3x on 3rd. Once the maximum is out there, it stays out there.

Add it up and folding hands off the table costs 0.610 antes per hand dealt. The hands you do play through return +0.561 antes. The difference between those two figures is the whole house edge. That is worth sitting with for a moment: the game is very nearly even once you are in it, and almost all of what it takes from you is taken from hands you never played.

What a settled hand looks like

That losing figure includes every hand you folded, which is why it looks brutal. The push band does real work: a pair of 6s through 10s returns all your chips and lands on 10.18% of hands, which is why the game feels less punishing at the table than 73.77% suggests.

The swings are far bigger than the edge

One standard deviation of a single hand is 9.84 antes. At a $5 table that is about $49 of spread around an expected loss of 24.6 cents. The edge is a slow leak; the variance is the weather, and over a session you will notice only the weather.

Almost all of that spread comes from two lines you will hardly ever see. Variance is built out of squared results, and four of a kind supplies 29.3% of that total with the royal flush adding another 25.4%. More than half the variance in Mississippi Stud therefore sits in hands that turn up once in 4,165 and once in 649,740 deals. Everything you actually experience (the pairs, the two pairs, the folds) contributes the smaller half.

What actually moves the number

Three things change your odds in Mississippi Stud, and only three.

• Your decisions. Between perfect play and the chart there is 0.014% of an ante. Between the chart and guessing there is a great deal more: every hand you fold that should be raised, and every hand you raise 3x that should be 1x, costs real money. The first two cards are where most of it is decided.
• The pay table on the felt. Not every table pays the same. One line off the standard table can cost more than a full percentage point, see payouts and pay tables.
• Whether you take the side bet. The 3-Card Bonus is a separate wager with its own 2.1357% house edge, and per dollar staked it is a worse bet than the base game. That is covered in is the 3-Card Bonus worth it.

Nothing else does. There is no betting pattern, no seat, no shuffle and no streak that turns 4.915% into a positive number. What good play buys you is a slower, cheaper session with more hands in it, and that, if the point is to enjoy the game, is the thing worth buying.

The quickest way to get a feel for any of this is to play a few hundred hands at the free table, which will tell you the correct decision before you act and keep the running statistics for you.

How these numbers were produced

Everything on this page is a counted result, not an estimate, so it is worth stating exactly what was counted and how. Anyone who wants to check the figures should be able to reproduce them.

If you find a figure here that does not reconcile, it is worth telling us. These numbers are meant to be checkable, and one arithmetic inconsistency in a widely republished return table is already flagged in the pocket guide.