House edge and element of risk

19 April 2018

By John Grochowski

QUESTION: I was going through the page on Mississippi Stud Poker at wizardofodds.com and got to the part on the house edge, and it lists a house edge of 4.91% and an element of risk of 1.37%.

Can you explain what that means? A 4.91% house edge seems to say this is a pretty bad game, almost as bad as the 5.26% on roulette. But that 1.37% compares more to the good games like baccarat, if element of risk is anything like house edge.

Is this a good game or a bad game?

ANSWER: I'd put Mississippi Stud on the pretty good games list.

The house edge tells you that on average, the house expects to keep 4.91% of your ante. If you begin with a $5 ante, the house expects to profit by about 24.55 cents per hand.

But your wagering doesn't stop at the ante. Using optimal strategy, additional bets will take the total wager up to an average of 3.59 times your ante per hand.

You won't bet that much on every hand. Sometimes you'll have poor cards and not make any bets beyond the ante. Sometimes you'll have good cards from the beginning and make the maximum bets of three times the ante at all three opportunities. On those sure winners, your total wager will rise to 10x the ante.

Over long-term play, that will average out to 3.59 times your ante. The average total wager with a $5 ante will be $17.95. But your average loss is still 24.6 cents, the amount already figured into the listed house edge.

So a second figure is needed to show you what to expect from your total risk. To do that, Shackleford divides the 4.91% house edge by the 3.59 average betting units, and gets an element of risk of 1.37%.

I generally use the same numbers, but with slightly different terminology — house edge on the ante and house edge on total action.

So if you start with a $5 ante on Mississippi Stud, you have an average total bet of $17.95 and an average loss of 24.6 cents.

If you play double-zero roulette, you don't have the same ante/bet procedure, and betting in nickel denominations, but let's use a $17.95 wager for a comparison. With a 5.26% house edge, your average loss would be 94.4 cents.

The house edge on Mississippi Stud, based on the ante, looks similar to double-zero roulette. But the element of risk/house edge on total action tells us you have a better shot to win at Mississippi Stud, where for the amount you can really expect to wager, average losses are much lower than on roulette.


QUESTION: Have you ever played in a casino that offered five-card Charlies? I ask because somebody called for blackjack in a home poker game — we let him deal five hands, no more — and he insisted Charlies were played in Vegas.

ANSWER: Five-card Charlies, where players win when five cards total 21 or less, are rare in casinos. I've played blackjack in dozens of different casinos, and never encountered one that paid off on Charlies.

That said, if a dealer is going to offer Charlies in a home game, take him up on it. I'd object to a game with a dealer edge being allowed in a home game, but five-card Charlies favor players by 1.45%. Depending on the other rules of your game, it might swing the edge to the player side of the table.