Math rules for video poker and craps

24 May 2018

By John Grochowski

QUESTION: I have a question about a multi-hand game that I play at times. (I usually play nickels Triple Play.)

The cost is the typical five per hand plus five more coins for the wheel feature. If in the first five cards you are dealt a hand that includes three of a kind — including four of a kind or full houses — a wheel at the top of the game spins. Various possible starting hands come up on the wheel and you play out the bonus.

An example of this was that my bonus hand was a draw to a Five Play hand with three aces dealt. You got paid based on the result. In this case one of the hands caught the fourth ace and I was paid 4,000 coins ($200 in a nickel). About a year ago on the same machine my bonus hand was four to a royal, and I caught one royal for 4,000 coins.

Is there anything mathematical that says "Good game to play" or "Bad game to play"?

ANSWER: The game you describe is Wheel Poker Deluxe. There is an earlier game called Wheel Poker, which required an extra bet of only one coin per hand instead of the extra five coins on Deluxe. The wheel on the earlier game had flat credit awards, instead of the possible starter hands on Deluxe.

IGT, the game manufacturer, designs its extra-pay video poker features with paybacks that are at least as high as the base game. If you're playing 8/5 Bonus Poker, with a 99.2% return with expert play, then your additional wager to activate a feature will also bring a return of 99.2% or better.

In the case of Wheel Poker Deluxe, Michael Shackleford of wizardofodds.com calculated the wheel bonus returns 100.9%. The effect is that the wheel raises the overall payback percentage of the game.

If you were to find Bonus Poker with an 8/5 pay table on Wheel Poker Deluxe, the wheel would raise the payback percentage from 99.2% with expert play to 99.9%. At a 7/5 pay table, Bonus Poker would become a 98.7% game instead of 98.0, and at 6/5, it would be 97.8 instead of 96.8.

It works the same way with other games. The overall payback is a little higher with the wheel than without it.

Because the wheel doesn't spin unless you get the strong starting hands, Wheel Poker Deluxe increases volatility. You can win big when the good starts come, but the extra bets mean you lose fast when you don't get the spinners.


QUESTION: You can take down most craps bets if you have to leave, but not pass or come. I'm told that's because of the house edge. What would you have to change to let players take down the bets?

ANSWER: Players have the edge on the comeout, where there are eight ways to win (six ways to make 7, two ways to make 11) and only four ways to lose (two ways to make 4, one each to make 2 and 12). If you let players take down their bets after the comeout, they'd always be playing with an edge. The house, which isn't in business to give money away, can't permit that.

If someone really wanted to allow pass players to take down bets after the comeout, the easiest solution without disrupting odds for other players would be to charge a commission for taking down those bets so the house would still get its edge. I don't see any great demand for such a move.