It's in the Dice

27 September 2022

By John Grochowski

QUESTION: Craps uses six-sided dice. So do most board familiar board games like Monopoly and Yahtzee, and some other casino games like sic bo and chuck-a-luck. My grandmother used to play bunco with six-sided dice.

But there are dice with different numbers of faces. Why do you suppose we settled on six sides and it's the others that seem weird? How do you think it would affect craps if 12 sides or some other numbers were used instead?

ANSWER: Six-sided dice are cubes and are easy to manufacture. Cutting extra faces requires more care and effort. Many such dice are essentially two pyramids fused at their bases. A 10-sided die is a five-faced pyramid attached at the base to another five-faced pyramid.

In craps. more faces would open more possibilities. The math on odds and payouts would have to be redone to reflect that.

With two six-sided dice, there are 36 possible rolls: one way each to make 2 or 12, two to make 3 or 11, three to make 4 or 10, four to make5 or 9, five to make 6 or 8 and six to make 7.

With two dodecahedrons -- 12-sided dice -- there would be 144 possible rolls, with the most common being the 12 ways to make 13.

With totals ranging from 2 to 24, there would be decisions to make on wagers to offer and their payoffs.

The rarest numbers with two six-sided dice are 2 and 12. A one-roll bet on 12 faces true odds of 35-1 and the common payoff is 30-1. Same with a bet on 2.
Use 12-sided dice, and the rare numbers are 2 and 24. True odds would be 143-1.

To get a house edge in line with the 13.89 percent on 2 or 12 with common dice, the payoff on 2 or 24 with 12 sides would have to be 123-1.

Would anyone make that bet when you'd win an average of only one bet per 144? There would need to be a trial time to see what flies with the public. Calculations and trials would need to be done for every potential bet.

That's all theoretical, of course. No one's likely to stray from six-sided dice anytime soon.

QUESTION: Video poker question. I was playing 8-5 Double Double Bonus Poker on a Ten Play machine and as dealt three Aces and two 9s. With the 8-for-1 payoff on full houses, that's 10 40-coin pays.

I know the strategy for the game says to discard the 9s and go for the Aces. But that risks getting only 10 three of a kinds for 150 coins. Am I wrong to hold the full house?

ANSWER: That's up to you and your tolerance for risk. Your average return if you hold the Aces and discard the 9s on 8-5 DDB is 63.27 coins per five wagered, or 633 coins on Ten Play. That dwarfs your 400 for keeping the full house.

There's a lot of variances. Sometimes you'll draw the fourth Ace for 800 coins on one hand, sometimes that Ace will come with a 2, 3 or 4 and kick the jackpot up to 2,000, and sometimes you'll draw the fourth Ace in more than one hand. Those create huge payoffs.

But as you know, you'll often be reduced to nothing but threes of a kind.

I would take the risk, confident that if I always play that way, sometimes I'll draw the big winners, and they'll more than balance the low-pay times. By the numbers, it's not a close call. But your tolerance for variance is up to you.