You Think You Know Craps? How about the Esoterra Version?

12 October 2005

By Alan Krigman

It's the 22nd century. You're vacationing at a casino resort on the planet Esoterra. And, while you're eager to try whatever exotic gambles the joint may offer, you'd feel more comfortable with a game having a familiar resonance. So, when you hear what appear to be the solid citizens bellied up to a rail in one pit hooting and hollering, you amble over and are pleasantly surprised to see them playing something oddly like craps.

Oddly like, but not identical to. You spot key differences. a) The dice aren't six-sided cubes with square faces, but four-sided pyramids with "equilateral" triangular faces (triangles with three sides of equal length). b) The layout is simplified. The only options are "boxes" for Place bets and areas for two distinct one-roll Field wagers. Further, the box numbers aren't 4, 5, 6, 8, 9, & 10 but 2, 3, 4, 6, 7, & 8. Moreover, the winning numbers in one Field are 2, 3, & 4, and in the other are 6, 7, & 8. There's accordingly no come-out roll or point; bettors bet and the shooter shoots. c) Place bets lose on a 5 rather than a 7.

You grab a brochure to check the payoffs. It tell you that all Place bets are booked in §5 (five glitzma) multiples and return the following: 2 & 8 pay 19-to-5, 3 & 7 pay 9-to-5, and 4 & 6 pay 6-to-5. Also, on the Low (High) Field, where you can bet in §1 increments, 2 or 3 (7 or 8) pay 1-to-1 and 4 (6) pays 2-to-1.

You want to know chances and edges before dropping hard-earned glitzmas on the layout. You're erudite enough to understand how these values are determined for craps, as played on Earth. And you're not afraid of a little arithmetic. So it makes sense to work them out for the Esoterra version. You therefore rush back to your posh suite, grab a pencil and paper, and start figuring.

Because the faces of the dice are numbered from one to four, you quickly jot down a chart that looks like the accompanying table. It gives the possible totals and the ways they can be formed.

Ways that various totals can be formed

from a pair of four-sided dice

total	combinations	ways
2	1-1	one
3	1-2, 2-1	two
4	1-3, 2-2, 3-1	three
5	1-4, 2-3, 3-2, 4-1	four
6	1-4, 2-3, 3-2, 4-1	three
7	3-4, 4-3	two
8	4-4	one

Your table confirms there are 4x4 or 16 ways the dice can land. A 5 is most likely total to occur, with four ways to be formed. You also see that 2 & 8 each have one way to result, 3 & 7 have two ways, and 4 & 6 have three ways. So the odds against winning on either 2 or 8 by having it appear before the 5, are 4-to-1 each. Likewise for 3 or 7, the odds are 4-to-2 (this reduces to 2-to-1) each. And for 4 or 6, they're 4-to-3 each. On the Low Field, the odds are 13-to-3 for either 2 or 3 and ditto for a 4; on the High Field, it's 13-to-3 for either 7 or 8 and the same for a 6.

Your prowess with the arithmetic you mastered in grade school is needed to get the edge for the various bets. Here's how. Multiply the bet times the ways to lose, subtract from this the payoff times the ways to win, then divide the difference by the bet times the total ways to reach a decision -- win or lose.

On 2 & 8 this is (§5x4 - §19x1)/(§5x5), which comes out to 1/25 or 4 percent. On 3 & 7 it's (§5x4 - §9x2)/(§5x6), which is 2/30 or 6.7 percent. And on 4 & 6 the edge is (§5x4 - §6x3)/(§5x7), which equals 2/35 or 5.7 percent. For the Low Field, per §1 bet, you have three ways to win §1 on 2 or 3, one way to win §2 on 4, and 10 ways to lose §1 on 5, 6, 7, or 8). So the edge is (§1x10 - §1x3 - §2x3)/§1x16 or 1/16, which equals 6.25 percent. The High Field yields the same edge using the mirror-image numbers.

You're now privy to a deep, dark secret the Esoterra casino bosses didn't want you to know: the edge on bets in this game is outrageous. Will you bypass it on principle? Or will you pursue the pleasure presumed by the poet, Sumner A Ingmark:

Though some things are wrong in many ways,
You'll probably do them anyways.