The Casinos Don't Offer New Games To Give Patrons a Break

31 May 2004

By Alan Krigman

Applying nebulous qualitative reasoning to precise quantitative quandaries sometimes yields correct conclusions. Often, not. The latter is usually the case in gambling. And this can be costly to players who think they don't have to do their homework.

An example involves a game generally called "crapless craps." In this dice variation, twos, threes, 11s, and 12s have no special roles during the come-out but become "points" if hit, to win or lose on subsequent throws. In regular craps, as every real or make-believe wiseguy knows, Pass bets win even money during the come-out on 11 and lose on two, three, or 12. In either version, sevens are also instant winners while fours, fives, sixes, eights, nines, and 10s are point numbers.

Many solid citizens believe the crapless rule favors players. They figure that sacrificing wins on 11s cancels the elimination of losses on threes since each of these results can occur two ways out of the 36 possible dice outcomes (1-2 and 2-1 for the three, 5-6 and 6-5 for the 11). This leaves the two and the 12,

which can each be formed one way out of the 36 (1-1 for the two, 6-6 for the 12). The two and 12 lose immediately in the standard game but still have a chance to win in the innovative format.

The "new" casino offerings of the past decade or so should raise a red flag about crapless craps. The bosses don't hire big-buck analysts to devise games that give smart players more of a break than they get using their brains. Rather, history shows their incentive to be to entice patrons with table games which seem serious yet are simple to learn, unintimidating, and have high house advantage. Crapless craps fails on simplicity and intimidation. And the notion that edge is lower than in the traditional implementation is readily dispelled by the numbers.

Since only the two, three, 11, and 12 differ in the versions, no other outcomes need be examined. Normally, on the come-out, of the 36 dice combinations, the 11 accounts for two wins and the others for four losses. In crapless craps, the three and 11 each can become points two ways out of 36. They win subsequently if the number repeats before the seven arises (two chances out of eight); they lose if the seven appears first (the other six out of eight). Likewise, in crapless craps, the two and 12 each have one way out of 36 to become points. They then win if the number

pops before the seven (one chance out of seven); they lose if the seven materializes first (the complementary six out of seven).

These results are shown in the accompanying table. The conclusion jumps out of the totals. Instead of two ways to win and four to lose out of 36 on these come-out rolls, the six possible outcomes give bettors on Pass 1.286 ways to soar and 4.714 to plummet.

Number of ways out of 36 that two, three, 11, and 12 can be resolved in conventional and crapless craps

conventional
win		lose
2	0	1
3	0	2
11	2	0
12	0	1
total	2	4

crapless
win	lose
1x(1/7)=0.143	1x(6/7)=0.857
2x(2/8)=0.500	2x(6/8)=1.500
2x(2/8)=0.500	2x(6/8)=1.500
1x(1/7)=0.143	2x(6/7)=0.857
1.286	4.714

To determine the impact on the edge in the game, subtract wins from losses for the two alternatives and divide the results by 36. This yields (4-2)/36 = 5.556 percent for the conventional game and (4.714-1.286)/36 = 9.522 percent for crapless craps. The offset between these two is 9.522 - 5.556 = 3.966 percent, which equals the additional house edge on Pass bets in the crapless game. This means that while a player who sticks to the tried and true pays the piper a theoretical commission just over $1.41 for

every $100 bet "flat" on Pass or come, the punter making the same wager at a crapless craps table donates upwards of $5.38.

Not that you can't earn good money on crapless craps. Or on any game with high house advantage. And, even the most astute gamblers can skulk home with empty fanny packs. So play with money you can afford to lose on games that suit your fancy. But don't con yourself into thinking you've uncovered a secret the casino bosses were trying to keep under wraps. For, as the cagey couplet cadger Sumner A Ingmark, cleverly cautioned:

Ask of yourself, "Why did they do it?"
Before you take the bait and rue it.