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# Are alternate place bets at craps as different as they seem?

24 May 2010

Craps offers a veritable smorgasbord of alternate bets. The wealth of wagers from which players can pick is both a strength and a weakness. Strength because of the ways bettors can tailor the action to suit their personal preferences. Weakness because the diversity of features can make comparisons confusing.

For the majority of solid citizens, though, the essence of the game is remarkably consistent. It involves money dropped on the Pass line prior to the come-out roll, usually backed-up by some Odds factor after a point is established, and one or more Place bets on specific numbers during the point roll phase of a hand.

Within this general style, flexibility remains as to the numbers on which to make the Place bets. The most obvious differences among the options are the bet sizes needed and the associated payoffs. Six and eight call for \$6 multiples and pay 7-to-6. Five and nine take \$5 multiples and pay 7-to-5. And four and 10 require \$5 multiples and pay 9-to-5. Somewhat less evident are chances of winning (and the corresponding odds to be overcome): five out of 11 (6-to-5) for six and eight, four out of 10 (6-to-4) for five and nine, and three out of nine (6-to-3) for four and 10. Yet more obscure is the frequency at which the bets are resolved: on the average, out of 36 throws, six or eight should win or lose 11 times, five or nine 10 times, and four or 10 nine times. Then, too, there's the edge: 1.5 percent for six or eight, 4.0 percent for five or nine, and 6.7 percent for four or 10.

If any of these characteristics clinch one bet or another for you, don't let a little arithmetic stop you. But enquiring minds want to know whether there's a yardstick that allows the choices to be compared on some kind of rational uniform footing.

Reducing each of the bets to its "even money" equivalent provides one such gauge. An even-money equivalent is a theoretical proposition having two parts – an amount at risk and the chance of a 1-to-1 payoff – with the same edge and volatility as an actual wager. The amount and chance, respectively, suggest the magnitude and directional bias of the impact on bankroll.

Consonant with common craps analyses, the even-money equivalents of the various Place bets can be determined by ignoring what are essentially pushes – rolls on which neither the number nor a seven pops and the wagers are not resolved. The figures differ when the expected frequen-cies of resolution are considered. That is, when edge and volatility are based not only on throws when wins or losses occur, but those when no money is exchanged after the dice come to rest. Including no-action tosses in the calculations is rarely done; however, it yields more meaningful comparisons because it anticipates outcomes over time rather than on individual bets won or lost at differing rates. The even-money equivalents for both cases are shown in the accompanying table.

```
Even-money equivalents of basic Place bets at Craps

Number	  actual    even-money    even-money
bet        amount    probability
wagered    of winning
Ignoring no-action throws
6or8	   \$6.00	\$6.47       49.88%
5or9	   \$5.00	\$5.88       49.66%
4or10	   \$5.00	\$6.61       49.50%

Including no-action throws
6or8	   \$6.00	\$3.58       49.94%
5or9	   \$5.00	\$3.10       49.82%
4or10	   \$5.00	\$3.30       49.75%
```

Here's an example of interpreting the data. When all throws of the dice are considered, bets on eight projected to win \$7 five throws out of 36 and lose \$6 six throws out of 36 are equivalent to \$3.58 wagers with 49.94 percent chance of paying \$3.58 and the complementary 50.06 percent of losing \$3.58 on every throw.

Know-it-alls may say that distinctions among Place bets are fatuous because Come bets are superior to any of them. Analogous reasoning would have it that labeling junk food with saturated fat content is senseless because the munching public should eat carrot chips instead. But junk food will rule anyway, so people can benefit by learning to select the best of the lot. Still, as the moralizing muse, Sumner A Ingmark, reminded the resolute:

When you have an idea you want to hold fast to,
Certain folks may have doubts, but you'll be the last to.