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# Taking or laying Odds at craps lowers the edge, but does it really pay?

17 September 2012

Pass and Come or Don’t Pass and Don’t Come are two-stage craps wagers. When a two, three, seven, 11, or 12 pops on the initial or “come-out” roll, these bets are resolved immediately. If a four, five, six, eight, nine, or 10 shows, the number becomes the “point” for subsequent rolls. The bet then wins if the shooter repeats the point and loses if a seven appears. Players can bet on these propositions “flat,” dropping their dough on the line and waiting for a result. They can also augment flat bets during the point phase of the roll with auxiliary wagers called “Free Odds” or, more simply, “Odds.” Flat bets give the joints 1.414 percent edge on Pass and Come, a bit less on Don’t Pass and Don’t Come. These are low values, but players can cut them further using Odds.

Here’s why. The payoff on the Odds exactly equals the chance against winning. During the second phase of the roll with points of four or 10, the bets have six ways to lose and three to win so they’re 6-to-3 (2-to-1) shots and the Odds pay 2-to-1. Likewise, fives and nines are 6-to-4 (3-to-2) propositions and the Odds pay 3-to-1. And sixes and eights miss six ways and hit five so they’re 6-to-5 affairs and the Odds pay 6-to-5. With no offset between chance and payoff on the Odds, the casino has no edge. Its“take” on the combined bet is therefore the same as on the flat part alone. For example, say someone starts with \$10 on Pass then adds \$30 in Odds. The bosses’ theoretical earnings stay at 1.414 percent of \$10 – \$0.14 – even though \$40 is in action for part of the roll. Were the \$40 to be bet flat, the house’s take would be 1.414 percent of \$40 or \$0.56. The allowable amount of Odds is expressed as a multiple of the flat bet. For instance, 3X odds means \$30 can be added to a \$10 flat bet, 5X permits \$50 to be added, and so forth.

The monetary equivalent of the edge is the critical factor. However, for comparison purposes, it’s useful to express edge for different Odds multiples as percentages. The usual calculation involves dividing the dollar equivalent of the edge for the flat bet alone by the sum of the flat bet plus (24/36) times the amount of the Odds. This, because the flat portion is in play throughout the coup while the Odds apply only during the average of 24 out of every 36 come-outs that yield points. The nearby table gives percent edge determined in this manner on Pass or Come bets for Odds multiples from zero through 10. As an illustration of using the data, the table shows that with \$50 flat, edge is 1.414 percent edge; betting \$10 flat and \$40 Odds, it’s 0.386 percent.

Effect of Odds on Pass and Come bets

```Odds multiple   edge
0        -1.414%
1        -0.848%
2	       -0.606%
3	       -0.471%
4	       -0.386%
5	       -0.326%
6	       -0.283%
7	       -0.250%
8	       -0.223%
9	       -0.202%
10	       -0.184%
```

In deciding whether to bet the Odds, solid citizens with given totals they’re comfortable risking on single propositions might wonder whether edge should really be the governing element. That is, are there criteria under which it’s preferable to wager it all flat rather than follow conventional wisdom and apportion the minimum possible flat and the maximum as Odds?

Since Ferrari dealers take coin of the realm and not percentages, players may prefer to consider the probabilities of winning and losing various amounts. With \$50 flat, chances are 49.29 and 50.71 percent of winning and losing \$50 per coup, respectively. With \$10 flat and \$40 Odds, overall probabilities are still 49.29 and 50.51 percent. Chances associated with various amounts are not uniform, however. On the win side, they’re 22.22 percent of \$10 (on the come-out), 5.56 percent of \$90 (point is four or 10), 8.89 percent of \$70 (point is five or nine), and 12.63 percent of \$58 (point is six or eight); average win is \$42.13. On the loss side, they’re 11.11 percent of \$10 (on the come-out) and 39.60 percent of \$50 (any point); average loss is \$41.23.

Yet another comparison can be made by folks whose goals are successful casino visits. Say your gambling budget is \$500. Betting \$50 flat, chances would be 43 percent chance of doubling and 24 percent of tripling your stake before going bust, regardless of how many rounds are needed. Betting \$10 flat with \$40 Odds, you have 47 percent chance of doubling and 30 percent of tripling your bankroll. Were your primary interest in time bellied up to the rail to keep trying for big bucks, the \$50 flat would give you 64 percent chance of still being in the game after 100 and 45 percent after 200 coups. Betting \$10 flat and \$40 Odds, your likelihood of still being in the game would increase to 72 percent after 100 and 54 percent after 200 decisions.

So, why do so many self-proclaimed craps experts bet more than the table minimum flat and less than the maximum allowable as Odds? When asked, the rhymster, Sumner A Ingmark, replied:

A leopard will sooner change his spots,
Than gamblers the way they take their shots.