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# What is so great about taking or laying Odds at craps?

9 April 2012

Pass, Come, Don’t Pass, or Don’t Come bets at craps pay flat – even money – for wagers made at the start of the come-out roll. This, whether the win is on the come-out or, subsequently, on the point. The house has 1.4 percent edge on these wagers. That is, the bosses figure you for a 1.4 percent theoretical commission – for instance \$0.07 – for every \$5 they book.

The reason the commission is theoretical is that you don’t pay it directly. Combined, the come-out and point phases of a bet on Pass or Come have 976 chances out of 1,980 to win and 1,004 out of 1,980 to lose. The house accordingly expects to finish 1,980 bets an average of 1,004 - 976 = 28 ahead, and 28/1,980 is 1.4 percent. Don’t Pass and Don’t Come statistics differ slightly – hardly enough to worry about. Results don’t work out precisely like this every 1,980 decisions, of course, but these values give the average rates at which players contribute to the casino coffers.

Pretend a Pass, Come, Don’t Pass, or Don’t Come wager isn’t settled on the come-out. You can then augment the flat bet with what’s called “free Odds,” or, simply, “Odds.” This auxiliary amount has no edge for either casinos or players because the payoff exactly mirrors the difficulty of winning so the math dictates that the net of successes and failures is a zero-sum exercise.

To illustrate the idea, picture a Pass or Come bet with a point of four or 10. This has six ways to lose and three to win so it’s a 6-to-3 (equivalent to a 2-to-1) underdog and pays 2-to-1. Imagine 9 million decisions on a point of four with players taking \$20 Odds. The bet is projected to lose 6 million times at \$20 for a \$120 million setback and win 3 million times at \$40 for a \$120 million gain. Overall, it’s a wash. Chances and payoffs for Pass and Come bets on the other possible points are: a) a five or nine has six ways to lose and four to win so it’s a 6-to-4 (equivalent to 3-to-2) shot and \$20 Odds pays (3/2)x\$20 or \$30; b) a six or eight has six ways to lose and five to win so it’s a 6-to-5 uphill battle and \$20 Odds pays (6/5)x\$20 or \$24.

One incentive for betting the Odds on Pass, Come, Don’t Pass or Don’t Come is that the edge is lower than it would be were the same total were wagered flat. To understand the effect, remember that the edge on a \$5 flat bet cost players an average of \$0.07. Increasing the bet with Odds neither adds to nor subtracts from this value. Therefore, if a player begins with \$5 flat and takes \$20 Odds, the casino still earns \$0.07. But \$0.07 is only 0.28 percent of \$25. A 0.28 percent edge on the total of \$25 isn’t quite right, though. The \$0.07 applies to \$5 on an average of 12 out of every 36 come-outs when a decision is reached on one roll, and \$25 on the other 24 when a point is established. On this basis, the edge might be more accurately calculated as (12/36)x(\$0.07/\$5) + (24/36)x(\$0.07/\$25) = 0.6533 percent. Still far below 1.4 percent.

Something else enquiring minds want to know is, if bets on Odds are ultimately break-even affairs, why put the extra money at risk and raise the chance of depleting a stake during a normal run of bad luck? Astute gamblers know the perils of overbetting a bankroll. The issue therefore shouldn’t simply be whether to leave a flat bet as-is after a point is established, or use the Odds to pump it up as a means of reducing the effective house advantage. It’s how much exposure an individual can afford to a single number, and how to apportion it between flat and Odds segments to minimize the erosive impact of the edge. If you’ve got \$25 to venture on a single proposition and the casino will book a \$5 bet, why not give the casino \$0.07 with \$5 flat and \$20 Odds, rather than \$0.35 with \$25 flat and no Odds?

Finally, owing to bets on Odds ultimately being break-even gambles, solid citizens may wonder why they should bother with them? The answer lies in the volatility. Anyone really worried about the long-term shouldn’t play negative expectation games at all because, after a statistically large number of decisions, edge becomes overwhelming. This would essentially apply to everything offered in a casino except blackjack played by proficient card counters.

Folks who enjoy the casinos typically focus on single sessions or visits, during which positive fluctuations arising from jackpots or proceeds from long run of successful low-payoff bets can swamp the edge and yield profits. Betting \$5 flat and \$20 Odds at craps with a point of nine pays \$35. One such win suffices to cover the \$0.07 per bet cost of edge on 500 decisions. Betting \$5 flat, a single win compensates for the \$0.07 per bet expense of edge on 71 coups. And betting \$25 flat, a single win likewise makes up for the \$0.35 cost of edge on 71 wagers. Still, lower house advantage isn’t always a bargain, because volatility swings down as well as up and the increased exposure may have its own penalties. As the poet, Sumner A Ingmark, advised:

Since adding Odds to bets at craps won’t make them win more often,
Put extra money up for grabs with thoughtfulness and caution.