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Best of Alan Krigman

Gaming Guru

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Playing It Smart: Don't underestimate the impact of the come-out on pass bets

3 November 2008

Pass, Come, Don't Pass, and Don't Come bets are the best wagers at craps in terms of edge or expected value. Pass and Come, for instance, win an average of 49.29 percent of the time. Alone, this success rate would put the house edge at 1.41 percent with an even-money payoff low, compared with most other games.

Of course, proficiency at craps involves reducing this edge by "taking Odds" after a point is established. This, because the house gets no juice on money wagered as Odds. To picture the effect, note that betting $10 flat on Pass risk $10 to win $10 theoretically earns the house 1.41 percent of $10, or $0.14. Say you take triple (3X) Odds, putting another $30 behind the line. Your $40 at risk then wins $70 on points of four or 10, $55 on fives or nines, and $46 on sixes and eights. However, the bosses still average only $0.14 for the coup.

Solid citizens making Pass and Come bets often focus on the point roll and give short shrift to the come-out. One reason is that more money is at stake on the point roll when bettors take Odds. Another is that come-outs are one-shots while point rolls last until the shooter repeats the number or throws a seven which can be a single toss but can in principle extend for eternity.

Such thinking belies the impact of the come-out. At this stage of a roll, of the 36 ways the dice can land, Pass and Come bets win on eight (1-6, 2-5, 3-4, 4-3, 5-2, 6-1, 5-6, & 6-5), lose on four (1-1, 1-2, 2-1, & 6-6), and move to a point on the other 24. Ignoring the points yields a conditional eight ways out of 12 to win a huge 66.67 percent. In absolute terms, expected win rate on the come-out is eight out of 36 or 22.22 percent.

Compare conditional win rates on the come-out and the points. For points, the conditional rates are the chances that established numbers will win. On fours and 10s, 33.33 percent. On fives and nines, 40.00 percent. And on sixes and eights, 45.45 percent. These are all far below the conditional 66.67 percent coming-out. More, the latter is over half so players are favored while the former are below this level so the house is in the catbird seat.

Comparisons of absolute rates are also revealing. For points, the values are the prospects a number will become the point then win. The figures are 2.78 percent for fours or 10s, 4.44 percent for fives or nines, and 6.31 percent for sixes or eights. Separately, these pale beside the absolute 22.22 percent for the come-out.

Collectively, the chance of any point being established then winning is 27.07 percent. The sum of the 22.22 percent on the come-out and 27.07 percent for points is the overall 49.29 percent. Bettors can therefore expect that 22.22/49.29 or 45.08 percent of their Pass and Come wins will occur during come-outs and the remaining 27.07/49.29 or 54.92 percent on point rolls.

The phases of a Pass or Don't Pass bet can also be compared using the "most likely value" of the money at risk. Conditionally, the most likely value of $10 bet on the come-out roll is $20 and on the point roll is zero. The most likely value of Odds taken on a point is also zero. All these by wide margins. Absolutely, the phases must be considered together because the most likely result of the come-out is the establishment of a point. And since the overall win rate is 49.29 percent, the most likely value of a $10 Pass or Come bet is zero although by only a narrow margin.

Realizing the importance of a win during the come-out should make you think twice before downgrading your advantage during this phase of a roll by using hedges of various types. It can also help you be prepared when an intellectual version of Plenty O'Toole, admiring your action, comments, "Say, you've played this game before." Instead of a wimpy comeback like James Bond's ("Just once"), you can say something that will knock her socks off, like "I'm taking full Odds on the point of five even though the chance of winning is only 40 percent because that part of the money pays 6-to-4." The perceptive poet, Sumner A Ingmark, had yet another cause to know the probabilities in the game:

Don't be a loser because you ignored,
The delicate balance 'tween risk and reward.
Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.