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Are taking and laying Odds at craps equivalent bets?28 December 2009
Dice devotees endlessly argue the merits of Pass and Don't Pass or, correspondingly, Come and Don't Come. Ignoring the psychology of betting "right" or "wrong" – "with" or "against" the shooter – these alternatives give the casinos an edge that differs only in the hundredths of a percent. That's a penny in $100.
Pass and Come (Do) bets can be expected to win 49.2929 percent of all trials, Don't Pass and Don't Come (Don't) bets in 49.2987 percent – discounting "bar 2" or "bar 12" pushes on come-outs. The former win more often during come-outs and the latter during point phases of hands. The trade-offs for the flat, even-money, parts of these wagers are therefore essentially self-cancelling.
The plot thickens for Odds on Pass and Come or Don't Pass and Don't Come with a point established. This, owing to differences in chances and payoffs for the various numbers. As an example, consider double Odds with $5 bet on one side or the other.
On Pass or Come, taking Odds means a $10 wager regardless of the point. Bettors are fighting chances of 2-to-1 to win $20 on four or 10, 3-to-2 to win $15 on five or nine, and 6-to-5 to win $12 on six or eight. On Don't Pass or Don't Come, laying Odds will win $10 regardless of the point. Players will be favored by 2-to-1 with $20 at risk on four or 10, 3-to-2 with $15 up for grabs on five or nine, and 6-to-5 with $12 vulnerable on six or eight.
In theory, the Odds have no edge and are a wash across all points on either side. So, for instance, double Odds taken on a $5 Pass bet and a point of four will average $20 won once for every $10 lost twice; that's $20 in and $20 out, a net of zero. Double Odds laid on a $5 Don't Pass bet also on four will average $10 won twice for every $20 lost once; again, $20 in and $20 out for a net of zero. The pattern holds for all the numbers.
Few solid citizens will experience enough throws in their lives for the net from Odds to approach zero except by coincidence. Like other casino gamblers, craps buffs usually focus on sessions or visits. At a typical 100 throws per hour, six hours might mean about 400 shots with points established and Odds working. During such a span, individuals may win or lose on their Odds bets. And, if two players made mirror-image "Do" and "Don't" wagers at the same table, their fates would be equal and opposite. That is, were one $100 up on the Odds alone, the other would be $100 down.
The effect at the session level can be demonstrated by a computer simulation of a million games having 400 point-throws. Tallies for double Odds taken on or laid against $5 Do or Don't bets with the various points are presented in the accompanying table.
Outcomes of bets on Odds alone after 400 point-throws based on computer simulations of a million sessions
session point "Do" wins "Do" loses outcome "Don't" loses "Don't" wins over $200 4 or 10 7.5% 7.1% $150-$200 4 or 10 6.2% 6.4% $100-$150 4 or 10 9.1% 9.4% $50-$100 4 or 10 11.8% 12.1% under $50 4 or 10 16.4% 13.8% over $200 5 or 9 5.9% 5.7% $150-$200 5 or 9 6.0% 6.0% $100-$150 5 or 9 9.5% 9.6% $50-$100 5 or 9 12.7% 13.0% under $50 5 or 9 16.5% 15.1% over $200 6 or 8 4.9% 4.8% $150-$200 6 or 8 5.8% 5.7% $100-$150 6 or 8 9.5% 9.8% $50-$100 6 or 8 13.3% 13.4% under $50 6 or 8 16.7% 16.0%
The data suggest: 1) Chances of agony or ecstasy on Odds during a session get smaller for greater amounts. 2) High wins and losses become more likely as the payoff-frequency skew rises from 6/8 through 5/9 to 4/10. 3) Happenstance more than the differences between the alternate bets determines how a particular session evolves. 4) Winning sessions on Do are more frequent than those on Don't; this doesn't conflict with the bets all having zero edge. It's like a more extreme but readily understood situation where one proposition is projected to yield 500 sessions in which players earn $1 and 500 in which they lose $1, while another is expected to yield 999 $1 losses and one $999 win. As the poet, Sumner A Ingmark, reminded partisans in the Do or Don't debate:
You learn a lot from averages, but oft there's more to know, So don't rely on them alone, to bet your hard-earned dough.
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