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Best of Alan Krigman

Gaming Guru

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Playing it smart -Should you take down craps bets on which you have an edge?

2 April 2007

Craps players who wager on Pass and Come can increase or decrease the amount they "take" as Odds during the point phase of a roll. But they must leave the initial "flat" part of the bet as-is. Solid citizens who wager on Don't Pass and Don't Come can change what they "lay" as Odds and also lower or remove their flat bets.

Pass and Come are restricted because bettors have an edge on the casino during come-out rolls. Then, these wagers pay even money on sevens or 11s and lose on twos, threes, or 12s. Out of 36 possible dice combinations, that's eight ways to win and four to lose so bettors are favored 8-to-4 (2-to-1) to win 1-to-1. When any of the 24 other dice combinations appear on the come-out, the money shifts to the "point" and players become underdogs. They fight chances of 6-to-3 on fours and 10s, 6-to-4 on fives and nines, and 6-to-5 on sixes and eights. Casinos won't let anyone have an 8-to-4 hammer at the start and not face the music later.

Conversely, Don't Pass and Don't Come lose on sevens or 11s and win on twos or threes during the come-out. That's eight ways to lose and three to win 1-to-1, a serious hurdle. However, if the barrier is overcome and the money goes to the point, the compensation is that the bet has an advantage during the second phase equal and opposite to the Pass/Come situation. Players have already paid their dues, so to speak; if they want to take down bets on which they have an edge, the casino will happily oblige.

Some doyens of the darkside routinely take Don't Come wagers off sixes or eights. They're figuring these aren't robust enough favorites and prefer to go through another come-out, hoping for a point with a greater shot at winning. This is false logic because the exposure during the come-out swamps any gain they can hope to achieve on a new point. Also, their "conditional" edge over the casino for money positioned behind the six or eight through the Don't Pass or Don't Come is not chicken feed. Every such flat dollar has an expected value slightly over $1.09.

Money moved to the other numbers through the Don't Pass or Don't Come has even greater edge for the player. A flat dollar behind a five or nine has an expected value of $1.20. Behind a four or 10, it's $1.33. Odds, regardless of the point, have no edge either way. A dollar in Odds has an expected value of $1.00.

Given that a bet has survived a come-out roll on the Don't side and has a statistical worth exceeding its face value, probability theory militates against taking it out of action under any conditions. But, were the laws of probability the only criteria to be considered, the issue would be immaterial because nobody would gamble in a casino anyway. Pretend, for instance, you'd gone through a Don't Pass and two Don't Come come-outs and had $10 each behind the four, five, and six. Say you don't lay Odds. On a seven, you'll recover your $30 and grab $30 profit, adding $60 to your rack. On any of your numbers, you'll lose $10 but not change the stack in your rack. If you take down your bets, your rack will grow by $30.

The expected value of the $30 at risk is $10.91 + $12.00 + $13.33 or $36.24. Imagine further that the shooter has been on a tear, but happily for you it's involved only eights, nines, and 10s.

Taking down your bets sacrifices a theoretical $6.24. But it adds a sure $30 to your rack. The alternative for the next throw is 12 ways to lose $10 (one of your numbers hits) versus six ways to win $30 (the seven pops). Are you wrong to give up the advantage? How would you answer if you had $500 in your rack? What about $5?

The decision you make is in the realm of what economists call "utility theory." It hinges on the strength of your aversion to losing $10 and the value you place on winning $30, subject to the 2-to-1 chance of feeling the pain and not the pleasure. Other salient factors are that the $6.24 is theoretical not real, and the advantage is based on averages not the here and now. Sumner A Ingmark caught much the same conundrum in his canto:

Your prosperity looks great on paper,
But you can't buy groceries with vapor.

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.