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# Can You Parlay a Casino to its Knees?

16 February 1998

You can make big bucks by parlaying high-payoff wagers at games like craps and roulette. The drawback of a hefty haul is that it won't happen often. And the richer the reward you seek, the less the chance you'll succeed. Still, you've seen solid citizens drop trifling side-bets on longshots - a dollar or two to supplement much more serious money elsewhere on the layout - and bring the casino to its knees by winning several of them in a row.

Parlaying is a simple idea. Go again after a win, risking the profit along with the original bet. The attraction is in what mathematicians call a "geometric progression," which multiplies numbers rapidly. Gamblers are more apt to think in terms of "betting with the house's money." And they take the "house's money" part as an article of faith, not to be shaken by blasphemy or logic about it being their own because they already won it.

Here are incentives for two typical craps parlays.

o Bets on hard six: win if the dice show three-three, lose on a seven or any other total of six. A \$1 bet pays \$9. Parlaying \$10 pays \$90. Then \$100 pays \$900. And \$1,000 pays \$9,000. Just four successive wins turns \$1 into \$10,000.

o Bets on aces: win if the shooter rolls one-one, lose otherwise. A \$1 bet pays \$30. Parlaying \$31 pays \$930. And \$961 - if the casino will book this much on aces - pays \$28,830. Just three successive wins turns \$1 into \$29,791.

One way to get a handle on the hope of harvesting the hoo-hah in a parlay is to ask what happens to a million players who try it. I'll give you answers for the hard six and the aces.

Say that a million Panglosses try to parlay \$1 on four successive hard sixes. Initially, 90,909 will win \$9 and 909,091 will lose. Of the first-round survivors, 8,264 will win \$90 on the second bet and 82,645 will lose. The third time, 751 of the remaining bettors will win \$900 and 7,513 will fizzle out. The final shot will find only 68 of the original million counting \$10,000 prizes on what they justifiably view as the best of all possible bets. So, the chance of winning this parlay is 68 out of a million.

Similarly, assume a million optimists attempt to parlay \$1 on three successive aces. For starters, 27,778 will win \$30 and 972,222 will lose. Of the first-round victors, 772 will win \$930 in the second lap and 27,006 will lose. On the last try, 21 of the original million will have converted their \$1 to \$29,791 (the rest will tell everyone they had a great time for only a buck). So, the chance of winning this parlay is 21 out of a million.

Have the lucky few, who scored big while risking only \$1, got the casino bosses upset? Not those who know their arithmetic.

With the hard six parlays, 68 players won \$9,999 each - a total of \$679,932; 999,932 players lost \$1 each - a total of \$999,932. The casino earned \$320,000 on the action.

With the aces parlays, 21 players won \$29,790 each - a total of \$625,590; 999,979 players lost \$1 each - a total of \$999,979. The casino earned \$374,389 on the action.

And what of dealers who claim runs of repeats happen "all the time?" It's not just a come-on. But it's no help, either. The odds against a shooter rolling one-one are 35-to-1. The odds against rolling the combination three times in a row are 46,655-to-1. But a dealer might watch something like 5,000 rolls every week. The odds against three successive one-one combinations in 5,000 rolls are roughly 8-to-1. So seeing such a sequence is not unknown over the course of time. And remembering it is as sure as you can get in a casino. What is unknown is when it will occur.

But that, of course, is what gambling is all about. As Sumner A Ingmark, the prognosticating poet, proclaimed:

An easy way to be a hero,
When odds are small but over zero:
Predict whate'er you set your sight on,
Eventually you'll find you're right-on.

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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.