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You Can Win 80 Percent of the Time... And Still Lose

2 March 2000

Casino gambling is expanding on land, sea, and if not in the air then at least in the cyberspace of the Internet. One result is that neophytes galore are dipping their toes into the wagering waters. And the buzzards are circling, ready to pounce on these naive new legions of lemmings with offers of secret systems.

A few schemes still claim they're "guaranteed to win." And a few hopefuls still want so badly to believe in the tooth fairy that they buy this balderdash. But pitches today are getting more sophisticated. Many systems are accordingly touted, not to win all the time, but to yield 80 percent or somesuch success rates.

You gotta admit it sounds much more reasonable. And, with a modest cushion for those rainy days, an 80 percent win rate oughtta be enough to quit that dreary day job and enjoy the good life in the fast lane. Er, oughtn't it?

Let's set the record straight. Yes, an 80 percent win rate is reasonable. No, it won't let you turn pro.

I'll show you the long and short of it using the "32 across" bet at craps as an example. For solid citizens to whom craps remains as much a mystery as the theory of relativity, this is actually six separate wagers. It involves \$32 -- distributed as \$5 to win \$9 on the four, \$5 to win \$7 on the five, \$6 to win \$7 on the six, \$6 to win \$7 on the eight, \$5 to win \$7 on the nine, and \$5 to win \$9 on the 10. When any of these numbers roll, players collect the indicated amount. They can do what they want with the original \$32 -- take the whole or part of it back, leave the bet in action, or press what's on all or some of the numbers. When the dice show a two, three, 11, or 12 there is no decision on the \$32 across. And when the seven rears its ugly head, the entire \$32 disappears into the casino coffers.

Of the 36 ways the dice can land, 24 will be winning numbers, six will lose, and six will be irrelevant. This means that 24 out of the 30 valid decisions will be winners. And 24/30 is 80 percent.

Say you make this bet with the idea of keeping it in action for one roll -- win, lose, or push. Your chances are exactly 50 percent of earning \$7 and just under 17 percent each of losing \$32, breaking even, or winning \$9.

What if you make this bet twice? Your chances are now about 30 percent of losing from \$25 to \$64, 3 percent of breaking even, and 67 percent of winning \$7 to \$18. Do it three times and your shot is roughly 42 percent of losing between \$14 and \$96, half a percent of breaking even, and 57.5 percent of earning from \$7 to \$27. With another try, the probabilities shift to almost 52 percent of a loss, around 48 percent of a win, and close to zero percent of a break even. Do you detect a subtle pattern here? As you continue making this bet, the chance of a net gain declines. Yet, each time, you had 80 percent chance of winning.

There's another way to look at success rate in a casino. This involves the likelihood you'll reach a target profit, making any specified bet, before depleting the bankroll you considered sensible when you were at home and didn't need reminding that the medium of gambling is real money.

To see how this works, assume you have a \$500 stake and bet \$32 across. By playing until you go broke or reach \$50 profit, you'll be a happy gambler about 82 percent of the time. If frequent \$50 conquests make you cocky and you decide to try for more, your overall win rate will drop rapidly. Balancing a \$100 win against the loss of a \$500 bankroll cuts you down to a 70 percent chance of victory. Shooting for a \$250 gain on a \$500 stake should lead to joy only about 39 percent of the time. And a double-or-nothing drive has a mere 17 percent chance of triumph. All this, on a bet which you correctly expect to win 80 percent of the time.

Wee wonder that the wordster, Sumner A Ingmark, warned:

Though facts expressed as numbers seem precise,
A touch of prudence often would be nice,
To separate what's value from what's price.

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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.