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Best of Alan Krigman

Gaming Guru

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Probability Laws Reign but Hunches Are Remembered

1 January 1993

Casino games are governed by the laws of probability (and those enacted by politicians, too). The same laws (probabilistic, not political) rule the entire known universe. You use them constantly, usually with no second thought. For instance, crossing a street, if the light's with you and the truck is braking, it's probably safe to go; if the light's against you and the truck is accelerating, it's probably unsafe. Likewise, smart players use probability to improve their chances for success. They know, for instance, that bets with the highest payoffs have the least chances of hitting, and that the odds oppose making money.

Say you play craps. The dice can land 36 different ways. Of these, six combinations total seven. So the probability of a seven on any roll is six out of 36, one out of six. Still, after a "no roll" when the dice land in the rail or on the floor, someone will say "Take my bets down. When the dice go off the table, nine times out of ten the next roll is a seven." Humbug! One time out of six the next roll is a seven, the same as always.

Maybe blackjack is for you. Every 13-card suit has seven cards valued seven or more. Your hand totals 15. You'll bust by drawing anything above six. If you haven't "counted" the cards already dealt, your expectation of busting on a hit is seven out of 13 54 percent. Basic Strategy weighs this probability against that of the dealer breaking with the exposed card, and tells you if your best move is to hit, stand, or surrender half your bet.

OK, you're a slot player. Modern slot machines are chrome-plated probability computers. Picture a three-reeler, with each reel programmed to stop randomly at any of 100 spots. Assume the jackpot symbol appears once on each reel. The probability of any reel stopping at that symbol is 1/100, 1 percent. The probability of the three reels each stopping at that symbol is 1/100 times 1/100 times 1/100 one out of a million 0.0001 percent. That's the probability you'll hit the jackpot on any pull. No matter if this machine's been hot all night, it's been lucky for you before, or you're using a system guaranteed to pay for itself in one day.

If the universal laws of probability reign in the casino, how come we're always hearing of bettors making a bundle on their hunches? Of solid citizens exalting conjecture over the cosmos. Several factors explain these apparent triumphs of the ridiculous over the sublime.

First, laws of probability are "nondeterministic." They give the likelihood, but don't predict the occurrence, of events. On a double zero roulette wheel, with 38 grooves, the probability of a 20 is one out of 38. After 37 spins, none being a 20, don't bet the ranch. The probability of a 20 is still one out of 38. The opposite is also true. If 20 hits and you parlay your bet on a hunch it will repeat, your chances remains one out of 38.

This leads to the second factor, selective memory. Imagine a roulette player who bets $1 on the 20 and hits. The payoff is $35. The player parlays, $36 on the 20, and wins again. The payoff on the parlay is a show-stopping $1260. The player, and everyone else at the table, will remember that winning hunch until dust returns to dust. What of the thousands of parlays made on hunches that cratered? They were fast forgotten because the players "only lost a dollar" and kept going another three hours.

Then there's "bragging rights." Those classy casino newsletters don't quote patrons who say, "I had a hunch I was gonna kill 'em, but I lost my shirt." We all enter with that winning feeling, but the only bragging is done by the few who actually leave blessed by the probability gods.

Finally, there's the admonition so admirably asserted by Sumner A Ingmark, the bettors' bard:

The wheels and the dice and the cards have no memory,
Casinos are where probabilities rule.
No system can change you from loser to winner,
And if you play hunches, you're playing the fool.

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.