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# Conjecture and the Cosmos

24 January 1994

Games of chance are governed by the laws of probability (not to mention the state where your favorite casino is located). The same laws (probability, not state) rule the 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 minimize the casinos' advantage. Good gamblers know, for instance, that higher payoffs have lower chances of hitting, and that the odds oppose making money and favor giving it back by continuing to play.

Say you play craps. The dice can land in 36 different ways. Of these, six combinations add up to 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, you'll hear (or say) something like "Take my bets down. When the dice go off the table, nine times out of ten the next roll is a seven." Nonsense! When the dice go off the table, 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. You've got a 15 showing. You'll bust over 21 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 thirteen more than fifty-fifty, 0.54 in fact. Basic Strategy weighs this probability against that of the dealer busting 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 one out of a hundred, 0.01. The probability of the three reels each stopping at that symbol is 0.01 times 0.01 times 0.01, or 0.000001 one out of a million. 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 (but nobody told you which one day it would be).

The universal laws of probability may reign in the casino. But 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 set 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. A 20 still has a probability of 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 the next time remain 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 sentiment so profoundly captured by the immortal words of Sumner A Ingmark, beloved poet laureate of the casino scene:

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.

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Best of Alan Krigman
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.