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Best of Alan Krigman

Gaming Guru

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Is the theory of streaks valid despite what the gurus say?

11 October 2010

Lots of solid citizens believe gambling runs in streaks and that talk about randomness is guru gobbledygook. The idea is that to win big on a small stake in a non-jackpot game, you have to amass larger and larger payoffs using "the house's money" to press your bets during hot streaks. Of course, to avoid losing it all when the end comes, you have to reliably foretell when the curtain is about to fall. The theory of streaks doesn't cover this part.

Picture what's supposed to be a truly random game -- flipping an unbiased coin. The chance of heads is 50 percent. No matter how long a run of heads you've encountered, the chance of another on the next flip is still 50 percent. More, the probability of a streak shrinks as its length grows. Prospects of two heads in a row are 25 percent, three are 12.5 percent, four and 6.25 percent, 10 are less than 0.1 percent, and so on.

Does an unlikely series of 10 successive heads imply that the game isn't truly random? Rather, that the coin or how it's flipped are biased in some way you can't explain, but can infer is the case from the results? Say an unknown phenomenon raises the probability of heads to 75 percent. The chance of 10 in a row rises by a factor of 56, from 0.1 to 5.6 percent. Of course, flips could actually be random because 0.1 percent isn't the same as zero and the chance of a particular run of 10 heads differs from that of such a run anywhere in an extended series of flips.

Slot buffs often get the impression that a machine is on a hot streak, building up through a chain of increasing payouts to a major score. It turns out that modern slot machines aren't really random. Their so-called "random number generators" actually generate "pseudo-random" sequences. This usually means that the numbers occur in repeating cycles or are calculated from what went before. But the cycles are too long and the math too complex to be of any practical help in anticipating what'll be next. And, compounding the uselessness of the departure from pure randomness, the sequences are generated continuously and a number is picked at the unpredictable instant a player triggers a round.

Roulette is susceptible to non-random results. Wheels aren't perfectly balanced and surfaces aren't absolutely smooth. Even if you can find a casino where balances and surfaces haven't been checked for years, the effect will be extremely small. Also, some dealers insist they can favor certain groups of outcomes by the way they spin the wheel and release the ball. If this has ever been proved conclusively, the test data are yet to be released.

Craps offers fertile grounds for hypotheses about non-randomness. Run your finger across the edges of dice brought fresh to the table. They're sharp. Run them again after the dice have been in play for a few hours. They've gotten smoother. Smooth edges increase the likelihood dice will slide rather than tumble over the tabletop. Also, consider the possibility that well-practiced shooters can influence the outcome of a roll by the way they set and throw the dice under the right combination of conditions. Couple this with the fact that all a person must do to have a lengthy and profitable hand is avoid throwing sevens. Now, think back to tables where someone "held the dice" for lots of throws. Was this shooter exercising a degree of control on which you could be comfortable betting. Or was just a fluke?

Card games offer rich opportunities to speculate about non-randomness. When withdrawn cards aren't replaced in the supply between rounds, depletion of ranks during a game alters the probabilities of subsequent draws. Further, shuffles are never perfect. So the way cards are picked up affect the order in which they're dealt after the shuffle. The former is the basis of card counting and the latter shuffle tracking in blackjack. Can you deduce from a series of good hands that you're in a favorable clump of the shoe? Or, were you just temporarily fortunate.

Would that there were means to distinguish bias from luck on the fly. Otherwise, as the punter's poet, Sumner A Ingmark, wrote:
It's not the wisest of techniques,
To bet the farm on gambling streaks.
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.