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Best of Alan Krigman

Gaming Guru

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Why Games Seem Cold More Often Than Choppy or Hot

22 October 1996

You're sensible. Not out to change your lifestyle by striking it rich during one lucky casino visit. You make conservative even-money bets at tables where the house has only a small edge.

You read somewhere, or figured out, or heard a high roller say this should win you about half your bets. So you're positive you should never fall too far behind, and can jump ahead by waiting for a few wins to pop in a row. Why, then, doesn't it happen more regularly? Why do games seem cold more often than choppy or hot?

Take blackjack. Sure, there are stretches when players and dealers go back and forth. But there are too many sessions during which dealers win hand upon hand, and too few when players do so.

Or, consider craps. Sure, some shooters hit points galore with plenty of numbers and naturals in between. And there are games where nearly everybody scores or where it's up and down. But more often, the dice circle the table with nobody repeating a point.

The phenomenon is real, maybe exaggerated, but not imagined. It has to do with what statisticians call "skew." It dominates longshot play, but characterizes short-odds games as well.

In blackjack, dealers normally win more rounds than players. But, three factors provide balance over long periods: 1) Payoffs are one and a half units for player blackjacks; losses are only single units for dealer blackjacks. Uncontested blackjacks can be expected on about 4.5 percent of all hands. 2) Players can split pairs, to exploit strengths such a nine-nine against a dealer six or to mitigate weaknesses such as an eight-eight against a dealer nine. Pairs which call for splitting occur on about 2.5 percent of all hands. 3) Players can double down when they're favored (not guaranteed, of course) to win the extra bet by drawing one card. With rules allowing doubles on any initial or post-split two cards, circumstances appropriate for this move can be expected on about 10 percent of all hands.

Even marathon blackjack sessions, though, don't qualify as "long periods" in the mathematical sense. When favorable factors arise - or succeed - nonuniformly, players experience the skew as a streak. And, because these events - together -? comprise only 17 percent of all hands, streaks are more apt to be cold than hot.

In craps, the probability of winning on the pass line is 49.29 percent - close to half. But pass is a two-stage bet. The first having 22.22 percent chance of winning with seven or 11 on the come-out roll. The second having 27.07 percent likelihood of neither winning nor losing on the come-out, but establishing then repeating a point.

Why do craps players remember runs of losing pass line bets? Solid citizens tend to discount their come-out wins and focus on whether the shooter repeats the point. This alters the ground rules. Once a point is established, the conditional probability of winning is only 40.61 percent - less than half. The corresponding chance of, for instance, five shooters in a row not making a point is then 7.39 percent - low, but well within the range players can expect to encounter during a typical game.

The perception of long cold streaks at craps is reinforced when players wager additional money after a point is established, say by taking odds or making place or come bets. These are longshots; they lose more often than they win but pay in inverse proportion to their chances. Odds, as an example, average 1.46 losses for every win; however, they pay $1.46 per $1 wagered.

So, don't make the common error of thinking that low house advantage and even-money payoffs mean you'll win about half your bets. Games with these features are still typically skewed to favor cold over hot or choppy stretches, compensating with occasional large returns. This emphasizes the need for sizing bets to bankrolls and exercising sufficient discipline to be able to ride through normal downswings. Sumner A Ingmark, poet lauded for looking askew at conventional wisdom, said it this way:

Good gamblers num ber among many talents,
The art to wait for all factors to balance.

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.