What Causes Streaks in Gambling?

28 January 1997

By Alan Krigman

Gamblers believe in streaks. A machine or table or dealer is hot or cold. Not "has been" hot or cold, "is" hot or cold. Meaning the past should continue into the future. Implying a cause - an inexplicable force, a mystical power, someone in the back room pushing the right buttons, that kind of thing.

So many slot stuffers don't stop with a tidy profit after a successful series of spins. The machine is on a streak! Sometimes such steadfastness is rewarded, corroborating their convictions. More often this dedication is disappointing, disproving nothing - just showing the machine really wasn't on a streak after all.

And countless table players press their bets after a win or two. They're on a streak! When hits continue and profits mount, it was because they knew about streaks. When the first defeat after a string of victories wipes out a big gain, it was because the run was only a teaser, or the flow of the cards changed when a blackjack bozo bet an extra spot, or the dice hit the chips the dealer stacked on the layout where the shooter was aiming.

Casino bosses, on the other hand, are disbelievers. If a game is giving away money, something must be amiss. A slot machine is on the fritz, a blackjack player is counting cards and tracking aces during the shuffle, the dice have been compromised, a dealer isn't following procedure.

Mathematically, the laws of probability anticipate streaks of various lengths in random processes. The likelihood they'll occur can be computed. And, although the odds of a protracted run when you've got your allowance on the line may be small, the chance of such a series during an extended set of trials may surprise you.

I'll use baccarat to illustrate the players' perspective. Baccarat buffs believe in streaks so strongly they keep track of results on little scorecards. The principal bets in this game, "player" and "banker", each win close to half of all decisions. The chance of a run of 10 winning player or banker hands in a row is a modest one out of 512. However, in 500 rounds, the chance of at least one such streak exceeds one out of five. A solid citizen could easily play 500 rounds during a casino visit, and therefore wouldn't find a 10-hand streak unusual. A frequent player would think such phenomena dominate the game, having seen them often.

A roulette example shows how some casino executives view streaks. In a year, a busy table might log 350,000 spins. Say the casino uses a fancy computer system to monitor and analyze such a table, for fear that if the wheel is somehow biased, certain players will be able to "clock" and exploit the effect.

One day, the computer detects the ball landing in one of the 19 numbers on half the wheel 20 times in a row. Goons are dispatched to close the game. As fate would have it, a player with a progressive wagering strategy and a system for covering half the wheel got to the table at the onset of this series, bet the right segment, and was making a mint. The casino bosses were sure they were being bamboozled. They knew the chance of any arbitrary half of the wheel winning 20 times in a row is a low one out of 524,288. They didn't realize that in 350,000 spins, the chance of at least one run in which any selected set of 19 numbers will win or lose 20 times in a row is a high two out of 13.

Had they closed the game sooner, say after the player had won 15 times in a row, they would have been exhibiting extraordinary paranoia and statistical naivete. The probability of at least one 15-win streak of this type in 350,000 spins is over 99.5 percent; the probability of five or more such runs is nearly 62 percent.

As a set of trials gets long, the probability it'll include a "streak" increases. So, over time in a casino where millions of bets are made every day, long runs of wins or losses can be expected. Not because of any motivating factors. Purely by chance. And creating a dilemma dolefully described by the poet, Sumner A Ingmark, thusly:

A gambling streak's good fortune, you win again and again,
The math predicts how often, but nothing can tell you when.