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Gambler's Fallacy


Errors in judgement are common among gamblers, which helps explain the exponential expansion of casinos, especially in the United States. However, one specific error has been made by mankind since judgement and decision making first intersected in the human mind - and it's now commonly known as the gambler's fallacy.

This fallacy, or error, explains the widespread belief that a gambling system like the Maringale, where a player keeps doubling their losing bet in anticipation of an eventual winner to get even with, will work. The gambler's fallacy is the belief that under fair conditions, the odds of an event happening will quickly even out and are apt to be exploited with future bets. In mathematical terms, the fallacy is the belief that when deviations from expected behaviour are observed, future deviations in the opposite direction are likely.

The classic example of this thinking is when a roulette player sees the roulette ball land on red six times and assumes that the color black is much more likely to be seen on the next spin because of the preponderance of previous red spins. Nothing can be further from the truth, of course, because each spin of the ball is independent from previous spins. There is no way to predict the landing of the ball unless the wheel is unbalanced or has loose frets, which could result in an unnatural progression of specific numbers or a color due to a biased wheel.

The Dice Have Ears

Harold Smith, Sr. who owned Harold's Club in Reno for many years held the belief that gambling outcomes could be influenced by the will of many people, such as a crowd at a craps game. He felt that if enough people were rooting for the right numbers, they would roll, and that saying the word seven during a big hand of shooting could stop the run of winners. However, his many years in the gaming industry convinced him that the odds of chance, like the spin of the ball or the turn of a card, could not be predicted by previous events. He thus rejected the gambler's fallacy.

However, what Smith should have admitted, at least to himself, is the fact that the dice have no memory. They don't recall that over the last hour, for instance, that the pass line won many more times than the don't pass line, so now it is time to even things out. The funny thing is, most gambling events do eventually even-out over the course of time, but the course of time may take an hour, a week, or even a year. Betting on something that might take a year to even-out is no way to enjoy your gambling.

The Lucky Streak

Poker player Doyle Brunson takes a different approach to the gambler's fallacy and streaks. He has a profound belief in streaks, feeling that he should take advantage of any good run of cards by playing even more hands, while the gambler's fallacy is the mistaken belief that small samples must be representative of the larger population. According to the fallacy, streaks will eventually end and be followed by a run in the opposite direction.

However, Brunson's belief that he should press his luck while on a good run of cards is based more on his table image and confidence, not independent trials of an unknown outcome. In poker, players make their own decisions based on the current game conditions - such as their own starting cards, and the players involved in the pot. When a player is winning many hands and plays with confidence, they make fewer errors and can actually manipulate their opponents. Roulette players can not manipulate the outcome of the next spin of the ball.

Who's In Control Here?

As explained in the Doyle Brunson example, where a successful poker player can have a measurable effect on the outcome of the game (a game of skill, not luck) and be in control of their own destiny, players like Harold Smith (at a game of chance, like craps) can not be in control of the outcome of the gamble - they can only be in control of their bets. However, people with strong will, who have an internal locus of control, are actually more likely to believe in the gambler's fallacy, simply because they feel that their gambling success is based solely on their own skill, not the luck of the draw!

Static Finite Outcomes and Changing Finite Outcomes

Readers and gamblers alike should understand that there is a difference between unchanging (static) finite outcomes (perhaps the possible outcomes on a roll of dice at the craps table), and finite outcomes that change based on previous events. At the craps table, the dice may total any number from 2 to 12 on any roll, but the odds will always be the same for each roll. Previous rolls have no bearing on the current roll.

Conversely, dealing with a changeable, finite number of outcomes (such as a deck of cards that has no aces left), the odds are actually changing as conditions change. If all the aces have been used on a deck of cards, obviously the dealer can not make a blackjack on the next dealt hand. This will not change until the cards are shuffled. These changes in deck conditions make blackjack card-counting possible. However, streaks can be severe even when one side has a statistical edge over the other.

In a large casino with 100 blackjack tables, some tables will win, and some will lose over the course of a day's play, but the casino as a whole will show a profit. By the end of a week's play, nearly every table will show a profit, but on occasion, a single table may be a loser for an even longer period of time. The same can happen on the other side of the table.

Blackjack card counter Kenny Uston, widely regarded as one of the finest players ever, used a counting system that game him an overall edge of about 1 percent over the house. However, he had a streak of 63-days where he booked a loser every single time he played.

And the flip of the coin - Doyle Brunson recalled, in his book Super System, that he once had a winning streak of 51 poker sessions. Streaks happen, and nobody knows when they will end. Keep that in mind before you bet with, or against a streak of any kind!

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