The gambler’s fallacy is a misconception which causes a bettor to make mistakes when gambling. Many common strategies employed in the casino are fallacious. A lot of the shared wisdom is nothing more than myth which needs to be debunked. This article discusses the original gambler’s fallacy, then gets into a wider discussion of the bad strategies and wrongheaded tips given from player-to-player.

Before I delve into a wider discussion, let’s discuss the original gambler’s fallacy: the law of averages. This is a common sense understanding of how probability works. Everyone agrees that the law of averages is real, except that (in a casino) there is no law of averages.


The Law of Averages

Go to a roulette wheel and you’re likely to see an electronic board with the last 10 or 20 winning numbers. Go to a baccarat table or the keno room and you’re likely to see something similar. Players attach a value to the idea that they can see what the last few spins, drawings, or hands have produced.

All of this is bunk. Except in a game where you count cards, whatever happened previously has no bearing on what’s about to happen. Players might think some numbers are “hot” and some numbers are “cold”. They might think a number hasn’t hit in a while and thus assume it’s “due”. That isn’t the case at all, because results are separate in a randomly generated game result. If you flip a coin and it comes up heads 10 times in a row, it still has a 50/50 change of coming up heads the next time, assuming the coin toss is fair.

How Probability Works

People have a flawed view of probability. The fallacy is their perception of what “large” and “small” samples are. To a player, 500 rolls of the dice seem like a lot. When talking about the probability, it’s not really a big number. The odds might suggest one set of outcomes, but the real-world results might not look like the probabilities for tens of thousands of bets, or perhaps more. When testing basic strategy in blackjack, experts test a billion hands.

The longer a game continues, the more likely the results are going to look like the odds. In a small sample of 100 or 500 or even 1,000 bets, the results might be wildly different than the odds. That is the bedrock the casino industry is built upon; players have to get lucky to win, but probability allows wild swings in fortune. A gambler can get lucky and win.


Randomization of Results

Whether people are randomizing results with a set of dice or a random number generator, gambling is based upon a random result. In a truly random game like craps, a player rolling a seven does not affect their odds of rolling a seven again. The odds are fixed, no matter how many times seven is rolled.

Progressive Betting

For that reason, progressive betting techniques like the Martingale are not a way to circumvent the house edge. If you have a losing streak, then increasing the wager in order to ride the law of averages back to a win is a gambler’s fallacy. By exponentially increasing your bet size, you are exponentially increasing the risk of ruin. You aren’t making it more likely you’ll win, but more likely that your losses will be catastrophic.

The Martingale betting scheme gives the illusion of beating the casino. If you start with a $5 bet using the Martingale scheme, you would double the bet every time you lost a roll: $10, $20, $40, $80, $160, $320, $640, and so on. As soon as you win a bet, you go back to the $5 wager. The wagering is such that, at the end of each sequence, you would be $5 ahead. This seems to assure victory, but it has a couple of fallacies.

One, no one can keep doubling their bet, no matter what. At a point, their bankroll is busted. Two, bet limits at tables also make it impossible to follow the strategy correctly during an unlucky streak. Three, what $5 player is going to risk $640 on a roll of the dice, especially if the strategy is to win back a total of $5.


Dice Control Techniques

Some craps players believe there is a way to weight the odds in one’s favor. Dice control is a controversial subject in the craps world. Respected figures like Stanford Wong have argued that dice control is a real way to beat the odds in craps. If so, it is a technique which is hard to master. Most novice dice shooters are not going to be able to master dice control. And for every expert who advocates dice control, there’s another who think it’s bunk. The upshot is any beginner reading this article should not assume they can walk into a casino and win with dice control. To do so is another fallacy.