One of the best things that any gambler of any level of experience can do is learn as much as he can about the mathematical concepts at play in casino games. Of particular importance is probability theory but there’s any number of other areas of study that are also helpful. You can find books on the subject or if you’re really ambitious, take a course at a local college. It’ll pay for itself. I spent most of my high school and college career trying to avoid math. I came to it later in life when I decided that I should understand the mathematical concepts involved in gambling and handicapping. The more I learned about the math of gambling the more successful I became.

Unfortunately, people with even a modicum of interest in math are the exception rather than the rule among gamblers. And this makes casinos and peddlers of ‘never lose roulette systems’ extremely happy. Having spent a good portion of my adult life in Las Vegas the mathematical ignorance on display in the casino was downright mind-boggling. On one level, I really could care less. There’s an old line about lotteries being a ‘tax on people who don’t understand math’. The same concept works at other casino games, sports betting, poker, horse racing and ‘real life’ pursuits like investing.


This brings us to what is known as the ‘Gamblers’ Fallacy’. The best way to explain it is by example and the easiest example to understand is a coin flip. Most people get the concept that on a single coin flip the odds of it landing heads or tails is 50/50. That’s why casinos will book Super Bowl coin flip bets at -110 or higher all day long. Since the ‘true odds’ are 50/50 or +100 no matter what happens they’re getting the best of it. In theory, a coin can be designed to be ‘top heavy’ or ‘bottom heavy’ and that will make one side or the other come up more frequently. For the sake of argument, however, we’ll just assume that this isn’t the case and the coin we’re flipping is 50/50 heads and tails.

Now, let’s say we flip the coin 10 times and it comes up heads every time. What are the odds that it’ll come up ‘tails’ on the next flip? If you said 50/50 you can go to the head of the class. If you said anything else then pay close attention to this article. The Gamblers’ Fallacy is the mistaken belief that if a random event happens more frequently in the short term it means that it will happen less frequently in the long term. Another way of explaining it is that if something happens more frequently in the short term–even numbers on the roulette wheel, for example–that at some point an odd number becomes ‘due’ and thus more likely. Still another way of explaining it–it’s the belief that random outcomes in the past will somehow influence random outcomes in the future.


Random outcomes just don’t work this way. Whether it’s at the slot machine, the roulette wheel or the craps table the reality is still the same–one random event or outcome has no influence whatsoever on future events. Unfortunately, the belief that they do is insanely common among even experienced gamblers. We talk about this in every form of gambling. Just because a slot machine or a video poker machine hasn’t seen a jackpot in an inordinately long time doesn’t mean that you’re more likely to hit one because ‘it’s due’. You can track all of the keno numbers you want–assuming the game is on the up and up and completely random it just doesn’t matter. Same deal with lottery numbers. No matter the game the reality is still the same–one random outcome has no influence whatsoever on a future random outcome.

For some reason, however, roulette players are especially beholden to the Gamblers’ Fallacy. Many casino roulette tables even have LED screens that record the last 10 or 12 numbers that have appeared on the wheel. Many roulette ‘systems’ are dependent on certain events becoming ‘due’. Once you understand the math it’s almost impossible to wrap your head around the fact that many people actually believe that if an odd number hits 9 straight times at the roulette table there’s a greater chance of hitting an ‘even’ number in the next few spins. Of course, the casino has no reason to disimbue people of this notion since it works very strongly in their favor.

Assuming that a game is truly random–and most land-based and online casinos offer truly random games–it’s essential to keep one salient fact in mind. The ball, dice or reels don’t have a memory. The RNG chip (random number generator) doesn’t either. It doesn’t care what happened in the past and neither should you.