I’ve always maintained that the best thing that any gambler could do for himself is take the time to learn a little math. Really, this applies to any number of other disciplines including sales and investing. Just reading a few books on probability theory–or, even better, taking a class in the subject–will immediately pay dividends in the form of bigger wins and fewer losses.

I’m not holding my breath that a stampede of gamblers will descend upon the Math Departments at colleges nationwide. It’s never made sense to me that gamblers have such an aversion to learning the math behind their games, or even a few simple mathematical concepts. They’d rather hold on to superstitions and myths about how to tell if a slot machine is ‘due’ or insisting that if red comes up 9 times in a row at the roulette table the odds of black coming up on the 10th roll are very strong. Since many use gambling as a form of escapism their desire to live in a fantasy world where the rules of math and logic don’t matter is understandable–as long as their bankroll holds out.

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One of the mathematical concepts that gamblers struggle with is the ‘Law of Large Numbers’. This concept was developed in the 17th century by a mathematician named Jacob Bernoulli and simply stipulates that the larger the sample size of an event the more likely it is to reflect its true probability. Even ‘squares’ understand this concept whether or not they know that it has a name. If you visit Las Vegas for five days in the middle of the Winter you might conclude that it has a cold, blustery climate. A resident who makes a judgment of the weather based on 365 days a year knows otherwise. The classic example is the coin flip–in the short term there will be variance and it’s not unusual to flip ‘heads’ 8 or 9 times in 10 tries. You’re significantly less likely to flip heads 80 or 90% of the time with 10,000 or 10 million flips.

This concept is very significant to gambling theory because there are so many ‘truly random’ events found therein. For some reason, however, many gamblers think that the ‘Law of Large Numbers’ doesn’t apply to them and the games they play. For example, a blackjack player that repeatedly busts when hitting 15 might think he’s ‘due’ to get a good card. The sports bettor who observes that a team has gone ‘Over’ the total in 10 straight games might incorrectly assume that the team is ‘due’ to play ‘Under’. A video poker player that quickly burns through $100 puts in another hundred thinking that it’ll ‘even out’.

In many casino games–particularly slots and video poker–the machines are designed to return a certain percentage to the player. The deluded gambler will use this as an example of why he *should* immediately put $100 back in a video poker machine. If his first $100 had a return near 0%, he argues, the next $100 will almost certainly do better since he’s playing a machine with 98% return. His problem is a failure to accept the ‘Law of Large Numbers’ or, more appropriately, the law’s inverse.


There is no ‘strategic input’ when it comes to slot machines. You pull the handle (or press a button) and the machine’s Random Number Generator (RNG) does the rest. The lack of player ‘control’ is probably why there are so many superstitions about slot machines. Some players insist that ‘lurking’ is a viable slots strategy. ‘Lurking’ is when you watch another player lose at slots and then jump on the same machine when he leaves. There’s not really any harm in it, but there’s also no benefit. It’s no different than people who track roulette numbers–a random event or series of random events have no influence on future random events. Dice, roulette balls and slot machines have no memory–they don’t “know” what happened in the previous ten or one hundred rolls. If you’re playing on a bank of slot machines that return 97% the longer you play the more likely you are to observe that rate of return. Of course, it could take millions of spins. In the short term, you can win a ton of money or lose a ton of money. Neither extreme has any influence on how the slot machines will pay in the future.