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# Gambler's Fallacy

10 April 2003

This time I'd like to talk about the Gambler's Fallacy. In researching this topic, I discovered that just about anything gamblers believe that is contrary to mathematical reality is considered a gambler's fallacy. Let's look at a few of those fallacies over the next few weeks.

The Odds Have to Even Out

This is the most common gambler's fallacy. The mathematicians call it The Doctrine of the Maturity of Chances. This fallacy says that something is more likely to happen in the future if it hasn't happened in a while. Conversely, something is less likely to happen in the future if it has been happening frequently.

In other words, the odds have to even out. If the 7 has been rolling a lot, it will go into hiding for a while so it makes the right probability. If you don't see too many red numbers, or even number, or low numbers on the roulette tracker board, the ball is going to land on more black, odd, or high numbers in the future so that red and black, odd and even, and high and low each occur about 50% of the time. If your slot or video poker machine hasn't hit in a while, it's bound to hit soon. As I always say, even the tightest machine in the world pays its jackpot once in a while.

Let's assume that this fallacy is true. You're playing your favorite machine and it's been so cheap that you're considering moving it from your favorites list to a different list. But you decide to stick with it because a cold streak has to be followed by a hot streak in order for things to even out.

Let me ask you this question: How do you know that the cold streak you're in now isn't balancing out a prior hot streak? The fallacy assumes that whatever is happening now is taking things out of balance and it will be followed by an opposite action to restore the equilibrium. What happens if what is happening is actually restoring the balance? What is supposed to happen in the future then?

Fortunately, we don't have to deal with these puzzles because the fallacy is a fallacy. It's not true. But I can see where people have problems believing that it isn't true because, from a certain perspective, it is true.

The odds will even out in the long run, but only in the long run. In the short run, anything can and does happen. But these short-run anomalies, hot or cold, are just drops in the bucket when you look at the millions of spins or hands played on a typical slot machine and the millions of throws of the dice at a craps table.

Notice that I didn't mention blackjack at all. Slots, video poker, and craps are all independent trial games. What has happened in the past does not affect what will happen in the future. Blackjack is not an independent trial game. The odds constantly shift as cards are dealt out of the shoe. In blackjack, what has happened in the past does affect what will happen in the future. That's the basis for card counting.

I can see another reason why some people have difficulty believing this fallacy is false. It sometimes seems like I'm contradicting myself. On the one hand, I'm saying that I can't tell you what's going to happen on a slot or video poker machine. Then, on the other hand, I'm saying that certain video poker and slot machines pay back more than others in the long run. If everything is random, how can I say with near certainty what a machine will pay back?

Let's say I have a paper bag and I put three ping pong balls--one white, one red, and one blue--in it. I close my eyes, reach into the bag, pull out a ball at random, note its color, replace it in the bag, and repeat the process. I keep track of the total number of times I've picked each color of ping pong ball.

Some weird things may happen in the short run, especially if I hit a long streak or dearth of one ball early on, but as I do this more and more, the number of times I've seen a color divided by the total number of draws will get closer and closer to 1/3.

If you put in many more colored ping pong balls--each color corresponding to a particular outcome--and you put in the appropriate number of each color to represent the likelihood of getting that outcome, you have a low-tech representation of a slot or video poker machine. If you perform our experiment with that paper bag, your results will keep getting closer and closer to the population in the bag.

I can't tell you what's going to happen next, but I can tell you what the overall results will look like.

John Robison

John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

You may hear John give his slot and video poker tips live on The Good Times Show, hosted by Rudi Schiffer and Mike Schiffer, which is broadcast from Memphis on KXIQ 1180AM Friday afternoon from from 2PM to 5PM Central Time. John is on the show from 4:30 to 5. You can listen to archives of the show on the web anytime.

#### Books by John Robison:

The Slot Expert's Guide to Playing Slots
John Robison
John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

You may hear John give his slot and video poker tips live on The Good Times Show, hosted by Rudi Schiffer and Mike Schiffer, which is broadcast from Memphis on KXIQ 1180AM Friday afternoon from from 2PM to 5PM Central Time. John is on the show from 4:30 to 5. You can listen to archives of the show on the web anytime.

#### Books by John Robison:

The Slot Expert's Guide to Playing Slots