A bit of inspiration came today as I heard that some big lottery pot was as high as $640 million here in the U.S. I’m not a gambler, and I will continue to abstain from this event as well. Although, I wouldn’t mind having a big pile of money like that. A lot of folks, especially here in Texas, enjoy spending a few bucks a week gambling on the various lotteries we have. If you just spend 5$ each week on gambling, that ends up being $260 a year. When your budget is as tight as mine, that’s nothing to brush off, haha!
More to the point, a lot of people look at statistics in some strange ways. We tend to do this automatically, across all cultures, throughout our species. The gambler’s fallacy comes into play here when we think that enough losses will lead to a win. Let’s look a few simple problems to help elaborate this.
Bob is playing a game with me that uses a 10 sided dice. Every time he rolls a 10, he gets one dollar. Every other time he pays me a quarter. Clearly the odds are in my favor! However, in the past 9 rolls, he has not rolled a 10. So Bob thinks “surely if the odds are one in ten, and I have not seen a 10 in the last 9 tries, the last roll will be 10!” Well, unfortunately for Bob, that’s now how it works. It turns out, as most of us know, that regardless of how many times you have rolled the dice before, it will always remain a 10% chance.
The way the fallacy works is actually our mistake in addition and mutual exclusivity. Here’s a new example to elaborate this point. A man owns a cinema and hires a bunch of high school kids to clean the theaters in the evenings. The owner notices that the employees only show up to work 20% of the time! This makes him angry, but he decides to simply hire 5 of these kids. “Clearly,” says the owner, “if each one of them has a 20% chance of showing up, there will always at least be one of them here! Because 20% x 5 = 100%!”
As I said before, just because one result does not occur (person A, B, C and D didn’t show up to work) it in no way influences the outcome of another independent variable (person E didn’t show up either). The simple answer is… hire people who show up to work! Also, remember the when variables are independent, their order or presence does not influence other factors.
One last classic example. Imagine I flip a coin four time and it lands heads every time. We know for a fact that the odds of someone flipping “heads, heads, heads, heads, heads,” is actually quite low (about 3% chance). So some people say, “ah ha, it will be tails.” Well not so fast. It is equally unlikely for someone to flip, “heads, heads, heads, heads, tails,” (about 3% chance). We must keep in mind that the odds of any combination 5 coin flips will always be about 3%, it just so happens that the order we see in my example is a pattern that we find recognizable and appealing. The coins have no memory of the flip before them, nor do they impact the flip that will come after them. If you haven’t thought much about statistics before, this may be a bit confusing, but I assume most of us understand this pretty well these days.
As for gambling, we see people justifying their behavior with “previous efforts.” The more time and energy you spend towards a particular goal, the harder it is to pick up and walk away from it. This is especially problematic when you have invested a large sum of money into a slot machine. You will be psychologically drawn to continue investing into it until you receive a payout. The gamblers fallacy and our justification of behavior has ruined a great deal of people.
From here I will begin posting a few bits of information regarding statistics and methods in psychology. In my next post, I will discuss variance and correlations in psychology!