The Gambler's Fallacy

You've probably never heard of the gambler's fallacy. If not, read on because if you're not familiar with it, you've likely fallen into its trap and it's costing you money.
The gambler's fallacy is a condition that besets nearly everyone at various times in their lives. However, as befits the name, it is famously frequent in gamblers and it is, of course, a fallacy.
It was discovered by psychologists and has been a topic of study for decades, and the "ol' perfesser" here is going to give a lecture on it. Get out your notebooks.
Gamblers are a superstitious lot - poker cheat poker players less so than slot junkies, but we've got our nutty beliefs. One of them is that "we're due" to fill a flush, that it's "our turn" to suck out on the river or that it's "about time" for us to rack up a 200BB win.
We think this because we haven't filled a flush the last 20 draws, or hit a miracle river card in the last 40 hours of play or had a multiple rack'em up session in months.
It is this belief that is the gambler's fallacy. And the reason it's a fallacy is that, no matter what you think, you're not due for anything, ever!
There is no increase in the likelihood that you will fill your flush just because you've missed the past 20. Having gone a hundred hands without hitting a two-outer has no bearing on the next river you pay to see.

Thought I was due there.

I've raised this topic with lots of players, some quite skilled. Almost invariably they tell me that they are due, that they have to fill that flush - eventually. When I push them, they typically give me some justification, a rationale that looks, for all the world, like it makes sense.
"Look," they say, "I'm not stupid. I know that the probability of hitting my flush hasn't really changed but I also know that things have to work out in the long run. It's getting to be a 'long run' because I haven't hit one in, like, forever.
"So it has to come along because things have to even out. In fact, that's what you math guys tell me. All this luck crap evens out in the long run."
If this feels familiar, if you've said (or thought) something like this, you're probably sitting there nodding your head. After all, the belief that the flush card is bloody, freakin' due is compelling, absolutely haunting.
But is it true? Nope. It's false. The awful truth is that things do not have to even out. The cards are under no moral stricture to treat you fairly.
And the long run is really marked cards, really long. Most people, poker players included, have trouble grasping this compelling mathematical truth.
As a result, they are likely to increase bet size or make marginal calls because they are convinced they are due. The real problem, of course, isn't the belief; it's acting on it that puts dents in your bankroll.
Playing cards are made of plastic. They do not have memories. They do not "know" that they just failed to fill your flush, again. They are being shuffled by a dealer or a machine and the order in which they emerged in the past has no bearing on their order in the future.
Each hand is independent of all preceding hands. The probability of filling a flush is not changed by previous outcomes.

Seriously. Thought I was due.

There are also, obviously, situations in poker where events are dependent on each other. If you saw someone flash a heart when they mucked their hand and you're on a flush draw, you know there are only eight hearts left in the deck.
Hence, the probability of hitting your draw is changed by previous events and the way you want to play the hand just changed subtly. Oddly, virtually everyone understands this second "dependent" case, but many, perhaps most, just can't wrap their brains around the first "independent" one.
And you don't have to be gambling or at a poker table to see this. Here's a study done some years back.
People were asked to guess which of two lights on a computer screen would come on. They were told that the sequence was random, that the light on the right was as likely to come on as the left.
Virtually every person playing this "guessing" game showed the gambler's fallacy. The more often one light came on, the more likely they were to predict the other side.
If there was a really long run, like seven lefts in a row, they picked the right side on the next trial nearly 100% of the time! When asked why, they said that the other one was "due."
Yes, things do tend to even out in the long run. But note the two qualifiers in that sentence, tend and long run.
"Tend" means just that, tend. It doesn't mean "must."
"Long run" implies an infinitely long run for mathematical certainty and, frankly, you don't have that kind of time. You should not expect, in any relatively short run of events, to see the outcomes conform to theoretical expectations.

Gambler's fallacy is most seductive, but it is a fallacy.

They are under no obligation to do so. In fact, they might not even be close.
The gambler's fallacy is most seductive, but it is a fallacy. Don't get suckered into thinking that you're "due" for anything other than random outcomes. And don't throw money into a pot based on this belief.
The probabilities have not changed and they don't give a fat flying fig how many times you missed your flush or how many times you've had to buy in already.
OK, if your brain doesn't hurt now, tune in again next week because I'm going to introduce another topic that you also need to understand, and it's even more counterintuitive.
It's the principle known in probability theory as "regression to the mean" and every good poker player understands it - although maybe not explicitly.