Random Events, Independent Events, and Probability

It’s normal for a person to look for patterns in random events. You could say that the human brain is hard-wired for this because of evolution.

In some respects, this search for patterns can be helpful. It’s the reason you can read letters and words on a page. It’s also the reason you can recognize someone’s face. These are complicated patterns, but the human mind has no trouble with them.

The problem for gamblers is that the human brain spots simple patterns where none exist.

That’s the topic of today’s post – random, independent events and how they affect probability.

Examples of Patterns That Aren’t Really There

Here’s an example of spotting a pattern that doesn’t really exist:

You come down with a cold, and you start drinking orange juice on the first day of your symptoms. A few days later, your cold symptoms go away. Your brain concludes that there’s a cause and effect relationship here that doesn’t exist.

Why doesn’t it exist?

Because colds almost always go away on their own after a few days anyway. The orange juice isn’t necessarily the cause.

This kind of false attribution of cause and effect can also be considered “anecdotal evidence.” It’s common on social media these days. Everyone can find a story about someone who suffered some kind of horrible after-effect of a vaccine, for example, even though the statistical data indicates that most people have a mild reaction – if any – to most vaccines.

What does this have to do with gambling?

We’re getting to that.

Most Bets Are Random, Independent Events

Most of the time, when you’re gambling, you’re dealing with random, independent events. Many gamblers see false patterns in their betting results and give those patterns significant meaning.

When a croupier spins a roulette wheel, the result is random. Despite what you’ve seen in movies like Casablanca, the casino has no control over the outcome. The result is also unaffected by the results of previous spins.

When a craps player rolls the dice, the result is random. Casinos don’t have any control over how the dice land. The results of a roll of the dice are also unaffected by what happened on previous rolls.

When a blackjack dealer gives you a hand, the result is also random. Depending on how long the game has been played, the result is usually mostly unaffected by the results of previous hands. But the composition of a random deck does change, which means that blackjack does have a pattern of sorts.

But it’s small, and most people aren’t skill enough to pick up on it.

Gamblers See Patterns Where None Exist

If you’re at a roulette table and paying attention, you might notice that the ball has landed on a black number 4 times in a row. Your brain immediately tries to find a pattern. Depending on your temperament, you might think that black is more likely to come up again on the next spin because it’s hot. Someone else might assume that red is more likely to come up since it’s “due.”

If you’re at the craps table, and a shooter has been on a hot streak for several throws, you might assume his hot streak will continue. Someone else might assume that he’s bound to lose eventually. Either assumption leads you to draw a conclusion about the probability of the next event.

If you’re playing real money blackjack and the dealer has busted several times in a row, you might think that you’re playing in a hot deck. Someone else might assume that the dealer is overdue for a win.

But all these assumptions are wrong.

And if you bet more money based on these perceived patterns, you risk losing a lot of money.

What Really Happens to the Probability of an Event in a Betting Game

The formula for an event’s probability doesn’t change based on what happened on previous bets. In fact, the formula for probability is a simple one.

To find the probability of an event, you simply divide the number of ways you can achieve that event by the total possible number of events.

Here’s where people get confused:

They know that it’s unlikely that the ball will land on black 5 or 6 times in a row, so after a few spins, they think the probability changes for the next spin.

But you’re not betting on the ball landing on black 5 or 6 times in a row. You’re betting on the ball landing on black on the next spin.

And none of those numbers have disappeared from the wheel. You still have all 38 numbers, and 18 of them are still black.

Systematic Approaches to Gambling Based on Perceived Patterns

You’ve probably read about the Martingale System so often that you’re tired of it, so I’ll use the Reverse Martingale as my example of how perceived patterns affect gamblers.

You might already know that the Martingale System advocates doubling the size of your bet after a loss.

It doesn’t take long to predict that the Reverse Martingale System advocates doubling the size of your bet after every win.

With either system, you have a win goal. In the Martingale, the win goal for each sequence is a single betting unit. You keep doubling your bet after each loss until you’re finally ahead by a single unit.

With the Reverse Martingale, you set an arbitrary goal for how many betting units you hope to win. For example, you might decide you want to win $100 in a session where you’re betting $5 per spin.

To achieve this, you’ll double the size of your bet every time you win, so your betting progression will look like this:

1. $5
2. $10
3. $20
4. $40
5. $80
6. $160

All you need to do is win 6 times in a row, and you’re up by $160, achieving your win goal.

The idea behind the Martingale System is that you benefit when the inevitable turn in fortune changes from the color that’s been coming up.

The idea behind the Reverse Martingale is to benefit from the inevitable hot streaks that occur.

But neither system works in the long run, because at the end of the day, you’ll still only win 47.37% of the time.

In the short run, either system will seem like it’s working. You’ll have the frequent winning session using the Martingale System, and you’ll see the occasional winning session using the Reverse Martingale.

But the losing sessions will eventually average out so that you’re seeing the kind of losing results that the probability would predict.

False Patterns in Other Games

Here’s an example from poker:

Poker players often expect things to happen again if they’ve happened recently. If you’re playing poker for a couple of hours at the casino, and you make your straight draw 2 or 3 times in one day, you’re going to overestimate your probability of drawing to a straight on the next hand.

On the other hand, if you miss your flush draw several times in a row, you’ll start to think it’s nearly impossible to hit a straight.

If your pocket kings get cracked several times in a row, you’ll turn into one of those boring Texas holdem players who are always complaining about how pocket kings are a lousy hand.

But each hand of poker is an independent event. The cards don’t have any memory of the previous hands. The dealer shuffles the deck prior to each hand. The cosmos isn’t conspiring against you or rooting for you.

I’ve seen poker players suggest that you can’t play a rush if you don’t acknowledge it, but the truth is – the rush is illusory.

Random events don’t mean anything at all.

We have rules for how they affect our betting, but the patterns that you see don’t exist.

I read a great book about poker which suggested that you adopt the following mantra:

“There is no pattern.”

What Should You Do With This Knowledge

If you’re a recreational gambler, you only have one thing you CAN do with this knowledge:

Accept that in most gambling games, the other party has a mathematical edge. Then act accordingly.

This means not gambling with money you can’t afford to lose. It means not trying to win enough money to pay the rent.

It means being okay with losing some money in the long run.

Conclusion

At the end of the day, the best way to look at your gambling is as an entertainment expense with a cost like any other entertainment expense. Sometimes you’ll win, but if you keep at it long enough, you’ll eventually lose your money to the grind.

Just don’t fall into the trap of thinking you’re recognizing patterns that will somehow help you win money in the long run.

Such patterns don’t exist.