Volatility in Gambling – What It Is and How It Works

Sometimes, when you’re reading about gambling—especially when you’re reading about gambling probability and/or slot machine games—you’ll run into the word “volatility.”

It’s an important concept if you really want to understand what’s going in the casino gambling world.

In this post, I’ll explain the concept of volatility in gambling and how it works in plain language that anyone can understand.

Volatility Measures the “Roller Coaster”

When you’re gambling over any length of time, you’re going to see your bankroll go up and down. You can think of this as the roller coaster. The idea is that you have a mathematically-predicted outcome that will come to pass eventually.

But the line from A to B isn’t a straight line; it’s a jagged line.


You’re going to see ups and downs based on your wins and losses.

Volatility is what makes you reluctant to walk away after you’ve won. After all, if you’ve already won this much, who’s to say that you won’t continue to see big wins or even bigger wins?

Gambling games have varying degrees of fluctuation that you can expect in your bankroll because of them.

And some gamblers prefer games that are more volatile, while other gamblers prefer games that are less volatile.

An Example of Differences in Volatility From a Movie

Years ago, Sydney Pollack directed a loose remake of Casablanca called Havana. It starts Robert Redford as a professional poker player, and the love interest is played by Lena Olin.

They meet on a cruise ship that has a casino, and a distracted Lena Olin is betting big stacks of chips on individual numbers. She doesn’t know what she’s doing, and she’s not even really paying much attention to what’s going on.

Redford, ever helpful, has her move her bet to one of the outside bets. I don’t remember if it was red or black, but I do remember that it was a color bet—red or black. It doesn’t matter, though.

She asks him, “Does this make it more likely that I’ll win?”


He replies, “No. You’ll still lose. It will just take longer.”

He’s actually mistaken about some of this. Yes, on an individual bet, you ARE more likely to win a single bet on red or black. The probability is 47.37%, in fact.

The probability of winning a single number bet, on the other hand, is 2.63%.

You’re clearly more likely to win the bet.

But the payoff for the two bets is dramatically different. You win 35 to 1 on a single number bet, as opposed to just winning even money on a bet on red or black.

The house edge for both bets, though, is the same. In that respect, the Redford character is right. If you play roulette long enough, you WILL eventually lose.

It’s inevitable.

But the single-number bets are more volatile than the bets on red (or black).

How the House Edge Works and How It Relates to Volatility

The house edge is the long-term expected loss rate on your gambling action. (Your action is the money that you risk.)

Over time, you’ll see wins and losses on any gambling game. Eventually, you’ll have so many wins and losses that you’ll be able to calculate a meaningful average of how much you’ve won or lost per dollar. The house edge is the mathematical prediction based on the likelihood of winning and the payout odds.

Going back to that roulette example, if you bet $100 on black, 47.37% of the time you’ll win $100, and 52.63% of the time you’ll lose $100.

To calculate the expected loss, you just multiply the amount you win by the probability of winning. Then you multiply the amount you lose by the probability of losing. Subtract one from the other, and you have the house edge.

$52.63 – $47.37 = $5.26

And since we’re using $100 betting units, it’s easy to convert that $5.26 into a percentage; obviously, it’s 5.26% of $100.

But you’ll never lose $5.26 on a single spin of the roulette wheel. It’s impossible. You’ll either lose $100 or win $100 (if you’re placing even money bets).

Even if you’re placing single-number bets, you can’t lose $5.26 on a $100 bet. You either lose the entire $100 or win $3500. (The house edge is the same, by the way).

The house edge only starts to “come true” after you get in a large number of bets. The more bets you’ve placed, the closer your results will get to the prediction. That’s called the “Law of Large Numbers.”

Volatility measures the short-term ups and downs along the way.


For example, if you win a $100 even-money bet 5 times in a row, which is entirely possible, you’ll be ahead by $500. That’s volatility in action.

If you win a $100 single-number bet twice in succession, which is also entirely possible, you’ll be ahead by $7000. That’s also volatility in action.

What Makes a Gambling Game Volatile?

Multiple factors make a gambling game “volatile.”

The first aspect of volatility is “hit frequency.” This is the mathematical probability that determines how often you’ll have a winning outcome.

If you’re playing a game where you’re going to win 47.37% of the time, that’s a high hit frequency, which generally makes for a low volatility.

If you’re playing a game where you’re going to win 2.63% of the time, that a low hit frequency, which generally makes for a high volatility.

The second aspect of volatility has to do with how much the bet pays off. On gambling machines, for example, different bets have different payouts that aren’t as related to the house edge as they are in roulette.

If much of the “return to player” is concentrated in outcomes that come up rarely, the game gets more volatile.

Video poker offers a good example.

Why Deuces Wild Video Poker Is a Relatively Volatile Game

The probability of getting a royal flush when playing Deuces Wild video poker is 0.002%. Since it pays off at 800 for 1, the return for this hand is about 1.6%.

The probability of getting four deuces is 0.02%. It pays off at 400 for 1, so the return for this hand is about 4%.

Between those two hands, you have 5.6% of the game’s overall return.

You’ll have a hand that wins nothing almost 55% of the time, and most of your return comes from the three of a kind. It pays off at even money, but you’ll see it about once out of every 3.5 hands. It comes up 28% of the time.

Most of the return of the game comes from the relatively common hand that’s basically a push (the three of a kind), and from the two hardest hands to get.

This makes for a pretty volatile game. Even if it’s a full-pay Deuces Wild game where you have an edge of 0.76% over the casino, you’ll spend most of your time on the game losing.

You’ll only see a royal flush once every 45,000 hands or so.


At 500 hands per hour, which is a pretty good clip, that’s 90 hours of play before you get a jackpot payout.

What’s happening to your bankroll during those 90 hours?

It’s getting smaller until you hit that win, but even then, it’s not a straight downward line. It’s a zig zag that’s trending downward, but with occasional spikes along the way.

The Most Volatile Games Usually Have the Highest Returns

I’m convinced that most casinos could offer games with break-even odds and still make plenty of profit.

Here’s how:

All they have to do is make sure they have a bigger bankroll than their players.

After all, compared to the average casino gambler, a casino has a basically infinite bankroll. Most casino gamblers will go broke before their long-term expectation of breaking even kicks in.

Volatility is also the reason professional gamblers need relatively large bankrolls. They need to avoid going broke long enough for their edge to kick in.

With everything I’ve discussed so far, do you think you can guess which casino games are the most volatile?

It’s the progressive slot machine games. Megabucks is the biggest game out there, and the jackpot starts at $10 million and grows from there.

But the odds of hitting that jackpot are 50,000,000 to 1.

At 500 spins per hour, you’d need to play for 100,000 hours before hitting that jackpot.

If you played full-time (40 hours a week), it would take you 50 years to hit that jackpot.

And for that entire 50 years, you’d be gradually losing money.

Conclusion

Most gamblers understand the house edge in a general sense. Some might have even heard of hit frequency and return to player.

But the concept of volatility seems to be beyond a lot of them. With any luck, after reading this post, you won’t be one of them.