If you’re reading about casino strategy, you’re bound to come across the word “volatility.” Most often, you’ll see it in connection with slot machines (as described in our slots volatility guide), but it’s an idea that applies to all casino games. Like return-to-player (RTP), online casino volatility is a property that makes one game different from another on a mathematical level.
As we said in our previous lesson on probability, every casino game ultimately boils down to odds – that is, payouts and win probabilities. RTP and volatility can both be calculated starting from a game’s odds.
RTP describes how much you expect to walk away with on average after a long time playing. However, volatility describes the swings you’ll experience in the short term.
Put another way:
If RTP is your destination, then volatility is the journey.
Games with high volatility are those that feature large payouts that hit less often.
Conversely, games with low volatility are those where you’ll win more often but receive smaller payouts.
Sometimes, the same game even gives you higher and lower volatility options. For instance:
- Betting on a number in roulette or a hardline in craps is a high-volatility play.
- Betting on a color in roulette or the pass line in craps is a low-volatility play.
Signal and Noise
Volatility isn’t just a casino concept. It comes up any time you have a pattern combined with randomness. Another way of saying that there’s a signal (the pattern) and noise (the randomness).
Think about listening to the radio when there’s some static on the channel. When the signal is strong and the noise is weak, it’s easy to hear the music. But if there’s a lot of static, it becomes harder to make out the signal.
Here’s another example from everyday life: the change of seasons versus the weather. Over time, it gets colder as winter approaches and then warmer again in the spring. That’s the signal.
But the weather also changes from day to day, pretty much at random. That’s the noise, and it often drowns out the signal in the short term.
So, even in the fall, Tuesday might be much warmer than Monday. If you didn’t know what month it was, you might not realize that winter was on the way.
If you imagine an alien planet with even more volatile weather, people living there might not notice the seasons at all because the swings would be so much bigger.
On the right, you see what a year-round temperature graph might look like for places with different levels of volatility in the weather.
Why Volatility is Enjoyable at the Casino
Most of us ordinarily prefer predictability to volatility. We want to hear the radio. We want to feel confident we’ll have nice weather for our summer barbecue.
Investors especially don’t like volatility. They want to know that their investments will perform well.
They hate volatility so much that they’re willing to accept a lower return to avoid it. The riskier the investment, the higher the expected return serious investors need in order to consider it.
And yet, at the casino, players often seek out games with high variance. Why is that?
Well, casino gamblers like variance for the same reason that investors don’t: because the noise can outweigh the signal.
Investments make money on average. It’s only because of volatility that investors sometimes turn a loss.
On the other hand, when you’re playing casino games, you’re paying for entertainment. On average, your bets will lose money. It’s the volatility that sometimes allows you to win over short periods.
If it weren’t for volatility, playing a 95% RTP casino game would mean you would always get 95 cents back every time you bet a dollar, for a guaranteed loss of five cents. Where’s the fun in that?
Think of your casino games like a roller coaster. Just rolling slowly downhill would be no fun. It’s the ups and downs that make it exciting, even though you’re probably ending up lower than where you started.
That said, you don’t always want the maximum possible variance in every game you play. A big part of casino strategy is picking the right level of variance for your budget, session length and desired experience.
The Math Behind Volatility
Casino guides often talk about volatility in subjective or relative terms. For instance, “craps is more volatile than blackjack,” or “Buffalo is a high volatility slot.”
However, it is possible to put a number to it. When slots manufacturers submit their games to regulators for approval, one of the things they need to specify is the volatility index (VI).
VI is the square root of another number called the variance.
Variance tends to be a big number and can vary widely, so taking the square root creates more convenient numbers. For instance:
- The variance for most slots is around 25 to 225
- This corresponds to a VI range of 5 to 15.
Many table games have VIs even lower than 5. On the other hand, playing a draw lottery like Power Ball or Mega Millions when the jackpot is over $1 billion has a VI in the tens of thousands.
Volatility Indices for Common Casino Games and Bets
Here’s a comparison of some common bets you might make at the casino, from least to most volatile.
|Game/Bet||Approximate Volatility Index|
|Even Money Bets (e.g. Roulette Red/Black)||1.0|
|2-1 Bets (e.g. Roulette columns or dozens)||1.4|
|Horn Bet (Craps)||2.1|
|Caribbean Stud Poker||2.2|
|8-1 Bets (e.g. Roulette corners)||2.8|
|Video Poker (Jacks or Better)||4.8|
|35-1 Bets (e.g. Roulette numbers)||5.8|
|Online Slots||5 to 15|
Calculating Volatility Index (Advanced)
If you know all the probabilities and payouts for a game, you can calculate the VI yourself. It’s a little involved, so feel free to skip this part if you’re not math-inclined.
Here it is as a formula:
Where Zi are the game’s possible prizes (including stake), Pi are the corresponding probabilities, and Rtp is, of course, the overall RTP of the game.
And here’s how to do it step-by-step if you don’t understand that notation.
Step 1: Square the payout, including stake
Start with the game’s top prize. Figure out the total payout on a $1 bet, including the bet itself. Then square that number.
For instance, an 8-1 result on a $1 bet pays out $9. Squaring that gives you 81.
Step 2: Multiply by the probability
Take the number from Step 1 and multiply by the probability of getting that result.
For instance, if you were 5% likely to get that 8-1 result, you’d take 81 x 5% = 4.05.
Step 3: Repeat for every prize and add the results
Work your way down the payout table, repeating that calculation for each prize. Add the results together.
Let’s say our game had only two payouts. The one above, and a 4-1 prize that’s 10% likely to hit. Repeating the calculation for that gives us (4+1)2 x 10% = 2.5.
Now, we’d add those two numbers together to get 2.5 + 4.05 = 6.55.
Step 4: Subtract the square of the RTP to get the variance
To get the game’s variance, we now just have to subtract the square of the RTP.
For our hypothetical game, the RTP is 95%. (Refer back to the last lesson for how to calculate that.)
Squaring that gets us 0.9025, so our variance is 6.55 – 0.9025 = 5.6475.
Step 5: VI is the square root of the variance
If we want VI, not variance, we take the square root of that result.
Here, our VI would be the square root of 5.6475, or 2.376.
Casino School: Probability
This has been Probability Lesson 3 of our four-part Casino School series. Next up is Probability Lesson 4: Calculating Probability.