Mathematics of casino games – RTP and volatility

Mathematics is probably one of the last things you want to think about when playing casino games; but believe me – you should! The good news is that I am not talking about advanced mathematics with complex formulas and calculations. Grasping the concepts of RTP and volatility in casino games is the core of the mathematics of these titles.

So, it would help if you learned to do the math (pun intended) before wagering real money in any online casino. Of course, the same goes for those who play free casino games. Mathematics, in terms of RTP and volatility, can help you understand what you can expect from a game and how to build a strategy that promises better returns in the long run.

As I said before, casino volatility and RTP are probably the most essential things about the mathematics of casino games. That's why I've created this Vegas Expert guide based on my knowledge and years of experience with the concepts.

On this page, you will learn all about Return to Player and how it affects your gameplay. I'll also explain the concept of volatility, how it differs from RTP, and why it matters at all.

What is RTP?

You probably guessed that RTP is an abbreviation, but did you know it stands for Return to Player?

Still, this term won't mean much to ordinary people, even in its extended form. For experienced players, this indicates how much they can expect in return after a gaming session on one of their favorite online casino games in the long run. This is the simplified description because there's more to this gambling mathematics than meets the eye.

More precisely, the RTP values, which are expressed in percentages, are provided by the software developers based on their test spins/rounds, usually measured in millions. Some providers base their RTP percentages on several billion spins/rounds. So, the main point here is to understand that this is a theoretical indicator.

In simple words, an RTP of 98% would mean that the machine pays out $98 for every $100 bet on it. Those missing 2% represent the house edge, i.e., the theoretical profit the machine makes for the casino.

Of course, things aren't so simple in practice. More on that comes right up next!

How does RTP affect players?

Before discussing the impact of RTP on players, I should note that not all casino games are the same. So, you can't expect a good RTP slot machine to offer the same value as a good RTP blackjack title.

For example, it's typical for modern online slots to have RTPs of 95% to 96%. Anything above 96% is a plus, while anything below 95% should be double-checked before trying.

Other casino game types have different average RTPs. For example, blackjack has a theoretical Return to Player of around 99%. Baccarat has above 98%, video poker above 99.5%, keno around 70%, and so on. Moreover, I'd like to remind you that some games may also have individual bets with different RTPs.

On top of that, you should know that the RTPs of free casino games are often not the same as the RTPs provided by specific casinos for real money play. We have a Return to Player percentage recommended by the provider acting as a default RTP. Still, online casinos can change it according to their needs. To stay safe, you should open the help file or check the game's info before playing it.

Still, you should never forget that this is a theoretical value. At times, a game may pay out much more than expected, and then during a so-called "cold" period, it may pay out significantly less.

What is volatility?

Your casino math will be incomplete if you skip the volatility. So, the volatility indicates the value of prizes you can expect and their frequency.

Generally, the volatility is described as low, medium, or high. Of course, there's no official table accepted by all brands, so it's not unusual to find providers labeling their products as low-to-medium or medium-to-high volatility. Some also use rating scales from 1 to 5 or 1 to 10.

Regarding this gambling math term, you should know that providers usually have titles with various volatility levels, unlike RTP. In other words, you don't have to focus on one provider because "they have high or low-volatility releases". As for the RTP, some developers use (almost) identical theoretical Return to Player percentages for all games.

How does volatility affect players?

Volatility definitely has an impact on gameplay. You can develop a suitable strategy when you get familiar with this value and understand what it represents. As I noted, most providers divide their products into low and high-volatility titles.

There's no right or wrong choice here. Everything depends on your preference and whether you're playing with a free casino bonus or your own money.

Low volatility slots and other casino games usually suggest lower wins, but this is only for the average wins you can expect in a single gaming session. So, it's not impossible to hit a big win in a low volatility game. However, you will see low wins more frequently, and don't be surprised to see many wins worth less than one time your current stake.

As expected, high volatility titles give you a chance to win bigger prizes on average, but the wins occur less frequently. So, it's fair to say that these are riskier options. Another thing that I should mention here is that high volatility games tend to have more bonus features. This is especially true for online slots.

If you have dilemmas about which option suits you best, I suggest trying medium-volatility casino games. That's right, you read that well. There are medium volatility games, too, and they bring the balance some players want regarding casino games' volatility.

RTP vs volatility

RTP and volatility in casino games have many things in common.

First, they both represent theoretical values based on tests conducted by the software provider behind them and are critical for measuring potential payouts. Second, this is technical information that many players relate to mathematics and don't pay much attention to. That's wrong because you can learn a lot about a game when you know these things.

Of course, these terms are not the same.

According to many experts, the Return to Player is more important than volatility. Some people may disagree with this claim, but I'll show you that it makes more sense.

The RTP is represented by specific percentages that go into decimals (exact numbers from 1 to 100 and two-digit decimals). On the other hand, the volatility level is described with three words – low, medium, or high. As I said, some providers have user rating scales, but even they have numbers from 1 to 10 and no decimals. Basically, RTP is more specific, while volatility is usually a broader term.

Furthermore, thanks to RTP, you can determine which game pays more than the others (in theory). Once again, I will mention the example with the slots. If one slot has an RTP of 95.52% and another promises 96.33%, the second has a better value for the player if the RTP is the only thing we discuss.

Other (non)mathematical things you should consider

In addition to RTP and volatility, there are other things players should consider when selecting a casino game. They are not necessarily related to mathematics but affect the outcome and expectations.

Maximum win limit

For instance, we have the maximum win limit as a factor. The best providers have titles in which the maximum winning amount is clearly stated. Usually, these values are represented by a maximum multiplier applied to the player's total bet.

Some online casino games have maximum win limits below 1,000x. Still, it's not uncommon to find releases with max win caps of 10,000x or even 25,000x stake, especially slots. Obviously, you want to be able to win as much as possible for the same stake.

Jackpots

Next, there's the opportunity to win a jackpot prize. Not all options provide this opportunity. Many players are attracted to such rewards and choose them even if the RTP is seemingly lower and the volatility is high. This is especially true for releases with progressive jackpots.

These slots usually can deliver massive rewards worth thousands or even millions of dollars. Typically, they have lower RTPs – 94%, 93%, or even 90% – but users hunting these life-changing prizes don't mind.

Conclusion

Before playing any online casino game, it's wise to check its RTP and volatility.

These values can tell you much about what you can expect from a title. Some are good for casual players, while others are popular among high rollers. One thing that's important to remember is that these are theoretical indicators based on tests that include millions of rounds.

In other words, just because you play a high volatility game doesn't mean you can expect many big wins after long sessions. Or that low RTP games will leave you with less money than you had at the beginning.

In any case, I recommend playing titles from reputable brands with visible RTP and volatility information. When you do this, you can set your expectations straight and make an informed decision rather than randomly picking a game and hoping for the best.