Return-to-Player & Variance

return to player
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The principles described in the post can be applied to every game of chance/casino game in which the punter goes against the house.

If we put it differently: all games where a casino collects bets and pays out winnings.

Every casino has a house edge, and they love your money!

There are thousands of slots and games waiting for you!

The most famous of these games are slot machines, Roulette, Blackjack, and Baccarat, but there are many others.

Speaking of slots, you will find different themes ranging from sports to popular fictional books and even famous characters from movies. For the old-school slot enthusiasts, there is always a fruity slot which is fairly easy to grasp.

Welcome to the world of online casinos! When you open a slot, there are details mentioned about the number of reels, ways to win, and even RTP.

Most of the punters probably know that these games are configured to give casinos some advantage in the long run. Otherwise, the casino owners would lose their money. This advantage is also known as the “house advantage” or “house edge.” Do remember this term as you are going to see it in reviews, comments, and even in this post.

House advantage is determined by the rules of each game and the winning rules in case of victory. If these rules are applied on numerous turns (sometimes even hundreds of thousands of times), casino owners can be sure that the sum of the bets collected will exceed the total amount of winnings paid. Statistics work in favour of the grand casino in the long run. Don’t let that bother you!

Despite the long-term statistics that are unfavourable to you, it is quite common to come to the casino, play, win, and walk away with the winnings.

The main reason is that your visit to a casino only consists of tens or hundreds of spins. In this case, there are not enough elements in the sample for the statistics to be met.

The result of your visit to the casino is then more determined by chance (or by your luck, if you want). It is this chance that helps lucky players win and beat the statistical advantage of the casino, although it is only in the short term.

To increase your chances of “beating statistics,” it is very important to know two basic parameters of each game: the Payout Ratio and the Variance. This is what we will focus on in this elaborate and informative article.

We will, then, tackle here the following points:

Are you ready to skim through the most informative article? Brace up for a lot of information on Return To Player.

Return To Player (RTP)

The RTP (also known as the Player Return Rate, Payout Percentage, or Redistribution Rate) of a game of chance or gambling is the long-term statistical rate of the total money earned divided by the total money wagered.

The opposite of the Payout rate is the casino margin. The casino Margin is calculated as 100% minus the Payout rate.

If the payout rate is 95%, then the casino margin is 100% – 95% = 5%.

Let’s take a closer look at the payout rates of some of the most popular games of chance.

  • Roulette RTP

At European Roulette, the probability of winning by betting on the black color is 18 (of black numbers) divided by 37 (of all numbers, don’t forget the zero). The payout is twice the bet.

The Roulette Payout rate is then 2 * 18/ 37 = 0.973 = 97.3%. The margin is then 100% – 97.3% = 2.7%. The Roulette set is configured to have the same RTP for all types of bets (color, number, etc.).

  • Blackjack RTP

As Blackjack rules can vary from casino to casino, it is obvious that the RTP may also differ. But generally, a blackjack game played by a player using the basic Blackjack strategy gives an expected RTP of about 99.5%.

At live and online blackjack, the expected RTP changes as the dealer distribute the cards in the game. In this case, the RTP is generally between 95% and 102%, depending on the cards left in the “Shoe.” This is exploited by the card counters – players who estimate the actual RTP of the blackjack game and try to bet high if the RTP is above 100%, to make a long-term profit.

  • Slots RTP

The Slots RTP is, in most cases, between 90% and 98%. The slot machine payout percentage is determined by the symbols on the virtual reels, the Paytable and other specific rules apply to each particular game.

Here’s how the payout rate is calculated:

Let’s imagine that you choose a slot machine to win a few tickets. For 24 hours, you and other players bet on this machine. Let’s assume that the sum generated by the bets reaches $6,000 and that the sum given to the players is $5,000.

To calculate the payout rate to players, you just have to do the following calculation: (5000/6000) x 100 = 83%. This slot machine, therefore, has an RTP of 83%. This percentage remains an average, so players can win more as well as less.


Return on Investment (ROI) is expressed as a percentage. It allows comparing investments taking into account the money invested and the money earned (or lost). It also allows you to orient your investment choices to the most profitable one.

roi or rtp

Here is the calculation of ROI:

Return on investment = (Net income or loss / cost of investments (bets))*100

In simple terms, ROI is the percentage of the money you earned divided by the money you “bet” to play.

Let’s imagine that you play 50 turns at $5.50, starting at $200. You will play for 50×5.50 = $275 in total.

Let’s say that at the end your bankroll, you have is $240. It means you won $40 for 275 played.

So, ROI = 40/275 (x100) is about a 14.5%

If you want to calculate the RTP of the last wager, it would be:
RTP = 5.50/275 (x100) = 2%

Hence, the only difference between ROI and RTP is that the latter is calculated only for one spin (and only ONE). In contrast, the former is calculated for an entire gambling period (say, for example, an hour, or a day).

Variance (Volatility) of Gambling

In simple terms, the variance (also called volatility) of a game determines how quickly your capital changes when you play the game.

When you play a low variance game, you often win small wins. In this case, your bankroll changes quite regularly, although, unfortunately, generally downwards.

In the case of a high variance game, you lose in a large majority of spins, but when you win, you win big. From time to time, the gradual declines are replaced by a significant gain.

The statistical distribution of gains can also describe the volatility of the game. As they are usually proportional to the size of the bet, this is the payout expressed in multiple bets.

When you bet on color at roulette, all winnings are paid as a double bet. When you bet on a single number, all winnings are paid 36 times the bet amount.

The volatility of slot machines is a little more complicated. You can make many different winning combinations.

For this reason, it is not so simple to describe the Variance of slot machines by a single digit, and game providers use only descriptions such as “low,” “medium or average,” and “high” for measuring the Volatility of their slot machines.

To illustrate, suppose a game without Variance and with a 98% RTP. In this game, a bet of €1 would bring in $ 0.98. The result of each round would be determined, and winning the game would be close to impossible.

Of course, no one would cherish the game, but it illustrates the fact that a high RTP is not all that matters.

Mathematical View of Gambling

It is vital to understand that the payout percentage expresses the expected payout of a single spin.

Suppose you bet $100 on Roulette and you win $1,200. Then you keep playing and bet 12 times $100 = $1200. The RTP must be used separately for each spin. In this case, the expected statistical profit of the casino would be ($100 + $1,200) * (100% – 97.3%) = $1,300* 2.7% = $35.1.

Kindly note: 97.3% is the RTP of European Roulette. If you continue to play with your previous winnings, then you should expect to lose more than the previously declared home edge of the game. Most players place bets on their previous winnings over and over again, losing some of the money each time.

If you want to be a wise punter, you need to distinguish between the RTP of the game (which only applies to one spin) and the expected return of the betting system.

The betting system is also determined by how the punters play throughout your stay at a casino or your entire session at an online casino. This includes the game selection, its variation, and settings, the size of your bets, and the decisions about stopping the game.

In the real world, if players place bets using their previous winnings, they lose even more. The RTP of a poor betting system can fall well below 50%. Even for blackjack – a game with a 99.5% RTP. As you will see going further, the RTP of bad betting systems is almost close to 0%.

mathematical view of gambling

The optimal betting system is one that has the same RTP as the game played. To do this, you should avoid placing bets using the money you have already won.

Note that Roulette is a very good game for this system because you can choose the odds of your bet.

Now we will demonstrate a very straightforward betting system. Note how the variance of the game affects the expected return of the betting system.

Imagine two players, X and Y), each of them showed up at a casino with a whopping hundred dollars.

Player X placed a bet of $10 on a number in the game of roulette.
Player Y placed a bet on a particular color.

Each of them left the casino if their funds exceed $500 or if they lose all their money. We simulated both players a million times, using a simple software routine with a random number generator.

Player X left the casino as the winner in 14.8% of his attempts. His average win was $648, and he played 16 rounds on average. It means his betting system’s RTP was approximately 95.19%.

NOTE: The RTP is calculated as a ratio of total gains to net losses. Net earnings are calculated at 14.8% * ($648 – $100).

The losses are calculated as the following: $100* (100% – 14.8%). Hence, ($648 – $100) * 14.8%) / ($100* (100% – 14.8%)) = 95.19%.

Player Y only managed to win in 5.15% of his attempts. His system had an average of $500 of “winning” funds and a total RTP of 21.42%. On the other hand, player Y thoroughly enjoyed playing much longer – on average, 274 laps.

From this valid example, you can make out that the variance of the game significantly affects your chances of leaving the casino as a winner. Player X’s system RTP was 4.4 times higher than the system RTP used by player Y.


Here are the most important things to remember:

  • The gambling payout percentage applies to only one spin. Your expected actual return will be lower due to the return of your previous winnings.
  • You lose statistically on every bet. The fewer bets there are, the less statistical profits there are for the casino.
  • The RTP of a betting system depends on RTP, the variance of the game, the size of your bets, and the rules when to go and whether you should continue playing.
  • Games with high Variance are generally more feasible. The biggest advantage of significantly higher Variance can easily beat the advantage of a slightly higher RTP.

Choose a slot wisely and always check the RTP. It is the most important factor that a high roller would check before playing for real money.

Of course, lady luck may knock on your door occasionally, but you must be a wise player and select the game according to its RTP.

Low rollers should especially skim through the details because they are new to the industry.


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