The principles described in this article can be applied to almost any game of chance in which a player plays against the house. In other words, all games where a casino collects bets and pays out winnings. The most famous of these games are slot machines, roulette, blackjack and baccarat, but there are many others.
Most of you probably know that these games are configured to give casinos some advantage in the long run. Otherwise, the casino owners would lose money. This advantage is also known as the “house edge” or “house advantage”.
The casino’s advantage is determined by the rules of each game and by the rules of how much money is won in the event of a win. If these rules are applied over a large number of rounds (sometimes even hundreds of thousands of times), casino owners can be sure that the sum of bets collected will exceed the total amount of winnings paid out. The statistics work in the casino’s favor in the long run.
Despite the long-term statistics working against you, it is quite common for people to come to the casino, play, win and walk away with your winnings. The main reason for this is that your visit to a casino consists of only tens or hundreds of rounds of play. In this case, there are not enough items in the sample for the statistics to be respected. The outcome of your visit to the casino is then more determined by chance (or your luck, if you like). It is this chance that helps lucky players win and beat the casino’s statistical advantage, although this is only in the short term.
To increase the chances of “beating the statistics”, it is very important to know two basic characteristics of each game: the redistribution rate and the variance. This is exactly what we will focus on in this article.
Gambling and Redistribution Rate (RTP)
The payout rate (also known as the return to player rate, payout percentage or RTP) of a game of chance is the long-term statistical rate of the total money won divided by the total money wagered. The opposite of the payout rate is the casino’s margin. The casino margin is calculated as 100% minus the payout rate. If the payout ratio 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 Redistribution Rate
In European Roulette, the probability of winning by betting on the color black is 18 (# of black numbers) divided by 37 (# of all numbers, don’t forget the zero). The payout is 2 times the bet.
The roulette payout is then 2 * 18 / 37 = 0.973 = 97.3%. The margin is then 100% – 97.3% = 2.7%. The roulette game is configured to have the same RTP for all types of bets (color, number, etc.).
Since the rules of blackjack may vary from casino to casino, it is obvious that the RTP may also differ. But generally speaking, a blackjack game played by a player using the basic blackjack strategy yields an expected RTP of approximately 99.5%.
In live and online blackjack, the expected RTP changes as the dealer deals the cards in the game. In this case, the RTP is typically between 95% and 102%, depending on the cards left in the “shoe”. This is exploited by card counters – players who estimate the actual RTP of the blackjack game and try to bet high if the RTP is greater than 100%, to make a long-term profit. On the other hand, casinos also have the means to detect these card counters and prevent them from playing longer.
Percentage of Slot Machine Winnings
Slot machine RTP is generally between 92% and 99%. Slot machine payout percentages are determined by the symbols on the virtual reels, the paytable and other specific rules applied to each particular game.
Variance (Volatility) of Gambling
Simply put, 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 prizes. In this case, your bankroll changes fairly regularly, although, unfortunately, usually downwards.
In the case of a high-variance game, you lose in a large majority of rounds, but when you win, you win big. From time to time, gradual declines are replaced by a large win.
The volatility of gambling can also be described by the statistical distribution of winnings. Since they are generally proportional to the size of the bet, this is the payoff distribution expressed as a multiple of the bet. When you bet on a color at roulette, all winnings are paid out as double the bet. When you bet on a single number, all winnings are paid 36 times the amount of the bet.
Slot machine volatility 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 number, and game vendors use only descriptions such as “low”, “medium”, and “high” to measure the volatility of their slot machines.
We have discussed slots, their RTP, and their variance in more detail in a separate article. To learn more about this topic, see our article on how slot machines work.
Just to illustrate, let’s assume a game with no variance and an RTP of 99%. In this game, a €1 bet would pay €0.99. The outcome of each round would be determined and winning in this game would be impossible. Of course, nobody would like this game, but it illustrates the fact that a high RTP is not all that matters.
Expected return from a betting system
It is very important to realize that the payout percentage expresses the expected payout from a single round of play. Suppose you bet $100 at roulette and win $1,200. Then you continue playing and bet 12 times $100 = $1200. The RTP must be used separately for each round of play. In this case, the expected statistical benefit to the casino would be ($100 + $1,200) * (100% – 97.3%) = $1,300 * 2.7% = $35.1.
Note that 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 stated house edge of the game. Most players place bets on their previous winnings over and over again, losing some of their money each time.
If you want to be a smart gambler, you need to distinguish between the RTP of the game (which applies to only one round of play) and the expected return from your betting system.
Your betting system is determined by the way you play throughout your stay at a casino or your entire session at an online casino. This includes the selection of the game, its variant and settings, the size of your bets and decisions about stopping the game.
It’s hard to imagine the RTP of a betting system that only takes into account one player. That’s why we always run simulations with at least a million players to get reliable results. The expected return on a betting system can be defined as a ratio between the overall winnings of players who have managed to reach their “target”, and the net losses of players who have not been so lucky.
In reality, 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 an RTP of 99.5%. As you will see, the RTP of bad betting systems is close to 0%.
The optimal betting system is one that has the same RTP as the game being played. To do this, you should avoid placing bets using money you have already won. Theoretically, the easiest way to do this is to bet your entire budget in one round. Then continue betting until you win or lose a satisfactory amount of money. Roulette is a very good game for this system because you can choose the odds of your bet.
Example: Suppose you have €100 to play roulette and you settle for a win of €900. Placing €100 on a square (4 digits) is almost the optimal strategy in this case. Either you will leave the casino with a nice amount of money or you will lose €100. The biggest disadvantage of this approach is that you will only play for a very short period of time.
How gambling variance influences the expected RTP of the betting system
Now we will demonstrate a very simple betting system. Note how the variance of the game affects the expected return of the betting system. Imagine two players, each of whom has shown up at a casino with $100.
- Player X bets $10 on a number in roulette.
Player Y places bets on color
Each of them leaves the casino if their funds exceed $500 or if they lose all their money. We simulated the two 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 an average of 16 rounds. This means that the RTP of his betting system was 95.19%.
Note: The RTP of the betting system is calculated as a ratio of net wins to net losses. Net wins are calculated at 14.8 per cent * ($648 – $100). Net losses are calculated as follows : 100 $ * (100 % – 14,8 %). Therefore (($648 – $100) * (100% – 14.8%) / ($100 * (100% – 14.8%)) = 95.19%.
Player Y was only able to win in 5.15% of his attempts. His system had an average of $500 in “winning” funds and an overall RTP of 21.42%. On the other hand, Player Y enjoyed playing much longer – an average of 274 rounds.
From this example, you can clearly see that the variance of the game significantly affects your chances of leaving the casino as a winner. The RTP of Player X’s system was 4.4 times higher than the RTP of the system used by Player Y.
How the bet size affects the RTP of a betting system
Winning amounts in games of chance are usually calculated using the size of the bet. The overall payout rate of your betting system is therefore also affected by the size of your bets. The rule of thumb is simple: The larger the size of your bets, the higher the payout rate of your betting system (usually). We assume that all other betting system rules and parameters, including the initial bankroll, remain the same.
We will use roulette again to demonstrate the effect of bet size on the results of a betting system. Players re-enter a casino with $100 and leave if their bankroll reaches $0 or exceeds $500. Player X bets $20 and Player Y bets $5 each round. Both players place bets on the color (red or black).
After simulating one million instances of Player X, we found that 10.9% of them managed to reach €500. This equates to a PRT of 48.68% and an average of 84 rounds played.
On the other hand, out of one million instances of player Y, only 0.88% managed to win (an average of 706 rounds, RTP of 3.55%). If Player Y wants to leave the casino with €500, he has to win 80 more spins than he loses. It seems that having such a “run” in roulette is quite rare.
The statistics are clear in this case. When you place low bets on a low-variance game, you may play longer, but your chances of winning a satisfactory amount of money decrease considerably.
One of the opposite sides of the variance spectrum is a combination of a high variance game with high bets. Player Z came to a casino with $100 and decided to play roulette on a single number. The results of the simulation show that out of one million Z players, only 2.71% managed to win. However, each of the winners walked away with $3,600 (PRT of 97.4%). Each of the Z-players played exactly one trick.
Here are the most important things to remember about this article:
- The gambling payout percentage applies to only one round of play. Your actual expected return will be lower because your previous winnings will be put back into play.
- You lose statistically on each bet. The fewer bets, the less statistical benefit to the casino.
- The RTP of your betting system depends on the RTP of the game, the variance of the game, the size of your bets, and the rules on when to leave and when to continue playing.
- The variance of the game is determined by the size of the potential winnings as multiples of the bet. The more the individual wins, the higher the gambling variance (considering a fixed RTP).
- Games with high variance are generally more favorable. The advantage of a significantly higher variance can easily outweigh the advantage of a slightly higher RTP.
- The higher the variance, the greater the chances of turning small amounts of money into huge amounts of money.
- The larger the bets in a round, the higher the RTP of your betting system, given a fixed bankroll.
- If you play for fun, look for games with a high variance and place smaller bets. A few wins could lead you to the desired win, otherwise you will lose your entire budget. Keep in mind that you are making a compromise between the length of your game and the RTP of your betting system.