Games of chance
Discovering payment ratio and variance
The principles described in this short article can be applied to virtually any game of chance where a player is playing against their home. Simply put, any game where a gambling establishment collects stakes and pays out possible jackpots. The most well-known of these video games are slot machines, roulette, blackjack and baccarat, but there are numerous others.
Most of you probably know that these video games are somehow designed to give the casinos a special advantage in the long run. Otherwise, the owners of the gambling establishment would lose money with them. This advantage is also known as home advantage.
The casino’s advantage is determined by the guidelines of the particular video game and by the payout rules in the event of winning. When these guidelines are applied over many, many rounds (often countless times), gambling establishment owners can be fairly certain that the quantity of wagers collected will exceed the total quantity of winnings paid out. The data works in the casino’s favor in the long run.
The main factor is that your visit to a casino consists of only numerous rounds of tens or hundreds of video games. It is this very opportunity that helps lucky gamblers win and beat the statistical advantage of the gambling establishment, even if only in the short term.
To increase the odds of “beating the statistic”, it really is important to understand two fundamental characteristics of any game – the pay ratio and the spread. That is exactly what we will focus on in this post.
We’re going to go over:
- Payout Ratio (RTP).
- Variance (volatility).
- RTP of a betting system.
- Conclusions.
Gambling and payout ratio (RTP)
The payout ratio (also called expected return, payout percentage or RTP – back to the player) of a gambling game is the long-term statistical rate of total money won divided by total money wagered. The opposite of the payout percentage is your house edge. Your house edge is calculated as 100% minus your payout percentage. If the payout percentage is 95%, then the house edge is 100%– 95% = 5%.
Let’s take a closer look at the payout percentages of some of the most popular gambling games.
Roulette Payout Ratio
At European Roulette, the probability of winning when betting on the black color is 18 (number of black numbers) divided by 37 (number of all numbers, don’t forget the absolute no). The payout is 2 times the bet.
The payout ratio of roulette is then 2 * 18/ 37 = 0.973 = 97.3%. The house edge is then 100% – 97.3% = 2.7%. The live roulette video game is set to have the same RTP for all types of bets (color, number, etc.).
Please note: American live roulette has an even much worse RTP and a bet type with a different RTP than all other bets. We go much deeper into this topic in our post on live roulette rules, betting and odds, so check it out if you want to find out more about roulette.
Blackjack RTP
Since blackjack rules can vary from casino to casino, it’s obvious that the RTP can vary as well. In general, however, a blackjack video game played by a player using the standard blackjack method offers an expected RTP of around 99.5%.
In online and live blackjack, the expected RTP changes when the dealer deals cards from the deck. In this case, the RTP is usually between 95% and 102%, depending on which cards are left in the “shoe”. This is exploited by card counters – players who estimate the actual RTP of the blackjack deck and try to bet high when the RTP is above 100% to make a long-term profit. On the other hand, gambling establishments also have methods to detect such card counters and prevent them from playing even more.
Slot Machine Payout Percentage
The RTP of slot machines typically ranges from 92% to 99%. The payout percentage of slot machines is determined by the characters on the virtual reels, by the paytable, and by other specific rules that apply to each specific game. If you’re curious about which slot machines have the biggest RTP, check out this Wolfie’s collection of the best paying slot machines.
What is Variance (volatility)
To put it simply, the difference (also known as volatility) of a game determines how fast your bankroll changes when you play the game:.
- If you play a low variance game, you will win small winnings quite often. In this case, your bankroll changes fairly evenly, though unfortunately usually downward.
- In a high variance video game, you lose in a large portion of the rounds, but when you win, you win high. Progressive dropdowns are changed from time to time by a big win.
Since they are typically proportional to the bet size, we are talking about the proliferation of jackpots expressed as a multiple of the bet. In roulette, if you bet on one color, all jackpots are paid out as twice the bet
The difference in slots is a little more complicated. You can hit many different winning combinations and win many different multiples of your bet. For this reason, it’s not so easy to describe the difference of slots with a number, and video game providers only use loose descriptions like “small”, “medium” and “high” for their slots.
We went into much more depth on the subject of slots, their RTP and the difference between them in a separate post. To learn more about this topic, read our article on how slots work.
The variation of a video game has a significant impact on your possibility of leaving a gambling establishment a winner. As a rule of thumb, “the bigger the difference, the better”:
- The first factor is that when you play a video game with high variation, it is much easier to win the amount that satisfies you in a video game round.
- The 2nd factor is that more rounds end in a loss, so you don’t wager as much of your previous winnings (which has an unfavorable effect on the RTP of your wagering system). Simply put, you lose faster.
- The 3rd factor is that if you can win a higher multiple of the bet, you can bet less to have a chance of winning the same amount. This in turn lowers the total amount of your bets and therefore your permanent losses.
For illustration, let’s assume a game with no variance and 99% RTP. In this video game, a $1 bet would pay $0.99. The outcome of each round would be fixed and winning in this video game would be difficult. Obviously, no one would like this video game, but it shows the reality that a high RTP is not all that matters.
Expected return on a betting system.
Let’s say you bet $100 on roulette and win $1200. The expected analytical casino profit in this case would be ($100 + $1200) * (100% – 97.3%) = $1300 * 2.7% = $35.1.
Note that 97.3% is the RTP of European live roulette. You can expect to lose more than the game’s previously stated house edge if you continue to play with your previous winnings. Most players place bets from their previous wins 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 video game (which only refers to a single round of play) and the expected return of your betting system.
Your betting system is figured out by how you play throughout your stay at a casino or your entire session at an online casino. This includes your choice of video game, its variant and settings, the size of your bets and when you decide to stop playing.
It is difficult to imagine the RTP of a betting system considering only one player. That’s why we always run simulations with at least one million players to get reliable results. The expected return of a betting system can be expressed as the ratio of the total winnings of players who hit their “target” to the net losses of players who were not so lucky.
Be aware that some sites confuse these 2 meanings. Their meaning of RTP can give the false impression that players statistically lose only a small portion of their money, which is the house edge of the video game. The rest of the money should then be redistributed among the winners (other players who won using the same method).
In reality, players lose more when they place bets with their previous payouts. The RTP of a bad betting system can drop 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 video game being played. Live roulette is a really great game for this system as you can choose the odds for your bet.
How the variance of the game affects the expected return of the betting system.
Now we will demonstrate a very simple betting system. Notice how the variance of the video game affects the expected return of the betting system. Imagine two gamblers, each of whom walks into a betting shop with $100
- Player X bets €10 on a number in live roulette.
- Player Y bets on a color.
Each of them leaves the gambling house if their bankroll exceeds $500 or if they lose all their money. We simulated both players a million times using a simple software application with a random number generator
Player X left the casino as a winner in 14.8% of his trials. His typical “winning” bankroll was $648 and he played an average of 16 rounds. This suggests that the RTP of his betting system was 95.19%.
Note: The RTP of the betting system is calculated as the ratio of net wins to net losses. Net wins are calculated as 14.8% * ($648– $100). Net losses are calculated as $ 100 * (100 %– 14.8 %). For this reason, (($ 648 – $ 100) * 14.8%)/ ($ 100 * (100% – 14.8%)) = 95.19%.
Player Y managed to win in only 5.15% of his bets. His system had an average “winning” bankroll of $500 and an overall RTP of 21.42%. On the other hand, Player Y had a much longer playing time – in typical 274 rounds.
From this example, you can clearly see that the variance of the video game significantly affects your chances of leaving the casino a winner. The payout percentage of Player X’s system was 4.4 times higher than the RTP of the system used by Player Y.
How bet size affects the RTP of a betting system.
So the overall payout ratio of your betting system is also affected by the size of your bets. As a rule of thumb, the higher the size of your bets, the greater (usually) the RTP of your betting system.
We will again use live roulette to demonstrate the effect of bet size on the results of a betting system. Player X bets $20 and Player Y bets $5 in each round of play.
- After replicating a million instances of player X, we found that 10.9% of them managed to reach $500. This represents an RTP 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 (about 706 rounds, RTP of 3.55%). If player Y wants to leave the casino with $500, he needs to win 80 more game rounds than he loses. It seems that such a “run” on live roulette is rather unusual.
In this case, the data is clear. If you place low bets on a low-difference game, you may bet longer, but your chances of winning a satisfactory amount of money decrease significantly.
On the opposite side of the difference spectrum is a mixture of a high variation video game and high stakes. Each of the winners went home with $3600 (RTP of 97.4%).
The proposed roulette betting system.
So a good betting system is a compromise between the odds of an acceptable win and its size, as well as the length of your stay at the casino.
What betting system should you choose if you want to play for a reasonable amount of time and have a great chance of winning at the same time? The variables are the size of a single bet and the type of bet (color/number).
The table contains the percentage of players who managed to win, the typical size of their win, the calculated RTP of such a betting system, and the average number of rounds played.
| Bet size | $0.5 | $1 | $2 | $5 |
|---|---|---|---|---|
| Number | 9,55% x $505RTP 42,76%3832 rounds | 13,9% x $511RTP 66,35%1083 rounds | 16,15% x $522RTP 81,27%292 rounds | 16,7% x $555RTP 91,21%52 rounds |
| Color | 0% | 0% | 0,0015% x $500 | 0,88% x $500 |
| RTP 0% | RTP 0% | RTP 0,006% | RTP 3,55% | |
| 7399 rounds | 3698 rounds | 1850 rounds | 706 rounds |
| Bet size | $10 | $20 | $50 | $100 |
|---|---|---|---|---|
| Number | 14,8% x $648RTP 95,19%15,9 rounds | 12,8% x $760RTP 96,88%4,73 rounds | 5,33% x $1 825RTP 97,12%1,97 rounds | 2,71% x $3 600RTP 97,40%1 round |
| Color | 5,13% x $500RTP 21,62%274 rounds | 10,85% x $500RTP 48,68%84 rounds | 15,94% x $500RTP 75,85%15 rounds | 17,9% x $500RTP 87,21%3 rounds |
As you can see, a much larger difference in bets on a number can easily beat bets on color, which are much larger in size. Note that if you bet $2 on color, your odds of getting to $500 are close to 0.
If your goal is to have a good time and have good odds, we recommend choosing a game with the highest possible difference and playing it with really small bets.
When it comes to live roulette and a $100 spending plan, betting $2–$4 on your lucky number seems to be one of the best options with a fixed bet type and bet size.
Note: This was a foundation for one of our roulette techniques. It is quite reliable and basic, however we have come up with and simulated other strategies that could be much better for you depending on your preferences. If you want to discover other fascinating methods to play live roulette, check them out.
Final words
Here are the most essential things you should eliminate from this article:.
- The payout percentage of games of chance only applies when considering a single video game round. Your real expected return will be lower due to re-betting on previous payouts.
- You will statistically lose on every bet. The fewer bets, the smaller the analytical return for the gambling establishment.
- The RTP of your betting system depends on the RTP of the video game, the variance of the video game, the size of your bets, and the guidelines on when to exit and when to continue playing.
- The variance of the game is determined by the size of the expected winnings as a multiple of the bet. The larger the individual wins, the higher the variance of the game (considering a fixed RTP).
- Games with high variance are usually more advantageous. The advantage of a significantly higher variance can quickly outweigh the advantage of a slightly higher RTP.
- The higher the variance, the greater the opportunity to turn small amounts of money into large amounts of money.
- The larger the stakes in a round, the higher the RTP of your betting system when you think about a particular bankroll.
- Look for high variance games and place smaller bets if you are playing for fun. A few wins could get you to your desired profit, otherwise you will lose your entire budget plan. Remember that you are making a trade-off between the duration of your game and the RTP of your betting system.