Home » Return to Player (RTP) - The Theory of Randomness

Return to Player (RTP) – The Theory of Randomness

Do professional players know when roulette, slots or blackjack are “hot” and use that to make a big profit? Or do sports betting pros know for sure that City will beat Manchester United in the upcoming derby?

The simple answer is NO. The myth of being able to predict such events has been around ever since people started placing bets but is to this day easily believable when you do not understand the core concept of gambling.

In reality, the income of a casino, a bookmaker, or a professional gamer for that matter is determined by just one figure, the Return To Player ( RTP). The factor is usually expressed as a percentage and the interpretation of this number often causes confusion. In this article, we’ll try to clear up a few things about what exactly RTP means and how it is calculated.

RTP, or return to player, is the average percentage of what players expect as a return on their bets and for example, on an RTP of 96%, you can expect in the long run a player gets on average £96 back on £100 in bets. Game RTPs should not be confused with winning probability, they are two different things, even though the winning probability affects RTP. Casino operators use it to calculate the revenue a game will generate in the long run. If the casino wants to make £40,000 in revenue on a 96% RTP game it needs players to wager £1,000,000 on it. Does setting up a casino still sound easy?

Casino operators make their revenue from the house edge, which is calculated: HE = 100% – RTP. Taking the example above, the house edge is 100% – 96% = 4%. They could lower the RTPs of their games to increase the house edge, which some providers offer, but then players would vote with their wallet and move to other casinos which offer the highest RTP.

GMBLRS examines the RTPs of almost every possible game available on the internet, and our site allows you to search for the best RTP-values in casino games and bookmakers [link to our bookers and casinos].

RTP: Putting it into Practice

The easiest RTP to understand is in lotto games. Imagine a lottery with 40 numbers (1-40) and players need to guess seven numbers correctly; so the lottery tip consists of seven numbers. Players bet on their favourite tip and the casino raises £10,000,000 in bets.

The casino might set the lottery RTP to 80%, which will give the casino a total of £2,000,000, all with no risk. The remaining £8 million will be split between the winning tips in a combination of completely correct guesses and those close enough to the drawn numbers. The casino can divide the £8,000,000 in any way they want. For example, paying out 50% / 25% / 25% to the top/middle/low tier winners with 7/6/5 correct numbers.

Now let’s assume with had 1/10/100 players guessing 7/6/5 numbers correctly. The £8 million will be then distributed accordingly. Note that while the casino pays out a large share of the total placed bet, it still as £2 million left as revenue.

  • The sole winner will take home 50%, which is £4 million
  • The winners from the second tier will each win an equal share of 25% of the £8 million, coming it at £200,000 each
  • The third group of 100 players will get the remaining 25% ( £2 million), each winning a still respectable £20,000.

The entire £10 million were funded purely by the bettors with the main part getting nothing back. But if the cost for a ticket was just £2 and one million players bought five tickets, then each spent just £10, hardly an amount that will bother them. The end result is happy winners, a satisfied lottery operator and the losing players got to dream what it would be like to win the lottery themselves.

In Toto games, RTP is calculated in a simple way; the bookmaker collects the bets and distributes x% to the players who made the correct bet. The higher the x, the higher the winnings of the players and in this way the bookmaker can offer bigger pots to entice the players. However, it must be remembered that bookmakers also have overhead costs and have to pay salaries, marketing costs, taxes and more from their house edge.

RTP in Fixed Odds Betting and Casino Games

Casino games and fixed-odds betting are also based on house advantage and RTP, but in these games, the RTP is calculated over an extremely long time. It can though fluctuate drastically over a short period, which is determined by the mathematical volatility of the game.

For fixed odds games, the RTP is calculated using the formula: odds * odds of winning. The probability should be set as a decimal number, i.e. 50% = 0.5. In fixed-odds games, the RTP is always theoretical, however, in the long run the RTP will align with the theoretical RTP. The game operators must have sufficient cash on hand as the RTP can temporarily exceed 100%, putting them temporarily in a loss situation.

Example – Coin Toss

Take, for example, a coin flip with a 50% chance of head or tails. The casino offers you a 19/20 odds for the correct guess for each of the two options. The theoretical RTP is then 1.95 * 50% = 97,5%. You bet for the game 5 times in a row. You will have a lucky streak and your return rate (or actual RTP) after this session will be a whopping 156%. So for a moment the casino has lost, but this doesn’t hurt them, because the longer they run this game the more real RTP will approach the theoretical RTP.

Example Sports Betting RTP

Let’s imagine the Manchester Derby – ManU vs City is this time expected to be flat and the odds of both home and away wins and draws are, according to the bookmaker’s best estimate, 33,3%. The bookmaker has set the following odds for the ManU – ManC game: 1: 9/5 X: 9/5 2: 9/5. Thus, the theoretical RTP for each odds is (2.80 * 0.33) = 0.924 = 92.4%.

In this example, the bookmaker would be happy to receive the same amount of bets on each possible bet – home win, draw and away win, in order to predict the inflow from this item. In betting, the theoretical nature of RTP is more unpredictable because no one can fully estimate the probabilities of a football match (although it is possible to make quite accurate predictions).

Imagine a situation where professional bettors have noticed that David de Gea’s concentration is not 100% good and that the professionals’ estimate the chance for a  City win at 38%. In this case, the theoretical RTP for the away win rises to 106.4%, and by playing City, the house advantage turns to the player. This is where the success of professional bettors lies; they can possibly calculate a more accurate estimate of the outcome of a football match, for example, and translate the theoretical RTP by more than one hundred percent.

It should also be noted that in this example, the probability of winning ManU will be lowered, which will actually give ManU bettors an even lower theoretical RTP. For a bookmaker, there is only risk in the bet if the stakes of the professional players are so high that the cash flow is heavily tilted towards City. In this case, the bookmaker may be forced to lower City’s odds.

RTP From the Player’s Perspective

It is always a good idea for a player to compete with bookmakers and casinos to get the best RTP. A professional player, on the other hand, will only play if the RTP is over 100%. The player edge (PE) is calculated using the formula (RTP -100%), which is the opposite of the house edge. If you want to be a professional gambler and make a living from gambling, you need to make big bets because the player’s theoretical profit is calculated using the formula RTP * wagered amount – wagered amount. Some of the best betting pros achieve an RTP of 103% – 105% only, thus, if you want to earn £30 000 per year with a 103 % RTP, you have to wager at least £1,000,000 during the year. Even if you don’t aim at becoming a professional, you can still easily find the best RTP-friendly games for you.

Slot RTP

Casino games often have different odds of winning and winning odds. For example, on Dead or Alive 2, the two scatters pay 2x your bet. The RTP value is the sum of the probabilities of any winning combinations in a single round and their odds. The typical RTP for slot games is 95-98%, but the best slot games reach over 99% RTP. In addition, some slot games have well under 95% RTP, so you should consider slot selection based on your own chances of winning, you can filter slot games based on RTP value with GMBLRS’s handy slot-listing.

Imagine playing Rich Wilde and the Tome of Madness, which has an RTP of 96.59%. You spin with a £1 stake per round. You play 100 rounds during the session, so your total betting amount is £100. Then the theoretical benefit of the house expressed in money terms is (100% – RTP * £100) = £3.41%. Of course, your actual win / loss for the session may be something else, you might have won £1,000. However, for a casino, this doesn’t matter in the long run, the more game rounds are played, the more likely it is that the actual RTP approaches the theoretical RTP.

Note that the RTP of slots may vary based on the mathematical model a provider is using. For example, in a jackpot slot, increasing the jackpot will improve RTP, it could even raise it above 100% (however, winning is unlikely, a large jackpot win will only increase the RTP value, not the winning probability). In addition, game providers offer their games with multiple RTPs, giving the operators a range to choose from, e.g. default RTP is 96.50% but the game is also offered at 94.50%. The exact RTP is always noted in the help files. While the games run seemingly similar, the lower RTP has quite an impact on your playtime.

Plus, some slot games may have an internal slot optimal strategy. This is typical of slots with reel locking capability. How well a player knows the correct locking strategy can significantly affect the RTP value.

Table Games RTP

For table games, the RTP is calculated using the same formula. That is, the sum of the probabilities of different winning opportunities multiplied by their probability of occuring. For example, roulette has 37 numbers, but guessing the correct number gives a factor of 36 [35/1]. The probability of a single number in a roulette round is 1/37 = 0.027 = 2.7%. Thus, the RTP in Roulette is 97.30%. This RTP comes true, whether you play any form of roulette betting. Without special circumstances, you will not be able to get a positive RTP on Roulette.

In Blackjack [internal to Blackjack], the theoretical RTP is higher based on what variant is played and how many decks are used. The standard RTP is 99.6% for single-deck Blackjack. However, this required you to play blackjack with an optimum strategy. By counting cards and modifying the optimization strategy, RTP can go up to over one hundred [internal to card counting]. This has been utilized by e.g. 21 movies by MIT students.

On table games, it is typical that RTP depends very much on how well a player can play the game. The luck of the casino is that random players who visit the casino are recreational Blackjack players. Of course, changing the odds and rules of the casino could worsen the Blackjack RTP, but that would quickly see players leaving. Due to the high RTP of the base game and certain special circumstances, Blackjack is one of the few casino games where professional gaming is possible

Main Conclusions

– RTP can be either real or theoretical; in lotto and Toto games it is real, in fixed odds games it is theoretical.

– House advantage is HE = (100% – RTP)

– RTP may also be above 100%; in this case, the player’s advantage is PE = (RTP – 100%)

– RTP is influenced by the player’s skill, for example in card games and sports betting.

– On slot games, the player’s choices are usually unaffected and have no impact on the RTP, except in special cases.

– The longer the game, the closer the real RTP is to the theoretical RTP

– It is recommended to choose games from providers with the best possible RTP.

Final Words

Enjoying your gaming sessions or placing bets on sports events and lotteries should always be the primary goal while keeping your spending in check to not go overboard. Especially slots are simply games of chance, hence, thinking too much about RTPs or strategy (which does not exist) will just spoil the fun. Still, it is advisable to choose slots with an RTP of 96% or higher as they will give you the most playtime in the long run.

On the other hand, tables games such as Blackjack should involve some strategic thinking and sports bets should be well researched. Overall, any type of gambling or betting will always have a house edge that puts the operator at an advantage, after all, they have to stay profitable to be around for the foreseeable future. With that in mind, remember that gambling should be seen as entertainment that will cost you money just like any other form of leisure activity.

Let’s Play!

Your GMBLRS Team