Mathematics of Gambling: RTP and House Edge Explained

Muhammad Kumar - Apr 29, 2022 | Reviews

Mathematics has always been in the casino's favor, now and in the future. If you play long enough, no matter how good or professional you are, you will lose.

No matter how lucky you are, the casino will always win in the long run. If you are wondering why, this article is for you.

Nick Hillier Yd5rv8 Wzxa Unsplash

The Mathematics of Gambling

Most movies about gambling idolise charismatic gamblers. These are "cool" characters and always play stylish games like blackjack or poker. Although they lose occasionally, they are lucky enough to win big when the time comes. They also spend time on the best online lottery sites in india and continue to look cool even when they're sitting in front of a computer. However, in real life, you will not see such gamblers. In fact, we can say with great certainty that there is no player who "has become a millionaire by gambling".

“Games against the casino always result in the casino winning in the long run because of the house edge,” says Tony Sloterman, Product Owner of Casino Bonuses Finder company. “This also applies to games like slots, roulette, poker, blackjack. There are some poker players who indeed make millions, but none of them play against the casino – these players play between each other. The best thing a casual player can do to increase their chances is to opt for games with high RTP and try to use casino bonuses to their advantage.”

So why does the casino always win in the long run? Isn't it possible for a lucky enough player to bankrupt the casino? Is it possible to make money by gambling? In this article on the mathematics of gambling, we answer all these questions.

RTP and House Edge: Most Important Terms You Need to Know

Every game you play in a casino - no matter the type - is based on mathematical foundations that are created by the casinos. Even relatively new slot machines have a history of over a hundred years. The history of card and table games goes back a few centuries. In other words, casinos have had enough time to perfect the maths underlying these games.

Casino Game


If learning that the games are designed by the casino isn't enough to convince you, we need to talk about the RTP and house edge. RTP is short for the word “return to player”. The “house” in the term house edge refers to the casino. Every gambling game in existence has RTP and house edge values. They are different (e.g., blackjack has high RTP – low house edge, keno has high house edge – low RTP, etc) but they always show the same thing: how much you will lose.

Let's try to explain with a simple example. The RTP of European roulette is 97.30%. Its house edge value, on the other hand, is 2.70%. This means:

  • If you deposit 100 INR on this game, you can win back up to 97.30 INR in the long run.
  • Your losses in this game (again, in the long run) will be 2.70 INR.

As can be seen, you can't earn more than your investment in the long run. You always lose money no matter what. RTP/house edge values ​​only determine how much you lose, not how much profit you can make. In order to make a profit, the RTP value must be positive (more than 100%) and the house edge must be negative (less than 0%). However, no existing casino game offers these values. The highest RTP belongs to blackjack and is just over 99% (with optimal gameplay). So even in this game, you will still lose money in the long run.

The Important Thing Is to Play Long Enough

The long-run here corresponds to an average of 1,000 spins/games. This means that your short-term gains or losses are not taken into account. When we say that you can win back up to 97.30 INR on a 100 INR investment, we mean this: if you deposit 0.10 INR for each spin and make a total of 1,000 spins, you will eventually see that you have won 97.30 INR in total. No matter how lucky you are, you will lose at least 2.70 INR. Moreover, these apply in an ideal scenario where everything goes well: if you're out of luck, you're going to lose a lot more.

Let's further explain by giving an example from the game of roulette:

  • The lowest paying bets in European roulette are red/black, odd/even, and low/high.
  • You bet on a total of 18 numbers on each of these bets. (There are 37 numbers on the wheel.)
  • So, your chance of winning is 48% (18 / 37)
  • These are the bets with the highest chance of winning at roulette. For all other types of bets, your chances of winning are below 48%.

If you have a 50% chance of winning a game, there is a chance that you will make a profit in the long run. The laws of statistics show that if you play such a game long enough, you will eventually win. But the same laws also say that in a game with less than 50% chance of winning, you will always lose in the long run. In any casino game, your chances are never 50%. Otherwise, the casino cannot win money. If you have a 48% chance of winning, your chance of losing is 52% – the casino is more advantageous. This applies to each and every casino game out there: your winning chance will always be lower than 50%.

Casino Games On Mobile

We Know What You're Thinking

We know what you're thinking: you know someone who has won a lot by playing slots, roulette, blackjack, or poker, right? The problem is:

  • A player who earns a high payout in a game will most likely continue playing and still lose his winnings. You will never know about it, as this part of the story is not told.
  • Even if the player moves away from the table, the same game will be played by hundreds of different players at dozens of different tables in the casino that night. The winnings of a single person will not affect the casino in any way.

Mathematics has always been in the casino's favour, now and in the future. If you play long enough, no matter how good or professional you are, you will lose – this is an absolute certainty. Therefore, you should view gambling as a casual pastime, choose games with high RTP to minimise your losses, and use gambling promotions wisely: that's all you can do.

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