Mathematics Behind Casino Games: Terms Return-to-Player Value, Volatility, Variance, and Hit Frequency Explained

Casino Games

As we all know, casino games are based on mathematics and chance. Yes, they look magical, but it’s actually mathematics. Whether you’re trying your luck at a casino or other online casinos, you’ll always find games that all work the same mathematically. They work with RNGs (Random Number Generators).

It’s the online pre-programmed mechanisms that generate random numbers in real time. And these numbers are converted online into symbols on slots or numbers. But they’re purely random and you have no influence over them. The mathematical metrics that describe how online casino games work are RTP, volatility, and hit frequency. And we will explain it in this blog post.

RTP (Return-to-Player)

Casino Games

This figure shows what percentage of deposits the game returns to the players. For example, the RTP value of 95% means that 95% of the player’s deposits go back to the player in the form of winnings on average. So it is not 100%, because the casino always has the house edge. This makes RTP the exact opposite of the house edge. To calculate the house edge of the game, you have to subtract the percentage of RTP from 100%

Every game has an RTP figure, but most often this figure is used in relation to slots because the given payout is easier to program in slots. In games like poker, the player can influence the result with clever strategies, but not at all in slot machines. The real RTP in poker can depend significantly on the given RTP. RTP values ​​are set by developers who developed the casino game.

They calculate this value for 10,000 games, so it’s about the money that the game pays out in the long term, over a longer period of time. You don’t have to expect it from a single game. On the casino games market, you can find games with RTP values ​​of 70-99%. The lowest RTP values ​​are found on slot machines in gaming arcades. Slots in online casinos usually have RTP values ​​between 92% and 99%. The higher the RTP, the higher the winnings.

Volatility

Volatility is the term from financial mathematics that is also used today in relation to casino games. Unlike the RTP, this factor says nothing about the amount of winnings (the RTP does that!), but shows how often the particular casino game pays out winnings. For example, some slot machines pay out less often, but have high jackpots.

Others, on the other hand, pay out frequently, but the amounts are small. The first slot machines have high volatility, and the second have low or medium volatility. Slot machines with high volatility have a lower probability of winning and are associated with higher risk. Slots with low volatility do not make players rich, but are suitable for players who want to protect themselves. There are also slot machines with medium volatility.

Variance

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We have already written that the volatility indicator is calculated based on several thousand or even millions of spins. Therefore, you do not have to expect to win 95 euros within an hour on a slot with 95% RTP. The real value that describes the payout and probability of winning the slot is called variance.

Hit frequency

Hit frequency shows how often you win in a game. This is close to the volatility. The slot’s hit frequency of 30% indicates that you can win on average after every third spin.


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