The Mathematics Behind Slot Machines: Payout Percentage

Edward Cunanan
3 min readMar 4, 2023

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Hit frequency is a key concept in the world of slot machines, and it can have a significant impact on the volatility of a particular game. In simple terms, hit frequency refers to the rate at which a slot machine will produce winning combinations, and it is typically expressed as a percentage.

For example, a slot machine with a hit frequency of 20% would produce a winning combination on approximately one out of every five spins. Conversely, a slot machine with a hit frequency of 5% would produce a winning combination on approximately one out of every 20 spins.

While hit frequency can vary widely between different slot machines, it is typically linked to the volatility of the game. In general, slot machines with a high hit frequency will have a lower volatility, meaning that they will produce more frequent, smaller wins. On the other hand, slot machines with a low hit frequency will have a higher volatility, meaning that they will produce less frequent, but potentially larger wins.

It’s important to note that hit frequency is just one factor that can impact the volatility of a slot machine. Other factors, such as the payout percentage, the size of the jackpot, and the number of pay lines, can also play a role in determining the volatility of a game.

Ultimately, the choice between a high hit frequency, low volatility game and a low hit frequency, high volatility game will depend on your personal preferences as a player. Some players prefer the thrill of chasing a big jackpot, while others prefer the steady stream of smaller wins that come with a higher hit frequency.

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Regardless of your preferences, it’s important to approach slot machines with a realistic understanding of their odds and outcomes. While hit frequency can impact the volatility of a game, it is just one factor to consider when choosing which slots to play. By playing responsibly and making informed choices, you can enjoy the thrill of slot machines without falling into the trap of chasing losses or false beliefs about how the games work.

One key mathematical concept in slot machines is the payout percentage, which refers to the amount of money that a machine will pay out over time relative to the amount of money that is wagered on it. For example, a slot machine with a payout percentage of 95% will pay out $95 for every $100 that is wagered on it, on average.

The payout percentage is determined by the machine’s programming, and it is typically set by the casino or gaming authority that regulates the machine. While different machines can have different payout percentages, most machines in a given casino will have similar payout rates, as these rates are typically regulated by gaming authorities.

Another important mathematical concept in slot machines is the random number generator (RNG), which is a computer program that determines the outcomes of each spin. The RNG uses a complex algorithm to generate a random sequence of numbers that corresponds to the symbols on the slot machine’s reels.

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