Slots Mathematics

Slots are immensely popular in both land-based and online casinos. They offer players a wide variety of exciting opportunities to win, with the progressive jackpot being the ultimate aim. As a player continues to play slots games, he/she could come across a host of various ways of winning, such as normal wins, scatter wins, holds and nudges, free spins, gambles and bonus games. In each of these there is a complex system of slots mathematics at play – and your chances of winning vary greatly according to what stage of the game is activated. For example, in bonus games you stand a much higher chance of winning than in normal play.

When we refer to the ‘chance of winning’ we draw heavily on the theory of probability, which is an essential part of gambling mathematics. To work out the probability of a particular win on a slots machine, you firstly need to use the Combin Funcion to calculate the number of ways that exist to form a particular combination, and then divide that figure by the total number of ways that exist to form any possible combination on the reels. For example, if you worked out that there are 250 ways to get a particular combination, and that there are a total of 250 000 possible combinations that a particular slots game could return, then the probability of your chosen combination coming up is 250/250 000 = 0.1%.

The Payout Percentage of Slot Machines

The payout percentage of slot machines is programmed into their electronically-programmable read-only memory (EPROM), and these figures can only be changed with proper authorization and approval from the relevant gaming authorities in a particular country/region. The correct procedures must also be followed to change the values for online slot machines. Slot machines typically have a payout percentage of between 85% and 98%, depending on the casino and the type of machine. The average house advantage for slots games has been calculated to be around the 9% mark.

Scaling Returns

The slot machines in most land-based casinos operate on a system of scaling returns; that is, it’s more worth your while to play higher denominations, as the payout percentage of these machines tends to be higher than that of the lower denomination machines. In other words, higher denomination machines have a smaller house edge than the lower denomination machines. However, online casinos tend to keep their house edges – and thus payout percentages – consistent across all denominations.

Read about the casino game mathematics of popular games, or have a look at out Gambling Mathematics glossary.