An Introduction to Casino Slot Game Mathematics

In a more traditional wagering game like craps, the player knows that certain wagers have almost a 50/50 chance of winning or losing, but they only pay a limited multiple of the original bet (usually no higher than three times). Other bets have a higher house edge, but the player is rewarded with a bigger win (up to thirty times in craps). Theoretically, the operator could make these probabilities available, or allow the player to choose which one so that the player is free to make a choice. Different machines have different maximum payouts, but without knowing the odds of getting the jackpot, there is no rational way to differentiate.
Consider what happens when the reel moves through the window, as the reel brings the scattered symbol (S) into each of the 3 possible positions (top, middle, bottom). In Slot Designer we can implement the game with the script shown on the right, and the basic statistical report for the pay rules on the left. All modern machines are designed using pseudorandom number generators (“PRNGs”), which are constantly generating a sequence of simulated random numbers, at a rate of hundreds or perhaps thousands per second. As soon as the “Play” button is pressed, the most recent random number is used to determine the result.
Especially on older machines, the pay table is listed on the face of the machine, usually above and below the area containing the wheels. On video slot machines, they are usually contained within a help menu, along with information on other features. One reason that the slot machine is so profitable to a casino is that the player must play the high house edge and high payout wagers along with the low house edge and low payout wagers.
We can also see that as the chance of winning increases the prize won must correspondingly decrease to achieve the same RTP. There is no standardized method of performing these calculations, designing spreadsheets, or even terminology. Different countries and companies for example refer to symbols as icons, and reel strips as reel bands. This document therefore uses the terminology defined by Slot Designer, the commercial product of the author. Roll-up is the process of dramatizing a win by playing sounds while the meters count up to the amount that has been won. In Slot Designer the window is described with the following code, which first defines the maximum size of the window, then defines which locations within it are used.

While we could pay both, it is more common to pay on the highest win only, hence the common rule on slot games of “Highest win pays on each payline”. 123goal This is also referred to as prioritization, as we order the priority of the pay rules, and determine which single rule to pay. Rather than perform all the calculations as probabilities, we usually count the number of winning combinations over the game cycle and divide by the cycle at the end.

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