Slot Math - Wild

 

In slot games, there is a common feature called wild symbols. Wild symbols can be seem as any other symbols except other feature symbols, such as scatters and multipliers

We have introduce the basic modeling process of line slots in the past articles. In this article, I will introduce which part need to be changed when the wild feature is added

Feature Introduction

In most slots, wild symbols do not have their own combinations and payouts. The main function is being seem as other symbols, so that the hit frequencies of other symbols could be higher

For example, in the picture below, if the symbols on second reel is not symbols J, this payline do not match any combination and players can get no payout, but if there is a wild feature added and the second symbol on this payline is wild symbol, it would match the {J,J,J,J,J} combination

                                             

The blue part is one of the payline

Also, wild symbols can be used in multiple paylines, when they go through the same position. Like in the picture below, there is blue and yellow two payline. Both of them go through the second row on reel 2 and reel 4. Symbols on other positions are totally different, but when those two overlap place have wild symbols, both payline match their combinations

Mathematical Modeling - Classic Slot

The example used in this article is the 5-3 slot which has 3 symbols and one wild feature. Its reels are arranged as picture below

Then, we should use COUNTIF to measure the amounts of symbols on each reels, but what is needed is that we should consider the impacts of wild symbols, which means the landing event is the sum of symbols themselves and wild symbol. The results are shown bellow:

For example, there are two symbol J on each reel, but the landing event is the sum of two symbol J and one wild symbol on each reel

The following steps are similar to the basic mathematical modeling process

In this example, wild symbols do not have its own combinations and payouts, so there would be no need to calculate their RTP. If the wild symbols have combinations, you need to list all possibilities and calculate their RTP respectively

Mathematical Modeling - Video Slot

The method to deal with the wild symbol is not much different between the classic slot and the video slot. Considering the wild when calculating the probability of the symbol appearing or the number of events is enough. The specific steps are shown in the picture below: