In the previous article, I already introduced the basic compositions of slot and some mathematical concept. Since this article, I will introduce the mathematical model of different types of slots and features
This article would start introducing the mathematical model of simplest 3-1 slot
The mathematical modeling process of slots can be seen as the process to get proper RTP. There is only one strict standard which is RTP should be mo more than 100%. Other RTPs are all ok, but in most cases, players can have best game experience when the RTP is about 95% to 97%, and that would be the target when we are building the mathematical model
Example Introduction
In this article, I will use a 3-1 slot with only two symbols and no feature as the example
Symbols on each reel are arranged as the picture above.
When symbols landing one each reels are same, players can get corresponding payout.The combinations are:
Combination 1: {Symbol 1, Symbol 1, Symbol 1,}, payout: 2
Combination 2: {Symbol 2, Symbol 2, Symbol 2,}, payout:12
(Black parts in upper picture are symbols 1 and white parts in upper picture are symbols 2)
As we can see, each reel has 5 symbols in total. So, there are 5 landing result of each reels. What is more is that each symbol landing on the windows can be understand as the independent event
Which means you just need to use the amount of total events of symbols landing on three reels divided by the counterpart of events that match the combination to get the winning chance of the combination
Then, you just need to use the chance times the payout, you can get the expectation of this combination
Finally, summing up all expectations, you can get the RTP of the slot
The calculation steps are as follows：
Step 1: Calculate the events amount
Total events: 5 * 5 * 5 = 125
Combination 1: 4 * 4 * 3 = 48
Combination 2: 1 * 1 * 2 = 2
Step 2: Calculate the winning chances
Combination 1: 48 / 125 = 38.40%
Combination 2: 2 / 125 = 1.60%
Step 3: Calculate the expectation
Combination 1: 38.40% * 2 = 76.80%
Combination 2: 1.60% * 12 = 19.20%
Step 4: Sum up all expectations
RTP = 76.80% + 19.20% = 96.00%
Modeling in Excel
Usually, we would finish the modeling process in excel
In the example, You can use the calculation steps shown in the picture below to complete the modeling process in Excel
Of course, getting the RTP is not the end of modeling process. We still need to find out the best settings to get the perfect game experience, but once you understand the upper content, you already understood the basic concept of slot math
You can try to change the symbols on each reels and try to get similar RTP by changing the payouts as practice
In following articles, I will introduce you how to build the models of more complex slots. The calculation methods would be different, but the steps would be similar
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