In this article, I will introduce you how to build the mathematical models of video slots with free game features/scatter symbols

The biggest difference between classic slots and video slots is the configuration table. Classic slots use fixed reels, while video slots use rate to control which symbols would land on the reels

Step 1. Configuration Table

Firstly, we need an initial configuration table for the model process. The rate means the chance that the particular symbol lands on reels. So, the total rate should be 100%

The table can be configured directly using percentages or X/10,000

Step 2. Calculate the Rates

There are two rates need to be calculated

One of them is the chance of landing on reels. All standard symbols need to add the rate of wild symbols because wild symbols can be seen as any standard symbols

Another rate describes the chance when symbols do not land on reels. You can get results by using 100% minus upper rates

Step 3. Calculate the RTP of Standard Symbols

These steps are relatively more simple. You just need to use the PRODUCT function to times the corresponding rates of each combination

Follow the upper steps, we can get the RTP of standard symbols in the free game too

In this example, the configuration table of the base game and free game are the same. So, they have the same standard symbols' RTP

Step 5. Expected Free Game Times

Owing to the stable triggering chance of free games, we can use Infinite series summation to get the expected free game times


Step 6. RTP

Finally, we can get the total RTP of this slot

1.1452 is much higher than the limitation of RTP. We need to change the configuration table to control it

The RTP of the base game is the standard symbols' RTP in the base game, and the counterparts of the free game need to times expected free game times

After that, we have an intact mathematical model of a video line slot, and we can start simulating the slots and changing the configuration tables to provide the best game experience