Slot Math - Grid

 

In this article, I will focus on how to build the mathematical models of grids, but there is something special we need to know first, which is grids often have a feature called cascading. Slots with cascading features can cascade winning symbols and drop more symbols on the reels, which means there could be multiple wins in one spin and there are countless situations after cascading. For those slots, using Excel to build the model and get the final RTP is not very practical. We need another tool to help us get the RTPs, which is the Simulation

Slot simulation normally means using programming to simulate slots that we designed to get more data like hit frequency, variance, and RTPs for some special slots, such as grids with cascading feature

Most programming languages can be used for slot simulation. Personally, I prefer using Python, because it is very convenient to read data from Excel documents by using Python, which can lower the difficulties when you are adjusting configuration tables and par sheets for a better game experience

So, in the following content, I will show you how to build the mathematical model of grids first, but it is more like a concept and double-check methods. In practical works, you have to know at least one programming slot for the mathematical calculation of grids. Then, I will show you an example of slot simulation which uses the same data we used in the first example

Example Game Rule

The example we use today is a 6-5 grid slot. There are 11 symbols in total. 9 of them are standard symbols, and 2 of them are feature symbols, which are scatter and multiplier respectively

When there are 8 to 9 or 10 to 11 or more than 12 same symbols on the window, players can get a win. These symbols would cascade after the win, and there would be some new symbols to fill the blanks

If players have at least one multiplier symbol on the reel and get a win, all payouts in this spin would times the sum of random values on multiplier symbols

Step 1. Configuration table

In this example, there are more basic settings than what we had in the previous article. Besides the landing rate of each symbol, we also need to set the rate of the random value of the multiplier symbol. Of course, you can combine them, like setting different landing rates of multiplier symbols with different random values

The rate of random value is pretty easy, you just need to make sure the sum of all rates is equal to 100%

When it comes to the rate of symbols, there is more than one way to do it. I will show you one way for the classic slot and one way for the video slot

For classic slots, building 6 fixed reels is not the difficult part. You can add the symbols on the reel based on the numbers you want, and use the RAND() function and filter in Excel to get the random order

                                This is only part of the reels. The intact one is much longer

Then, it would be a little tricky. We need to use an array formula to calculate the number of events that there are different numbers of these symbols on the reels. Do not remember to click "Ctrl + Shift + Enter" to activate the array formula. After that, you can list all possibilities and use the PRODUCT function to times the corresponding rate for the hit frequencies and expectations

For video slots, this step could be much easier. Owing to the wining requirement has nothing to do with the order of landing symbols. All positions on the window can be seen as the same position, which means we can use only one rate to control all reels

Step 2. RTPs

I am prone to use one big par sheet to calculate the RTP of the grid slot. Mostly because I do not expect to only use Excel to calculate the final RTP of the slot with the cascading feature. Using one big sheet can help me simplify the steps of the calculation

This chart is not a must for mathematical modeling of grids. If you just want to know how to get the RTP of the grid slot, you can skip the modeling process in Excel and focus on simulation. Actually, more and more companies pay more attention to the simulation skills of slot designer

However, if you are interested in mathematical processes, I believe building a big chart like this would be very interesting for you, let along you can use it to check the correctness of the simulation before you add the cascading feature

I would like to add these check parts to the simulation. You cannot be too careful in the calculation

In this example, we can find that the RTP in Excel is 54.55%, which is the RTP without the cascading feature. Now, we build the simulation in Python for this example and check what we can get after 1,000,000 spins

The result of the simulation is close enough to what we get in Excel. There are not likely to be some simulation errors

Then, we can turn on the cascading feature, and you can find the result in the picture below:

In this case, we can say that the RTP of this this grid slot is 71.38% to 76.41%

Of course, this RTP is much lower than what we need. So, next step is change the par sheet and configuration table for a better game experience. Also, you can add more data statistic in the simulation, such as variance and hit frequency