Slot Math - 3-3 Slot

The previous article introduced the probability calculation method of 3-1 Slots. This article will expand the window to 3-3

The increase of window size directly affects the fact that there is no longer only one payline. 3-3 Slots has a total of 3*3*3 = 27 ways to connect. Of course, not all ways have to be selected as paylines

This article will use Lucky Streak 3 launched by Endorphina as an example to introduce the mathematical modeling process of 3*3 Line Slots

Game Brief Introduction

Lucky Streak 3 is a 3-3 line slot with no special feature. There are 5 symbols in total, and when you get three same symbols landing on one payline, you can get corresponding payout. The paytable is as follow:

Considering there is only 3 column, there is only one combination for each symbol

This game have five payline, which is shown in the picture below:

                                           

The green part is the position of payline

What is more is that normally you can divide slot into two types. The classic slot and video slot. You can differ them by what control the landing symbols

If there is a physical reels, this is a classic slot

If landing chances of symbols are controlled by the rate of landing on the windows, it is a video slot

Two of them are very common in the market, and you can find both example in the following content

Mathematical Modeling - Classic Slot

If it is a classic slot, you should build 3 physical reels at the beginning. The order of symbols on the physical reels is fixed, and connected end to end

You can improve game experience by rearrange the order, but the RTP would be the same

In this case, you can use "COUNTIF" in excel to get the number of each symbols on each reels

Then, you can calculate the winning chance of each symbol's win. What is more important is that this winning chance only represent the theoretical hit frequency, the actual hit frequency need further simulation

Finally, use the winning chance times the payout, you can get the expectation of each symbol, and you can get final RTP by sum them up

If you have read my last article, which is about the mathematical model of 3-1 slot, you will find that even the window is larger and there are more than one paylines, the calculation steps are still the same, and you don't need to times the payline to get the total RTP

This is because in line slot, you need divide bet by the amounts of paylines. Timing the amounts of payline when you calculate the payout and dividing bet by them, you will get the same result. So, in line slots, the RTP of one payline is the RTP of the slot

Mathematical Modeling - Video Slot

The biggest difference between steps of classic slot and video slots is how to calculate the winning chance

Classic slot have limited symbols which means limited events. You can get the amounts of total event s and particular events to get the winning chances

In video slot, things would be much more easier. You just need to multiply the rate of this symbol on each reel to get the winning chances

Firstly, you should set the rate of each symbols. Of course you need adjust them before publishing the slot for the best game experience

Because some programming cannot calculate 0.1 properly, normally I would use X/10,000 to represent rates

Then, considering this 3-3 slot only have one combination for each symbol, you can calculate the RTP drectly

Last but not least, in most cases, when the rate of a video slot is equal to total amount divided by the symbol amount of a classic slot, they would have same RTP

Taking last article as an example, we get the following RTPs by using the classic slot method in those two cases

When we using rate which is equal to the total amount divided by the symbol amount, the RTPs are the same