Slot Math - Ways(1)

 

In this article, I will introduce you to the basic mathematical modeling process of way slots. The biggest difference between the modeling process of line slots and way slots is that way slots have to consider the amount of symbols landing on each reel, because the more same symbols on one matched reel, the higher payouts players would get

Step 1. Configuration Table

In this article, I will introduce a 5-3 classic way slot

First of all, we need 5 reels of symbols. As you can see, this slot has 3 standard symbols, which are J, Q, and K, and two feature symbols, which are wild and scatter symbols

Wild symbols can be seen as any standard symbols on the reels

When there are more than 3 scatter symbols on any place of reels, the free game would be triggered

Step 2. Calculate the Numbers

There are two number which is needed for further calculation. The expected number of symbols landing on the reels and the number of events that symbols do not land on the reels

For the expected numbers of landing symbol parts, we need to use the COUNTIF function to get the actual numbers of each symbol. Then, we can use those numbers times the amounts of rows, which is 3 in this example

When it comes to calculating the no-landing chance, it would be a little bit complicated. We need to use an array formula to calculate the number of events that do not include the specific symbol among the three connected Symbols on the reels

The three symbols behind the reels are the three symbols at the beginning of the reels, for connecting end to end.

Step 3. Calculate the RTP of Standard Symbols

These steps are relatively more simple. We just need to remember that the sum of the expected RTP needs to be divided by the constant of this slot. In this example, the constant is 100

Then, we can use the first three steps to get the RTP of standard symbols in Free Game too

Step 4. Expected Free Game Times

In this example, there is only one scatter symbol on each reel. We can calculate the expected times by listing all possibilities or BINOM.DIST function. Both ways should get the same result. You can click the links below to get more information about those two different methods:

Considering there is no limitation of extra free game triggering in the free game and the triggering rate remains stable during each spin, we need to use Infinite series summation to get the final expected time. The formula in Excel would be "=Expected times in Base Game / (1 - Expected times in Base Game)"

Step 5. RTP and Adjustment

The RTP of this example way slot is shown in the picture below:

Free game's RTP is equal to its standard symbols' RTP times expected free game times

After that, we get the intact mathematical model of this 5-3 classic line slot and we can change the configuration table to get a better RTP now. We just need to be more careful about some settings which affect the method we use. For example, if there are some connected scatter symbols in one reel, we should change the way we calculate the expected free game times