Newbie Question About Real World Slot Math

Hello everyone,

My question isn't tied to any specific math problem, but I'd like to understand how math is done in slot machine design.

I'm not a mathematician (and have never worked as one), but I've done some math for a few quite simple hobby projects. For those, I calculated exact RTP values using Excel (actually, LibreOffice Calc, since I use Linux), or by writing console applications that either ran full game cycles or recursively computed the entire game.

However, real slot games often have much more complex mechanics and math. At least for me, it hasn't been obvious how to calculate exact RTP values for such games (if I were a mathematician for them).

My question about real slot games math:
Are all slot games designed with an exact (theoretical) RTP calculation in mind? Or is it acceptable to calculate an RTP from running simulations (e.g., running millions or billions of spins)?

It's exact. The casino can choose which of several RTP values to set that machine. That selection sets the probabilities of any wins ==> one RTP. If the RTP was the result of running simulations, there would be only one, unchangeable, RTP.

Quote: KevinAA

It's exact. The casino can choose which of several RTP values to set that machine. That selection sets the probabilities of any wins ==> one RTP. If the RTP was the result of running simulations, there would be only one, unchangeable, RTP.
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Kevin, thank you for your reply!

After sleeping on the question, I see that the problem was described somewhat muddled (I'm not a native speaker).

I understand that one (or multiple) RTP is chosen beforehand. The same applies to the game rules.

So, suppose a casino wants a new game with some fancy rules. They give the rules, the desired RTPs, and some other data (unfortunately, I don't know the real-world process) to the mathematician and tell him to design the game. Before starting the design process, the mathematician studies the input data and realizes that it's impossible to analyze such a game mathematically. Nor is it possible to run the full game cycle. The only way would be to calculate the game by running a simulation (millions or billions of spins). So, are simulations used to design/analyze games in the real world?

Quote: KevinAA

It's exact. The casino can choose which of several RTP values to set that machine. That selection sets the probabilities of any wins ==> one RTP. If the RTP was the result of running simulations, there would be only one, unchangeable, RTP.
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I believe that you are incorrect. I only remember exact math for reels, but some bonus games are done through simulation so the exact RTP can not be proven.

Quote: DRich

Quote: KevinAA

It's exact. The casino can choose which of several RTP values to set that machine. That selection sets the probabilities of any wins ==> one RTP. If the RTP was the result of running simulations, there would be only one, unchangeable, RTP.
link to original post

I believe that you are incorrect. I only remember exact math for reels, but some bonus games are done through simulation so the exact RTP can not be proven.
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DRich, thank you for your reply!

Another question just occurred to me: is the math checked during the certification process?

Quote: AnotherBill

Another question just occurred to me: is the math checked during the certification process?
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Yes, each of the labs has math nerds or outsources it and verifies it against the math submitted by the manufacturer.

Quote: DRich

Yes, each of the labs has math nerds or outsources it and verifies it against the math submitted by the manufacturer.
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Oh! It looks like my efforts to develop tools for calculating certain types of games were in vain :(

Quote: AnotherBill

Quote: DRich

Yes, each of the labs has math nerds or outsources it and verifies it against the math submitted by the manufacturer.
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Oh! It looks like my efforts to develop tools for calculating certain types of games were in vain :(
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Not at all. Although the game makers and regulators calculate these games, the resulting information is not typically public knowledge…

Quote: camapl

Not at all. Although the game makers and regulators calculate these games, the resulting information is not typically public knowledge…
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camapl, thank you very much for your clarification!

Since I couldn't find a way to calculate those games manually or in Excel (or it would have taken an eternity), I developed those tools. I spent quite a lot of time creating algorithms to make the tools fast enough. I don't think the regulator's mathematician would do the same, if the game isn't easy to analyze.

But I find your comment very valuable. It gives hope :)

BMM's website has a list of example docs to submit for math analysis: All supporting materials, calculations, source code, and results associated with the game’s math model.

Quote: itsmejeff

BMM's website has a list of example docs to submit for math analysis…

itsmejeff, thank you very much for such a great reply! Things are getting clearer now…