Newbie Question About Real World Slot Math
July 27th, 2025 at 2:59:17 AM
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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)?
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)?
Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.
July 28th, 2025 at 12:12:45 AM
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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.
July 28th, 2025 at 1:38:17 AM
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Quote: KevinAAIt'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?
Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.
July 28th, 2025 at 4:49:22 AM
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Quote: KevinAAIt'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.
You can't know everything, but you can know anything.
July 30th, 2025 at 1:19:47 AM
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Quote: DRichQuote: KevinAAIt'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.
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DRich, thank you for your reply!
Another question just occurred to me: is the math checked during the certification process?
Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.
July 30th, 2025 at 8:31:53 AM
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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.
You can't know everything, but you can know anything.
July 30th, 2025 at 9:48:24 AM
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Quote: DRichYes, 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 :(
Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.
July 30th, 2025 at 9:54:16 AM
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Quote: AnotherBillQuote: DRichYes, 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…
I want to start wearing a T-shirt that reads, “Don’t feel sorry for me. I’m an AP!”
July 30th, 2025 at 11:05:32 AM
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Quote: camaplNot 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 :)
Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.
July 30th, 2025 at 6:38:05 PM
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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.
July 30th, 2025 at 9:38:48 PM
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Quote: itsmejeffBMM'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…
Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.
October 13th, 2025 at 11:46:56 AM
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I think this is slightly sad :(
Would love to see all kinds of detailed stats before putting serious playtime into a slot. Why do we think publishers or casinos don't want to publish this data ?
Would love to see all kinds of detailed stats before putting serious playtime into a slot. Why do we think publishers or casinos don't want to publish this data ?
October 13th, 2025 at 11:51:23 AM
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Quote: omI think this is slightly sad :(
Would love to see all kinds of detailed stats before putting serious playtime into a slot. Why do we think publishers or casinos don't want to publish this data ?
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Sadly, "Never smarten up a chump" cuts both ways.
May the cards fall in your favor.
October 13th, 2025 at 3:03:47 PM
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Quote: omI think this is slightly sad :(
Would love to see all kinds of detailed stats before putting serious playtime into a slot. Why do we think publishers or casinos don't want to publish this data ?
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My guess: trademark/copyright protection. If someone knew exactly how your game worked, they could make their own version and offer it to casinos cheaper.
October 14th, 2025 at 12:34:47 AM
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Quote: ThatDonGuyQuote: omI think this is slightly sad :(
Would love to see all kinds of detailed stats before putting serious playtime into a slot. Why do we think publishers or casinos don't want to publish this data ?
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My guess: trademark/copyright protection. If someone knew exactly how your game worked, they could make their own version and offer it to casinos cheaper.
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That sounds a very reasonable take, but I'm not sure how difficult it really is - you could analyse API results for a few hundred thousand demo spins and have enough of a clear idea to reverse engineer the maths to something at least very close (I seem to remember someone doing this for Starburst years ago, and proving that a jackpot screen was actually un-winnable).
My guess is that there is the expectation that it would "destroy the magic". Which it might do for many players; sometimes I have to accept that my brain is weird and that just because it would increase the magic for me, that doesn't map to most other players.
Am trying to code a new type of spin simulator; one which models play types
Something like ::
have 5 player personalities (always bets lowest amount, always bets so that they have 100 spins in the bank, doubles bet size after doubling bank roll, & etc)
then do thousands of simulations for each of these players and log stuff like highest cash-out possible, number of spins played in session, number of bonuses hit.
I actually think this would be just as meaningful info as plain RTP.
Will knock something together in the next few days and post it here :)
October 14th, 2025 at 1:54:57 AM
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Quote: omQuote: ThatDonGuyQuote: omI think this is slightly sad :(
Would love to see all kinds of detailed stats before putting serious playtime into a slot. Why do we think publishers or casinos don't want to publish this data ?
link to original post
My guess: trademark/copyright protection. If someone knew exactly how your game worked, they could make their own version and offer it to casinos cheaper.
link to original post
That sounds a very reasonable take, but I'm not sure how difficult it really is - you could analyse API results for a few hundred thousand demo spins and have enough of a clear idea to reverse engineer the maths to something at least very close (I seem to remember someone doing this for Starburst years ago, and proving that a jackpot screen was actually un-winnable).
My guess is that there is the expectation that it would "destroy the magic". Which it might do for many players; sometimes I have to accept that my brain is weird and that just because it would increase the magic for me, that doesn't map to most other players.
Am trying to code a new type of spin simulator; one which models play types
Something like ::
have 5 player personalities (always bets lowest amount, always bets so that they have 100 spins in the bank, doubles bet size after doubling bank roll, & etc)
then do thousands of simulations for each of these players and log stuff like highest cash-out possible, number of spins played in session, number of bonuses hit.
I actually think this would be just as meaningful info as plain RTP.
Will knock something together in the next few days and post it here :)
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I did that with video poker with a 99% paytable. Unlike a slot machine, the probability of winning any particular prize is known.
I created several scenarios (bankroll, cash out after a big win, cash out after winning a certain amount), ran millions of simulations for each, and discovered, not surprisingly, the average loss as a percentage of the amount wagered was 1%.
The differences were in the probability of winning anything vs busting out. More aggressive cash out strategy leads to higher average profit (if win) at the expense of higher chance of busting out.
The most conservative cash out strategy is to cash out if you are ahead by even one bet unit. This maximizes the probability of winning something (and minimizes the probability of busting out) but the average profit if win is very small.
October 14th, 2025 at 6:44:32 AM
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Quote: om… you could analyse API results for a few hundred thousand demo spins and have enough of a clear idea to reverse engineer the maths to something at least very close …
… (I seem to remember someone doing this for Starburst years ago, and proving that a jackpot screen was actually un-winnable). …
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Some time ago, I had a chance to look into reel configurations for few online slots and to calculate their RTP. The obtained results matched those specified in the slots descriptions. There may be as much as billions or even tens of billions combinations in total. But there are very few jackpot combinations (it may be only one or few dozens). So, a few hundred thousand spins may not provide that much chances to win a jackpot screen but they should provide quite precise RTP.
Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.
October 14th, 2025 at 8:34:55 AM
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Quote: omQuote: ThatDonGuyQuote: omI think this is slightly sad :(
Would love to see all kinds of detailed stats before putting serious playtime into a slot. Why do we think publishers or casinos don't want to publish this data ?
link to original post
My guess: trademark/copyright protection. If someone knew exactly how your game worked, they could make their own version and offer it to casinos cheaper.
link to original post
That sounds a very reasonable take, but I'm not sure how difficult it really is - you could analyse API results for a few hundred thousand demo spins and have enough of a clear idea to reverse engineer the maths to something at least very close (I seem to remember someone doing this for Starburst years ago, and proving that a jackpot screen was actually un-winnable).
My guess is that there is the expectation that it would "destroy the magic". Which it might do for many players; sometimes I have to accept that my brain is weird and that just because it would increase the magic for me, that doesn't map to most other players.
Am trying to code a new type of spin simulator; one which models play types
Something like ::
have 5 player personalities (always bets lowest amount, always bets so that they have 100 spins in the bank, doubles bet size after doubling bank roll, & etc)
then do thousands of simulations for each of these players and log stuff like highest cash-out possible, number of spins played in session, number of bonuses hit.
I actually think this would be just as meaningful info as plain RTP.
Will knock something together in the next few days and post it here :)
link to original post
I disagree with the "destroys the magic" hypothesis. The players that don't care how the trick is done won't go looking for the information.
You can do a Monte Carlo analysis, but that would require a very large number of spins - especially on machines where not every symbol is equally likely to land on the main payline. You say you are using "demo spins"; what makes you so sure that those are random?
October 14th, 2025 at 8:52:15 AM
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Quote: ThatDonGuy… You say you are using "demo spins"; what makes you so sure that those are random?
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They may be random but, in the same time, differ from "real" reels.
Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise.
