RNG and Reel Position?

Hey there - financial analyst guy who knows how to do a little math here and there. I've really gotten into comp hustling/APing slots and VP at casinos over the last couple of years and the resources I've found here and elsewhere have been invaluable to me. Having said that, because I can do math and complex formulas and such, I am interested in learning some more about the dynamics of the machines themselves in terms of how they operate and so on. I did some searches specific to this topic already on the forum but I don't know that the specific questions I had in mind were answered.

I understand how the RNG operates and how the function of it is likely written and used by the slot machine games at some level. The part where I am slightly unclear but think I get it is this - the RNG spits out a number, that number is used to populate a reel position, and depending on the number of reels, that's how many times the RNG gets asked to produce a number. Where I am less clear is how that leads to a display of reels on the screen. To use a specific example: if I play Phoenix 2x/3x free games which has three physical reels but many paylines, does the RNG determine the center reel (or top or bottom, I guess it is irrelevant) position and then if you win in a diagonal line, it's more or less a lucky accident?

Alternately, with a video slot, are the reels consistent during standard play (not during a bonus) when betting the same amount at the same denomination? I assume this is the case based on things I've read about how some of the calculations were done for games like Buffalo Link/Ascension that seems to suggest using analysis of slowed reel footage spliced together to determine what full reels resembled and thus how many potential winning combinations existed. If there are 20 reel positions in a 5x4 video slot and each of them was RNG determined independently, I can't imagine it would be easily possible to do the math on when that might go positive since I don't know how you'd know how many reel positions the RNG was working off of and how many were in a win condition.

Sorry if this seems exceptionally repetitive for questions here but I'm just trying to figure out things about how machines work before I invest time in thinking about how to calculate probabilities.

I wrote an introductory pdf/book on on how to calculate slot maths. I can't link to it but its a pdf called "Elements of Slot Design" on the site for the tool Slot Designer. Its very basic, but will give you the idea of the basic principles and some industry terminology. Note that modern games are far more complex than what I described and you'd not be able to reverse engineer many of them if that's what you're planning on doing.

Quote: RobertMuir

I wrote an introductory pdf/book on on how to calculate slot maths. I can't link to it but its a pdf called "Elements of Slot Design" on the site for the tool Slot Designer. Its very basic, but will give you the idea of the basic principles and some industry terminology. Note that modern games are far more complex than what I described and you'd not be able to reverse engineer many of them if that's what you're planning on doing.
link to original post

Thanks - this is indeed very helpful as it describes persistent state features, progressives, et al. I work in academia and have some experience with R (I've worked on large data sets as part of published research previously) and was thinking of, yes, basically reverse engineering games and trying to figure out if I could create a consistent model which could be adapted across persistent state games as rolled out assuming I had a good reference on the makeup of the virtual reels.

Correct me if I am wrong here, but with regards the referenced patent US4448419A, does this also mean that video slot reels are often subject to position being determined by virtual reel? Obviously without knowing then how many positions the virtual reel has, there wouldn't be any way of being able to compute the RTP regardless of whether or not I knew the full video slot reel strip(s) and those reels were nonrandomized from game-to-game/within bet amount/within denom.

edit: Also, while I've done some light lit searches to this topic previously, is there much in the world of academic publishing that is relevant to a nascent advantage player?

There's no consistent model used when designing games in the first place, so there's not much hope of deriving one afterwards. Having said that, for advantage play perhaps you only need a very simplified model of the game. I can't say I know too much about this as its not something I'm interested in.

Virtual reels is mainly used on stepper games, though some game designers use them for video also.

I believe I've published the most advanced material on slot maths, and its very very simple. There's a few papers, but nothing obviously useful in academic publishing last time I looked.

Slot Games are probably a lot more complex than you're thinking.

Quote: RobertMuir

Virtual reels is mainly used on stepper games, though some game designers use them for video also.

I can't imagine any reason someone would want to use virtual reels on a video slot. The whole idea of virtual is to map a large set to a small set, on videos there is no reason to have a small set.

Quote: RobertMuir

There's no consistent model used when designing games in the first place, so there's not much hope of deriving one afterwards. Having said that, for advantage play perhaps you only need a very simplified model of the game. I can't say I know too much about this as its not something I'm interested in.

Virtual reels is mainly used on stepper games, though some game designers use them for video also.

I believe I've published the most advanced material on slot maths, and its very very simple. There's a few papers, but nothing obviously useful in academic publishing last time I looked.

Slot Games are probably a lot more complex than you're thinking.
link to original post

I don't want you to get the sense that I think they're not insanely complex. I'll happily admit what I'm looking to do is aspirational but I mean, shoot high, right? I'm waaaaay far off from that if I'm asking questions like this. I'm the sort of person who wants to know everything about the stuff I've enjoyed previously and gaming has replaced some other hobbies because I've aged out of them and have sufficient income to actually really enjoy this now.

Quote: VirtualBalboa

The part where I am slightly unclear but think I get it is this - the RNG spits out a number, that number is used to populate a reel position, and depending on the number of reels, that's how many times the RNG gets asked to produce a number. Where I am less clear is how that leads to a display of reels on the screen. To use a specific example: if I play Phoenix 2x/3x free games which has three physical reels but many paylines, does the RNG determine the center reel (or top or bottom, I guess it is irrelevant) position and then if you win in a diagonal line, it's more or less a lucky accident? link to original post

Yes, that's exactly it. When I code a slot, my RNG picks the center stop for each reel. When I do the code to figure the RTP, I just use that one center payline, because the RTP is the same no matter how many paylines you have, and it's faster to test 33M combos rather than 33M combos x 30 paylines, taking a lot more time just to get the exact same result. In actual gameplay, the code again just picks for what symbol to position on the center payline, then tallies up the wins on all the paylines.

Quote: VirtualBalboa

Alternately, with a video slot, are the reels consistent during standard play (not during a bonus) when betting the same amount at the same denomination?...

Sorry, I didn't really follow. What I can tell you is that the reels for video slots show every single stop as they spin (unlike physical electromechanical reels, which use a physical reel of 22 stops married to a virtual wheel of like 128 stops). And 20 stops seems like for a video machine, I'd expect at least 32. I use 32 when I code slots for clients. That's 32^5 = 33,554,432 combinations. And yeah, without access to the slot's PAR sheet, figuring when a jackpot goes high enough to make a machine positive is tough to impossible.

And to be clear, the RNG doesn't determine the game's RTP. The RNG just picks the numbers. What determines the RTP is the # of each symbol on each reel, married to the paytable. Some of my articles might be of use to you:

• All about PAR sheets
• How slot machines work
• How to program a slot machine
• Slot machine advantage play

Quote: MichaelBluejay

When I code a slot, my RNG picks the center stop for each reel.

What would you do when there's 4 symbols visible on the reel rather than 3? I use the top position.

Quote: MichaelBluejay

When I do the code to figure the RTP, I just use that one center payline, because the RTP is the same no matter how many paylines you have, and it's faster to test 33M combos rather than 33M combos x 30 paylines, taking a lot more time just to get the exact same result.

This is the common case, but its not correct for all games.

Quote: RobertMuir

Quote: MichaelBluejay

When I code a slot, my RNG picks the center stop for each reel.

What would you do when there's 4 symbols visible on the reel rather than 3? I use the top position

I've never coded a four-row game, just three-row games, but if I did, I suppose I'd use the top row.

Quote: RobertMuir

Quote: MichaelBluejay

When I do the code to figure the RTP, I just use that one center payline, because the RTP is the same no matter how many paylines you have, and it's faster to test 33M combos rather than 33M combos x 30 paylines, taking a lot more time just to get the exact same result.

This is the common case, but its not correct for all games. link to original post

Would love to hear of an example where that's not the case. I believe you, I just haven't done any games like that.

Quote: MichaelBluejay

Sorry, I didn't really follow. What I can tell you is that the reels for video slots show every single stop as they spin (unlike physical electromechanical reels, which use a physical reel of 22 stops married to a virtual wheel of like 128 stops). And 20 stops seems like for a video machine, I'd expect at least 32. I use 32 when I code slots for clients. That's 32^5 = 33,554,432 combinations. And yeah, without access to the slot's PAR sheet, figuring when a jackpot goes high enough to make a machine positive is tough to impossible.

And to be clear, the RNG doesn't determine the game's RTP. The RNG just picks the numbers. What determines the RTP is the # of each symbol on each reel, married to the paytable. Some of my articles might be of use to you:

• All about PAR sheets
• How slot machines work
• How to program a slot machine
• Slot machine advantage play
link to original post

This along with prior posts actually answers my question; I was wondering whether or not the virtual reels were, for lack of a better word that I can think of, "real". What I mean by "real" that is that is I assume that when a specific RTP for the machine is selected by the gaming company, the reels of a video slot machine for that RTP are the same on spin 1 as spin 10,000 with the same symbols correlating to the same numbers in the RNG in the same proportions in the same location.

Pure example, not actually saying this is how it is programmed: If I sit down and play Buffalo, for the number 222 on Reel 1 the space on the virtual reel for a 100 credit bet at penny denomination is always going to be a Buffalo if it is a Buffalo the first time I play it in base game. Similarly, if I play an otherwise identical Buffalo machine that has been set at an identical RTP, Reel 1's position for number 222 on 100 credit/1c is always going to be a Buffalo. Or perhaps to more succinctly put it - the game doesn't RNG both the reel positions and what is on the reels to provide a completely random experience every single time, but adjustments in the RTP lead to changes in the number of reel positions, what is on the reel positions, et al. with the reels themselves staying constant in base game (or constant within bonus games).

Quote: VirtualBalboa

I was wondering whether or not the virtual reels were, for lack of a better word that I can think of, "real".... link to original post

You've got it right: video slot reels are indeed fixed. They don't change, except that the base game reels and the bonus game reels can be different (and if so, it says so in the game rules). And two games with the same titles but different RTPs will have different reels from each other. But yes, when you sit down and start playing the game, the reel stops are not gonna jump all over the place.

Quote: MichaelBluejay

Quote: VirtualBalboa

I was wondering whether or not the virtual reels were, for lack of a better word that I can think of, "real".... link to original post

You've got it right: video slot reels are indeed fixed. They don't change, except that the base game reels and the bonus game reels can be different (and if so, it says so in the game rules). And two games with the same titles but different RTPs will have different reels from each other. But yes, when you sit down and start playing the game, the reel stops are not gonna jump all over the place.
link to original post

OK, I've got a question. Sorry if it sounds like a dumb question, or if it's already been asked and answered because I can't see where it has precisely been asked and answered.

Is the result of each reel fair? By fair, I mean if a reel has 22 stops, are the chances of any particular stop being the result 1/22?

If so, it seems like solving the machine should be easy once you characterize all the stops on each reel. If not... I'm stumped.

Quote: AutomaticMonkey

Quote: MichaelBluejay

Quote: VirtualBalboa

I was wondering whether or not the virtual reels were, for lack of a better word that I can think of, "real".... link to original post

You've got it right: video slot reels are indeed fixed. They don't change, except that the base game reels and the bonus game reels can be different (and if so, it says so in the game rules). And two games with the same titles but different RTPs will have different reels from each other. But yes, when you sit down and start playing the game, the reel stops are not gonna jump all over the place.
link to original post

OK, I've got a question. Sorry if it sounds like a dumb question, or if it's already been asked and answered because I can't see where it has precisely been asked and answered.

Is the result of each reel fair? By fair, I mean if a reel has 22 stops, are the chances of any particular stop being the result 1/22?

If so, it seems like solving the machine should be easy once you characterize all the stops on each reel. If not... I'm stumped.
link to original post

The answer is yes assuming they do not have a virtual reel mapping. In the old days the answer was always yes, but since the Telnaes patent virtual reels were introduced and most mechanical reels today use virtual reels. On a mechanical reel game with physical reels they generally have 22 reel stops. If it has three reels the largest odds would be (22*22*22) to 1 which is 10,648. If a game has a payout larger than 10,648 to 1 on the paytable you can assume it has virtual reels.

Quote: DRich

Quote: AutomaticMonkey

Quote: MichaelBluejay

Quote: VirtualBalboa

I was wondering whether or not the virtual reels were, for lack of a better word that I can think of, "real".... link to original post

You've got it right: video slot reels are indeed fixed. They don't change, except that the base game reels and the bonus game reels can be different (and if so, it says so in the game rules). And two games with the same titles but different RTPs will have different reels from each other. But yes, when you sit down and start playing the game, the reel stops are not gonna jump all over the place.
link to original post

OK, I've got a question. Sorry if it sounds like a dumb question, or if it's already been asked and answered because I can't see where it has precisely been asked and answered.

Is the result of each reel fair? By fair, I mean if a reel has 22 stops, are the chances of any particular stop being the result 1/22?

If so, it seems like solving the machine should be easy once you characterize all the stops on each reel. If not... I'm stumped.
link to original post

The answer is yes assuming they do not have a virtual reel mapping. In the old days the answer was always yes, but since the Telnaes patent virtual reels were introduced and most mechanical reels today use virtual reels. On a mechanical reel game with physical reels they generally have 22 reel stops. If it has three reels the largest odds would be (22*22*22) to 1 which is 10,648. If a game has a payout larger than 10,648 to 1 on the paytable you can assume it has virtual reels.
link to original post

These threads are my favorite… drich define fair

Quote: AutomaticMonkey

Quote: MichaelBluejay

Quote: VirtualBalboa

I was wondering whether or not the virtual reels were, for lack of a better word that I can think of, "real".... link to original post

You've got it right: video slot reels are indeed fixed. They don't change, except that the base game reels and the bonus game reels can be different (and if so, it says so in the game rules). And two games with the same titles but different RTPs will have different reels from each other. But yes, when you sit down and start playing the game, the reel stops are not gonna jump all over the place.
link to original post

OK, I've got a question. Sorry if it sounds like a dumb question, or if it's already been asked and answered because I can't see where it has precisely been asked and answered.

Is the result of each reel fair? By fair, I mean if a reel has 22 stops, are the chances of any particular stop being the result 1/22?

If so, it seems like solving the machine should be easy once you characterize all the stops on each reel. If not... I'm stumped.
link to original post

Reels are weighted. As for "fair", the games have a house edge.

Here is a reverse engineered Sizzling 7s from IGT for the S+ chassis (not guaranteed to be correct, but it does match the "bible")


here are sizzling 7s reel strips that could work. do not know what the actual game uses as I don't have the part number.


is it fair? Kinda. The representation on a game like this sort of matches the reelstrips. The strips on a more complex game would look nothing like actual weights because they have way more virtual stops, but are still mapping them to 22 reel stops.

Quote: itsmejeff

Quote: AutomaticMonkey

Quote: MichaelBluejay

Quote: VirtualBalboa

I was wondering whether or not the virtual reels were, for lack of a better word that I can think of, "real".... link to original post

You've got it right: video slot reels are indeed fixed. They don't change, except that the base game reels and the bonus game reels can be different (and if so, it says so in the game rules). And two games with the same titles but different RTPs will have different reels from each other. But yes, when you sit down and start playing the game, the reel stops are not gonna jump all over the place.
link to original post

OK, I've got a question. Sorry if it sounds like a dumb question, or if it's already been asked and answered because I can't see where it has precisely been asked and answered.

Is the result of each reel fair? By fair, I mean if a reel has 22 stops, are the chances of any particular stop being the result 1/22?

If so, it seems like solving the machine should be easy once you characterize all the stops on each reel. If not... I'm stumped.
link to original post

Reels are weighted. As for "fair", the games have a house edge.

Here is a reverse engineered Sizzling 7s from IGT for the S+ chassis (not guaranteed to be correct, but it does match the "bible")


here are sizzling 7s reel strips that could work. do not know what the actual game uses as I don't have the part number.


is it fair? Kinda. The representation on a game like this sort of matches the reelstrips. The strips on a more complex game would look nothing like actual weights because they have way more virtual stops, but are still mapping them to 22 reel stops.
link to original post

It would be very unusual for a game to have the same strip on all three reels.

Quote: heatmap

Quote: DRich

Quote: AutomaticMonkey

Quote: MichaelBluejay

Quote: VirtualBalboa

I was wondering whether or not the virtual reels were, for lack of a better word that I can think of, "real".... link to original post

You've got it right: video slot reels are indeed fixed. They don't change, except that the base game reels and the bonus game reels can be different (and if so, it says so in the game rules). And two games with the same titles but different RTPs will have different reels from each other. But yes, when you sit down and start playing the game, the reel stops are not gonna jump all over the place.
link to original post

OK, I've got a question. Sorry if it sounds like a dumb question, or if it's already been asked and answered because I can't see where it has precisely been asked and answered.

Is the result of each reel fair? By fair, I mean if a reel has 22 stops, are the chances of any particular stop being the result 1/22?

If so, it seems like solving the machine should be easy once you characterize all the stops on each reel. If not... I'm stumped.
link to original post

The answer is yes assuming they do not have a virtual reel mapping. In the old days the answer was always yes, but since the Telnaes patent virtual reels were introduced and most mechanical reels today use virtual reels. On a mechanical reel game with physical reels they generally have 22 reel stops. If it has three reels the largest odds would be (22*22*22) to 1 which is 10,648. If a game has a payout larger than 10,648 to 1 on the paytable you can assume it has virtual reels.
link to original post

These threads are my favorite… drich define fair
link to original post

I would consider a game fair if it adheres to all applicable rules.

Quote: heatmap

drich define fair link to original post

Although this question wasn't directed at me, I'd like to address it. Is gambling math, "fair" simply means a game in which the payout matches the odds, so there's no house edge. In this case "fair" isn't an ethical/unethical position, it's an objective description of whether the game has a built-in profit for the casino. All casino games are "not fair" in the sense that there's a house edge, but that doesn't mean they're "unfair" in the sense that there's deception or cheating, because there's not, the games are just structured so that the player will lose a small portion of their bets in the long term.

Quote: MichaelBluejay

Quote: heatmap

drich define fair link to original post

Although this question wasn't directed at me, I'd like to address it. Is gambling math, "fair" simply means a game in which the payout matches the odds, so there's no house edge. In this case "fair" isn't an ethical/unethical position, it's an objective description of whether the game has a built-in profit for the casino. All casino games are "not fair" in the sense that there's a house edge, but that doesn't mean they're "unfair" in the sense that there's deception or cheating, because there's not, the games are just structured so that the player will lose a small portion of their bets in the long term.
link to original post

OK I was using the term slightly differently, in that a gaming element (itself) is fair when it matches the outputs one would statistically expect upon normal inspection. So if you have a standard deck of 52 cards one card of each of 4 suits and 13 ranks is present, that is a fair deck. If you have a standard casino die that is not loaded, the faces are flush, and all the numbers are where they belong, that is a fair die. That casino craps has a house edge is caused by the rules of casino craps, not the dice. If you sneak loaded dice into a craps game everything is now different.

So my original question could be reduced to, if you had three 22-sided dice, regular polygons, uniform density and surface quality (i.e., "fair" 22 sided dice) would that simulate a slot machine with three 22-stop reels? Looks like the answer was "Might have been back in the day, but with a modern slot machine, probably not." Good enough for me. That would make them more like a bonus wheel on a table game than a Big 6 wheel.

there is an equal probability of picking each individual position on the reel. I assume that because the way I would do it is pick a number from 1 to the amount of symbols on a reel.

This is independent of the amount of symbols on each reel. The amount of symbols on each reel is also a probability.

Just because you have an equal chance of each position being picked, does not imply that you have a fair chance of getting each symbol picked on each reel. Each reel can contain different amounts of each symbol, and therefore an unfair chance (according to your definition) of picking specific combinations overall.

Quote: AutomaticMonkey

So my original question could be reduced to, if you had three 22-sided dice, regular polygons, uniform density and surface quality (i.e., "fair" 22 sided dice) would that simulate a slot machine with three 22-stop reels? Looks like the answer was "Might have been back in the day, but with a modern slot machine, probably not." Good enough for me. That would make them more like a bonus wheel on a table game than a Big 6 wheel. link to original post

That's pretty much it. The Telnaes patent which pioneered virtual reels was granted in 1984. The electromechanical slots I'm familiar with since I first played them in 1998 have 22 physical stops, with virtual reels of many more. I don't know how many slots that non-virtual reel machines had prior to the virtualization of reels. And for video slots, I can't imagine a slot would have as few as 22 stops.

Your question is at the heart of the recent lawsuit against IGT, which makes the Wheel of Fortune slots. One some flavors of Wheel of Fortune, the progressive jackpot is won by hitting the Jackpot slice on the bonus wheel, and on other flavors you get the progressive jackpot by lining up the Wheel of Fortune symbols in the main game. On the former flavor, the bonus wheel is certainly virtualized, so even though there are 22 slices (stops), the chances of hitting the jackpot slot aren't 1 in 22, it's 1 in A Lot. Nevada law says that machine representations of real-world objects must have the some odds to not be misleading. So, for example, video poker has to use a standard 52-card deck, games that use dice have to have a 1 in 6 chance of landing on any number, etc. The virtual reels on slot machines have gotten a pass because there's not really a real-world equivalent of a slot machine reel. But the bonus wheel on Wheel of Fortune looks a lot like a roulette wheel and a Big Six wheel, doesn't it? Can we really expect players to automatically understand that it's not a fair wheel? I recently heard someone tell his phone, "Siri, what's five times eight?"

So, I side with the plaintiff on this one, if for no other reason that I think it's a travesty that slot makers and casinos keep the jackpot odds and RTP a secret. I think there ought to be transparency (jackpot odds and RTP stated directly on the machine), it's only fair. And since they don't want to be voluntarily transparent absent regulation, then fine, they get sued.

Quote: MichaelBluejay

So, I side with the plaintiff on this one, if for no other reason that I think it's a travesty that slot makers and casinos keep the jackpot odds and RTP a secret. I think there ought to be transparency (jackpot odds and RTP stated directly on the machine), it's only fair. And since they don't want to be voluntarily transparent absent regulation, then fine, they get sued.
link to original post

Can a slot machine be certified if the RTP is not specified?! Before receiving a game certificate, it is checked by special laboratories

Quote: Dobrij

Quote: MichaelBluejay

So, I side with the plaintiff on this one, if for no other reason that I think it's a travesty that slot makers and casinos keep the jackpot odds and RTP a secret. I think there ought to be transparency (jackpot odds and RTP stated directly on the machine), it's only fair. And since they don't want to be voluntarily transparent absent regulation, then fine, they get sued.
link to original post

Can a slot machine be certified if the RTP is not specified?! Before receiving a game certificate, it is checked by special laboratories
link to original post

The gaming regulators to require to see the full math for RTP and probabilities. In the past the regulators would independently do the math to make sure it matches what was submitted by the manufacturer.

The gaming regulators to require to see the full math for RTP and probabilities. In the past the regulators would independently do the math to make sure it matches what was submitted by the manufacturer. Every machine comes with a PAR sheet that gives all of that information. The casinos also get that PAR sheet for every single game on the floor.