Slot Machine Calculation Algorithm

You are playing a three-coin slot machine. You only are playing two coins at the time. The jackpot is hit. If you had been playing one coin, or if you had been playing three coins, would it still have gone off at that point?
  1. Slot Machine Algorithm Example
  2. Slot Machine Calculation Algorithm Formula
  3. Slot Machine Algorithm Hacks
  4. Algorithms In Machine Learning
  5. Slot Machine Rng Algorithm

If you had put in one or three coins the outcome would likely have been entirely different. The machine is constantly drawing random numbers and the numbers that were drawn at the moment you spin the reels determine the outcome. So, if you had played fewer or more coins you would have spun the reels at a different moment and thus the outcome would have been different.

Hey Shack I hadn't been to the site in awhile and I just wanted to compliment you on the new sleek look. I know you initially wanted to stay away from the banners but they do help pay the bills eh?
Congratulations also on the new gig with Casino Player, I enjoy it the site and your occasional posts on bj21. As someone who works in the industry, admittedly not slots, I was under the impression that the more recent slots have the RNG stop the moment the first coin drops, so it really doesn't matter if you play 1,2, or 3 coins -- the symbols will line up the same. Have I been misinformed? According to your previous answer I apparently have. Keep up the good work and I'll stay in touch, thanks and best wishes.

Thanks for the kind words Dave. You're right that it was the money that finally made me accept the banners. It is my understanding that when the player presses the button to spin the reels the random numbers are drawn at that instant, which determine where the reels stop, and ultimately what you win. The number of coins bet does not matter.

Understanding slot machine math can be daunt ing for even the most seasoned individual. You do not hav e to be an accountant, analyst, or even a statistician to understand the fundamentals of slot math. The take-away is to know why this math is so important.

How many numbers does the RNG (Random Number Generator) pick for each spin in a slot machine? Is it three numbers (1 for each reel) or is it 1 number that's mapped to a unique combination of symbols for all 3 reels?
This is a great website!. FYI - A guy missed the Megabucks jackpot (7.9M) yesterday because he had just two coins in. To the best of your knowledge, when does the RNG stop and determine your outcome? If it stops on the first coin, then he blew it. If it is on the last coin, he could have had an entirely different outcome. My guess that the stop time is set by the individual manufacturer, and there is no regulation telling him when to do so. Just wondering if you knew different.

Thanks for the compliment. The outcome of the game is determined when the player initiates the spin. The game is constantly drawing random numbers, even when not played. The random numbers chosen at the moment the button is pressed to spin the reels determine where the reels stop, which determines what the player wins. So, if the player bet three coins he would have pressed the button at a different moment, causing a different outcome.

Slot
Have you noticed when you look sideways past the right reel on IGT games there are 4-5 counters inside the machine labeled 'coins in, coins out, jackpots' or similar wording? I was just wondering what your experience with the counters was. Is there any way to get helpful information from those? Thanks for your time.

No, that information won’t help you at all. Your odds are always the same on every spin, regardless of the counters.

I have heard it is illegal for a slot machine to deliberately have too many near misses. Can you tell me what you know about this?
Machine

To answer your question I asked a well connected gaming consultant and he said Nevada regulations state that one stop on a reel can not be weighted more than six times more than either stop next to it. So if a jackpot symbol were weighted by 1 and both bordering blanks were weighted by 6 then there would be 12 near misses for every one time the reel stopped on the jackpot symbol. This would be the maximum allowed near miss effect. My own results detailed in my slot machine appendix 1 back up this theory well. The red double seven was the highest paying symbol and I saw the blanks above and below it about 5 to 6 times as often:

Double Strike Actual Results

SymbolReel 1Reel 2Reel 3
Blank250248291
Double red 7525155
Blank259292262

The same source said that New Jersey and Mississippi likely have adopted the Nevada regulations.

This is not a game theory question, but I figured since you answer dating questions you might handle this. I had a dream recently where I sat down at an open slot machine. I was getting my player’s card out of my pocket when a guy came up from behind me and put money in the machine. I told him it was my machine and hit the cash out button and gave him his ticket. He said he had his eye on the machine and since he had his money in first it was his machine. I turned to call a slot attendant and while I was doing that he put his money in again, pushed the button and hit a jackpot. In my dream we then had an argument over who gets the money, the person who clearly had the machine and intended to play it or the person who unsolicited put the money in the machine. I realize this is a bizarre situation but who do you think would win the argument?

My understanding is that the person who is pressing the buttons gets the money. I asked Brian, who helped with the last question, about this. Here is what he wrote, which I agree with.

In the scenario described, the person who put in the money and pressed the buttons would receive the jackpot.

What I find interesting about this question is the paradox that in all likelihood, the jackpot never would have occurred without this chance encounter.

As you know, the random number generator in the slot machine is continuously working even when the machine is not in play. So even though one patron feels cheated, their run-in ultimately led to pressing the spin button at that exact millisecond when the RNG was on the winning combination. So, if one patron had acquiesced, there is never a jackpot to fight over.

I have used your site to knock down myths and betting systems with many friends and your proofs always win the day. On the Pink Panther (and some others) there is a bonus round that presents a screen with pictures from which to pick. Behind some are coin amounts and others have a symbol that ends the bonus round. Once you are presented with the bonus board the placement of the symbols cannot be changed, can they?

Thanks for helping in the fight against betting systems. First let me say that I have never worked for a major slot machine company and don’t have direct knowledge of this. However, I know many people in the industry and those I trust pretty much are in agreement on this topic.

That said, it is my understanding that in all forms of electronic games, including video slots, video poker, and video keno, the outcome is usually determined the moment you make your decision. Meanwhile the possible outcomes are constantly being shuffled, thousands of times a second. I can’t speak for every slot machine but I believe that with the major U.S. slot makers the outcome is not predestined but depends on the exact microsecond you press the button to make your play.

First, love the site, very informative! Background: When using a Random Number Generator (RNG) to determine certain payouts for a finite set, such as 1 million lottery scratch off cards, the RNG can be programmed to drop non-pay or add pay selections so as to keep a more even distribution of winners throughout the finite set of cards created. The goal is to maintain a more even distribution in the cards along with the payout percentage as required. Is this, or can this programming be done in Nevada? The law of averages would indicate no need for this, but is it not theoretically possible for a signed 97% slot machine to payout 95% one year and 99% the next year unless some control on the RNG was made?

Thanks for the kind words. Scratch cards and pull tabs can indeed be printed in batches. These batches will have a specified number for each win, and the return of the overall batch will be exactly as the maker intended. In some jurisdictions, where only pull tabs are legal, the outcome can be displayed to the player on a video monitor, in the form of a slot or video poker machine. However, in Nevada, that is not how slots work. Each play is completely independent of the past. A machine programmed to average a 97% return, could indeed pay under 95% or over 99% over a year, especially if not heavily played.

Mathpro
Hi,
What would you say are the pros and cons of writing an exact algorithm for calculating RTP's etc. versus just simulating?
I am writing my master thesis in mathematical statistics about casino slots and have written an algorithm for getting exact values for the slot game which I can't name. The process is time consuming and the algorithm takes a couple of days to run on my laptop.
I know that the industry standard is to run simulations since they're faster to code, more adaptive and usually runs faster(well that depends on how many runs etc.), but I'd like to know the value of my algorithm.
All answers are appreciated,
Thank you!
dwheatley
A simulation is unlikely to get the right frequencies of jackpots for a slot machine, even over days of computing time. An exact algorithm is very useful for calculating the risk of extreme casino payouts.Slot Machine Calculation Algorithm
Wisdom is the quality that keeps you out of situations where you would otherwise need it
HughJass
From IGT:
'Gaming regulations require that gaming devices must have random outcomes of game play results. In order to satisfy this requirement, games of all types use a random number generator (RNG) software algorithm to determine game outcome. While the game is in the idle state, i.e. waiting for someone to deposit a coin or push a play credit button, the RNG algorithm is called hundreds of times every second. The RNG has approximately 16,000,000,000,000,000,000 possible outcomes and, depending on the game type, there will be many billions of outcomes that map into any set of cards, or keno balls, or slot machine symbols. This ensures that all IGT games are completely random, just as if the cards were dealt from a perfectly shuffled deck.'
To my understanding, the RNG's stack has multiple outcomes of all possible events in proportion to their respective probabilities. A moving pointer stops when you deposit the first coin or when any bet button is depressed - 'Bet One', 'Bet Max', 'Deal', etc. The outcome to which the pointer is pointing is revealed to the player. While this doesn't directly answer your question, I hope that this helps.
DRich

Hi,
I know that the industry standard is to run simulations since they're faster to code, more adaptive and usually runs faster(well that depends on how many runs etc.), but I'd like to know the value of my algorithm.
All answers are appreciated,
Thank you!


It is? I would say that on majority of casino slot machines the math has been solved and not simulated. Just get a hold of some PAR sheets and you will be able to understand it better.
Living longer does not always infer +EV
CrystalMath

It is? I would say that on majority of casino slot machines the math has been solved and not simulated. Just get a hold of some PAR sheets and you will be able to understand it better.


I agree with DRich. I calculate almost all of my games without the use of simulations. I prefer to have live calculations in Excel so I can modify games quickly. I do write simulations for many games, but that is to get a better estimate of the volatility and as a sanity check. I also wrote code that counts all hits, which works for most games, and it only takes seconds to run.
I heart Crystal Math.
RobertMuir
Hi Mathpro, I think you'll find the value of your algorithm is mainly if you're trying to get a job in the gaming industry. Some companies employ people who have skills in this area (computer simulations and algorithms), either in game design or technical supporting roles for them. You should have an advantage over others starting out. While obviously I don't know what its is, chances are the algorithm itself doesn't have much real value - you probably won't be able to sell it to anyone.
I've been more or less where you are 12 years ago (which is what prompted me to make an account here and reply), and the gaming industry doesn't work the way you think it does. It doesn't help that there's almost nothing published on slot design. I've come up with lots of clever algorithms and its very difficult to do anything with them. I have in the end, but its a long hard road.
There's lots of smart people in the industry and there's been a lot of work in this area, and Excel is still very much in use. I've spoken to a lot of people in the industry and there's very very few companies that design games by simulation (for random games like USA class III anyway). I think there may be a few types of games that are done by simulation simply because there's no other way, but even if they are not exact (and sometimes simulation is exact) people still do them, so its not clear the value here either.
Having said all that, I'm interested in algorithms and would be interested in hearing more when you publish it.
AxelWolf

Hi Mathpro, I think you'll find the value of your algorithm is mainly if you're trying to get a job in the gaming industry. Some companies employ people who have skills in this area (computer simulations and algorithms), either in game design or technical supporting roles for them.

What if you cave the ability to easily identify a RNG over a live game by just looking in the short run??
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
beachbumbabs
Administrator

Hi Mathpro, I think you'll find the value of your algorithm is mainly if you're trying to get a job in the gaming industry. Some companies employ people who have skills in this area (computer simulations and algorithms), either in game design or technical supporting roles for them. You should have an advantage over others starting out. While obviously I don't know what its is, chances are the algorithm itself doesn't have much real value - you probably won't be able to sell it to anyone.
I've been more or less where you are 12 years ago (which is what prompted me to make an account here and reply), and the gaming industry doesn't work the way you think it does. It doesn't help that there's almost nothing published on slot design. I've come up with lots of clever algorithms and its very difficult to do anything with them. I have in the end, but its a long hard road.
There's lots of smart people in the industry and there's been a lot of work in this area, and Excel is still very much in use. I've spoken to a lot of people in the industry and there's very very few companies that design games by simulation (for random games like USA class III anyway). I think there may be a few types of games that are done by simulation simply because there's no other way, but even if they are not exact (and sometimes simulation is exact) people still do them, so its not clear the value here either.
Having said all that, I'm interested in algorithms and would be interested in hearing more when you publish it.


Hi, RobertMuir, and thanks for signing up! Please check your Private Messages.

Slot Machine Algorithm Example

If the House lost every hand, they wouldn't deal the game.
RobertMuir

What if you cave the ability to easily identify a RNG over a live game by just looking in the short run??


In that case you'd be able to make a lot of money, at least until you got arrested. Gaming systems are designed and tested to make that impossible, so unless you find a bug or poorly implemented system I don't think there's a realistic chance of doing that.

Slot Machine Calculation Algorithm Formula

Ahigh

From IGT:
'Gaming regulations require that gaming devices must have random outcomes of game play results. In order to satisfy this requirement, games of all types use a random number generator (RNG) software algorithm to determine game outcome. While the game is in the idle state, i.e. waiting for someone to deposit a coin or push a play credit button, the RNG algorithm is called hundreds of times every second. The RNG has approximately 16,000,000,000,000,000,000 possible outcomes and, depending on the game type, there will be many billions of outcomes that map into any set of cards, or keno balls, or slot machine symbols. This ensures that all IGT games are completely random, just as if the cards were dealt from a perfectly shuffled deck.'
To my understanding, the RNG's stack has multiple outcomes of all possible events in proportion to their respective probabilities. A moving pointer stops when you deposit the first coin or when any bet button is depressed - 'Bet One', 'Bet Max', 'Deal', etc. The outcome to which the pointer is pointing is revealed to the player. While this doesn't directly answer your question, I hope that this helps.


I implemented a random shuffling algorithm while at IGT. The state of the shuffled deck begins with a deck that is already shuffled and shuffles it again. I stored shuffled decks and I randomly chose one of the n decks of pre-shuffled decks using another random number generator to start the state of the perfectly shuffled deck. This prevents the condition where you can't have more variations in the results of the shuffle than you have random number seeds when starting with a known state. Just calling a random number generator hundreds of times per second alone doesn't solve the problem for every random number generator. You are still limited by the number of possible seeds, for example, if you do this.
http://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle

Slot Machine Algorithm Hacks


None of these ideas were patented, and the intellectual property for this methodology was invented before working for IGT. But hopefully this gives you some insight as to techniques which can be used to reassure that every possible result is easily attained over a large enough period of time even without depending on super fancy random number generators which can also solve the problem all on their own with enough seeds to cover every possible case.

Algorithms In Machine Learning


Slot Machine Rng Algorithm

I personally believe that proper design always trumps depending too heavily on a random number generator alone. There are multiple sources to obtain entropy, and digital storing state inside the machine that is constantly affected by internal and external source of entropy in addition to random number generators always keep things from being exploitable better than a random number generator that is well known with a limited (even 64-bit) number of seeds and starting from well-known or assumed states (like a sorted deck). Just having a 64-bit seed random number generator isn't good enough. You also have to ensure that you're covering the full spectrum of seed values as well to avoid well-known sequences of random numbers and general results from those well known sequences that could lead to exploits.