The Basic Mathematics of Slot Machines
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- čas přidán 2. 08. 2024
- This link should get you a copy of the spreadsheet I used in the video:
drive.google.com/file/d/19-OE...
A quick demonstration of how slot machines at the casino do their thing, followed by a breakdown of the mathematics, statistics, and probabilities of a simple, sample slot machine game. Would you play a games like these at the casino once you know exactly how it is stacked against you? What about the other games available?
Bradley Sward is currently an Associate Professor at the College of DuPage in suburban Chicago, Illinois. He has earned a Masters degree in Software Engineering from DePaul University, a Masters degree in Computer Science from the University of Illinois at Springfield, and two Bachelors degrees in Computer Science and Molecular Biology from Benedictine University. Prior to teaching, Bradley worked for five years in the field of casino gaming on a variety of video slot machine and poker games. The Village People have been permanently etched into his brain.
I'm writing a thesis right now on casinos and this video helped me so much thank you !!!
Recent mathematics graduate. I am dying to get into this field. I built my own slot machine over the last month, along with documentation of the math model. Working on building a new one implementing bonus games
GitHub?
Hey were you successful ? Now trying to make my own slot machine
So,no matter which way I go I'm screwed in the long run. Thanks!
Great content very informative video I have subscribed.
Hey Bradaley, thanks for the awesome video! Really nice work of breaking it down and explaining it in laymens terms - very easy to digest from someone without mathematical background! Would you possibly be interested in breaking down some of the more unique virtual slot games such as megaways where the player when reaching a win, symbols explode and fall down becoming replaced with different symbols (allowing the user to keep on winning off one spin). Regardless, thanks for the awesome breakdown! Would love to see an even more advanced mathematic of slot machines video in the future if you havent already made one!
hahahaha
Nice video, Tell Sirvatka I said hello...
One question. How to work a Cascading Reels Slot? speaking about math model?. If you have 7-7-7 these explode, then falls other symbols for refill the missing, how to work the process math? (statistics). Too, any cascading reel spreadsheet it will be helpful for me. Regards.
thanks for the video. I'm curious about the bet amount. You were putting in what would pay if a certain combination pops up. Does that or can that change with the denomination or the bet amount? In other words for the $30 payout if someone was rolling $3 spins that would be a great win if they were rolling $45 spins they would still call it a loss
There was actually a few cheat devs that programmed a "cheat" code into machines for an example if someone had a $5.00 bet and $20.5 balance at the 3rd min of an hour, placed a 2$ coin, 1$, coin 2$, 1$ note and then a 10$ note before the 4th min, you'd win the jackpot next spin
i can tell you (and if you really want to see) that the slot machine manufacturers CAN increase luck by at the least one (that i know of) method... it works like this... this is particularly in slot tournaments... what they do is generate more outcomes in the background .. the result that has BETTER results is shown... and even though its illegal to swtich the results AFTER the results are generated.. its not illegal to do this because it is generated in the background (i think) (IANAL)
This stuff is fascinaitng to me. I'd love a gig working with slot machines when I graduate
I've been trying to figure out how to program a slot game on a ti-83... I can't wrap my head around how to test the random select or 'spin' up against the pay table. Three slots would be 999 combinations; would I have to label each of the 999 options as win or loss? There has to be an easier/cleaner way to code this.
It has been a few um decades since I programmed my TI to play Pac-Man at like one frame per second, so I'm not sure what you have access to in the current year. But something like parallel arrays or a map structure would work pretty well. Turn the three slot values into a three digit number and then check the map/array/whatever. You're right that you want to test the symbols and not the values of the reel stops themselves.
@@bradleysward Thanks for the reply! I'll have to look into parallel arrays to see if I understand. I started out trying to building a couple of matrices to cross refrence each other and beginning to see why it can get confusing and very, VERY slow.
Have you thought about developing a full blown slot or two? I'd love to work with you if you have the skillset
How can you find out the payout percentage at a given casino? Would be nice if by law the casino would have to provide that info.
These are some of the standard RTP ratios that machines are implemented with,
- 96% (house edge 4%)
- 94% (house edge 6%)
- 90% (house edge 10%)
- 84% (house edge 16%)
I was told that some machines may have an RTP below 85%, so as to yield the house a higher edge.
Here you don't count the times when you get in-between 2 items do you ?
hi sir . is it for online slot games that the server determines the jackpot, not coding?
On online slot machines I believe they have a server running the calculations, same as a mechanical slot machine just in a different location
Imagine they ran it user side 😂
In the Rules of the Aristocrat game Dragon Link it states that the odds for hitting a Grand, Major, Minor or Mini improve Proportionally to your wager? Does that mean that the virtual reels in the bonus game have more Major, Minor and Mini balls and more balls in general proportionate to your bet size. Meaning they would make different virtual reels in the bonus based on bet size?
Those progressive jackpots are predetermined. Example, if the major hit at $700, as soon as hits, the next major jackpot is set, and it's based on the coin in/coin out/current variance at that time. But the biggest takeaway if from Aristocrat's patent...(for linked machines).....A bank of 6 Dragon Link machines in a circle, IT IS CONSIDERED ONE SLOT TERMINAL/ASSET. Those 6 are running off one chipset linked together
@@kostasgiannoulias1111 I’m talking about how the spin and hold bonus is determined based on the bet placed. Does it pick from a higher pay table with more balls to win the grand with more major and minor balls with higher wagers scaled proportional to the bet
So think of it as minimum bet is 1 ticket, max bet is 4 tickets. So basically you get more chances based upon how many times “ you entered “ the pot. But in reality it’s chosen on predetermined spins and whoever lands that certain spin doesn’t and will often never be maxed out, but it’s chosen before first spin in that scenario and resets to chosen spin when reset.
Most progressives will literally tell you that you’re about to win it, and often next spin boom. OR it just appears.
I was wondering if casinos have a minimum amount per hour that they require from a slot machine design? ie $250/hr. Also how do casinos mitigate the risk of large jackpots?
Thanks for your interest and question! It's all based on percentages. Each game has many setups from 85% to 99% or so. Casinos on strip Vegas generally are 85% and as you go off strip you play more to the local population. Some games are rentals, and some are purchased outright. My grandparents had a mechanical machine way back that didn't hit for a year and then hit three times in one night. They had a grand prize policy for us that had to be modified after that night... The casinos would feel the same way! The fun of probability in the short term versus the long!
What I was going for was something like are slot machine designers are using a risk of ruin, or a some statistical formula to asses likeliness to lose a high prize before recouping the money. Like I'm sure they make the odds proportionally higher the larger the is to hit. ie. $100 might be $300 in for every $100 as opposed to $1,000,00 prize might be 300X that amount in before it hits.
Can you explain put options ? Is that the same as a slot machine?
Yes
Can you upload the spreadsheet so we can play with it?
Also, does it seed once when powered up, or every time a coin is inserted, or simply keep reseeding at random intervals while running? Does changing the seed chage the odds?
One more question. Doesn't the bonus round change the overall machine odds if you decide to give out more than 30 (in your example) 25% of the time? I realize you are giving 50, 25% of the time and less than 30 75% of the time, but the time it pays 50 means the overall odds are not 93.3% when that happens, right? If so, what would be the proper way? Thanks!
I just added a link in the description. It's rather hard coded so there isn't too much interactivity there! :)
In my experience, the seed generator keeps pumping out a string of numbers, whether they get used or not. I am certainly not a mathematician and never got to see the underlying code, but all code has to pass many levels of certification so it must work as advertised.
Oh yes, the expected value for the bonus game has to remain consistent to match everything computed with the base game. Every credit given has to have it taken away somewhere else, and vice versa. So to add more credits to the bonus game, but still keep the percentage almost exactly the same, you have to remove some from the base game.
This is all well and fine in stand alone machines. However certain casinos are Server Based meaning that their payouts on their machines can be set at any time based on total income the casino is receiving. In particular when the casino is not busy payouts to the floor are less compared to when its busy.
So Server based casinos do and can control slot payouts and in my opinion should all be banned as this is a form of control and manipulation taking random play away from the player which is an unfair advantage.
Very smart sir. All people have to do is read us patents owned by these companies. This is allowed because the casino technically stays in good standing (within the regulations) over the course of its operation.
@@kostasgiannoulias1111i imagine that it’s also the easiest argument to make since people aren’t going to notice unless they play 5-10k$ a day or are autistic savant obsessed with processed past payouts and obviously never going to happen.
Slots are not mysterious to me but yet absolutely baffles me at the same time? I don’t believe that every spin is random for every game. Maybe a few old ones
Are you familiar with aristocrat slot machines and how they work?
I'm Indonesian. i like to listen to you talk .. but it's too fast i find it hard to understand .. you are smart smart.
Have a question my girlfriend goes to Northfield Casino in Ohio the machines since 2024 the slot machines I've been really hard on payout she doesn't have a lot of money and there really is no payout why is that Annoying It's a single Casino
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