Newer slots will require you to know a bit about computer circuitry, but the classics just need a screwdriver, wrench and a magic touch. (OK, you probably need more tools than that.) Watch the videos below to understand how the slot machines work and what’s required for common repairs.
Today, the mathematics of slot machines. The University of Houston mathematics department presents this program about the machines that make our civilization run, and the people whose ingenuity created them.
Mathematicians first got interested in randomness by studying games of chance. Ever since, the histories of mathematics and gambling have been intertwined. Clever gamblers use mathematics to look for the smallest advantages, and casinos use sophisticated mathematical tools to devise new ways of drawing in players.
Indeed, a patent granted to the Norwegian mathematician Inge Telnaes in 1984 transformed the gambling industry. Prior to Telnaes’ invention, slot machines were essentially mechanical devices. Besides being difficult to tune and maintain, mechanical slot machines suffered from an essential problem: Let’s look at a machine with three reels, each with 12 symbols, with one of those 12 symbols a cherry. The likelihood of getting three cherries, and winning the jackpot, is 1 in 1,728. If the casino wants to make money, the jackpot payout should be, say $1,700 on a $1 bet. That does not seem attractive by today’s standards. However, the only way to increase the payout is to decrease the chances of hitting a jackpot.
Adding another reel is a possibility. For instance adding a fourth reel in the previous example would get us to a jackpot of about $20,000. But people do not like machines with more reels — they intuitively, and rightfully, feel that extra reels diminish their chance of winning. Another possibility is to put more symbols on each reel. But the astronomical jackpots you see in casinos today would then require truly enormous machines.
Inge Telnaes proposed a simple solution: Let a random number generator — a computer chip — determine the combination of symbols that appear when the reels stop. In other words, use a chip to control where the reels stop on a spin, but create the illusion that the wheels stopped on their own. The number of possible outcomes on the slot machine does not change. However, by reprogramming the chip, the operator has full control over the likelihood of each of the different outcomes. For instance, the operator could make the three cherries appear only once in a million spins.
This was a brilliant insight: Suppose I pick a number between one and a million. Would you be willing to bet that you can guess that number? The answer is probably not. But let a computer chip pick such a number, put the chip in a machine with blinking lights and spinning reels, and many people will be more than willing to make the bet. It is simply because what people assume is happening in a slot machine is very different from what is actually happening.
The Magician oil painting by Hieronymus Boschfrom between 1475 and 1480
The history of gambling is also intertwined with that of a less reputable group — tricksters and swindlers. In the long run, the only sure way to make money by gambling is to create the illusion that your opponent can win, while keeping the odds firmly on your side. And that gives those who know math a very solid advantage.
I'm Krešimir Josić, at the University of Houston, where we're interested in the way inventive minds work.
NOTE: In the example with three cherries, I assumed that one only wins in the case the spin results in three cherries, and there is no other winning combination. In actuality, there are typically many winning combination, and as a result, the jackpot would have to be even smaller.
The following story in Wired Magazine shows the drawbacks of the new generation of slot machines — they are easier to hack and to counterfit than their mechanical counterpart http://www.wired.com/magazine/2011/07/ff_scammingslots/.
Here is a more exhaustive discussion of the history of slot machines, and the random number generators within them http://catlin.casinocitytimes.com/article/non-random-randomness-part-1-1243. You may want to scroll towards the end of the article to read about how flaws in the design of gambling machine resulted in somebody picking 19 out of 20 winning numbers in a game of KENO — and doing so 3 times in a row. That person walked away with $620,000, but only after some controversy.
Both images are from Wikipedia. The slot machine image was taken by Jeff Kubina.
For more mathematics in everyday life, visitkjosic.wordpress.com.
This episode was first aired on September 7th, 2011
Slot machines are the most popular gambling game in most United States casinos, but the number of players who really understand how they work is terribly small.
The purpose of this post is to explain what slot machines are and how they work in language anyone can understand.
Frankly, I think most people who understand how slot machines really work avoid playing them. And I think some of the people who play slot machines and think those games are cheating are daft in their reasoning, too.
If you pay attention to what I’ve written in this post, you’ll know the truth about slot machines.
And when you know the truth, you can make a decision about whether to play as an educated person instead of as a rube.
Modern slot machines are powered by computers and electronic devices, but that wasn’t always so. Understanding how those computers and electronics produce results requires some understanding of the history of slot machines and how they worked in the past.
What makes a slot machine a slot machine is the presence of spinning reels with symbols on them. Early version of slot machines used actual physical reels, springs, and gears to create random results.
On the front of these machines was a window with a horizontal line across it. This represented the “payline.” If symbols lined up and matched on the payline, you won a prize amount.
At first this was money, but eventually, slots were outlawed. Many bar and pub owners replaced the monetary prizes with fruit-flavored candy and sticks of candy to get around the new laws.
The traditional, classic symbols on slot machine reels are still based on those older machines. This is why you find so many slot machines with cherries, apples, and bars on them. (The bars represent sticks of gum.)
The early slot machines used the same strategy to make money in the long run that modern slot machines do. They gave you odds of winning that weren’t commensurate with the payout amount.
This is best explained using some mathematical examples.Let’s say you have a simple 3-reel slot machine game with 10 symbols on each reel. This slot machine only has 1 winning combination, too, and it costs $1 per spin to play.
There are 1000 possible combinations of symbols on a 3-reel slot machine of that description, but only one of them is a possible winner.
If that winning combination pays off 950 for 1, the casino has a clear advantage, right?
Over 1000 spins, you’ll lose $1000, but on that single winning spin, you’ll win $950 of it back. You’ll lose $50.
That is, of course, a theoretical result based on long-term mathematical expectations. In the short run, anything can and often will happen when you’re playing slots.
And real slot machines are more robust than that. They have more winning combinations with lower prize amounts, but all the prize amounts multiplied by all the probabilities of winning always result in a number less than 100%.
That number is called the payback percentage.
Modern slot machines use the same kind of math and game-play, but instead of using a complicated system of gears and stops, they use computer programs to create the same kind of odds. This has perks for the player, but it has drawbacks, too.
On a traditional mechanical slot machine, the probabilities are straightforward. If you have 10 different symbols, the probability of that symbol showing up on a payline in a spot is 1/10.
With a computerized slot machine, the designers can use any kind of weighting that they want to. One symbol might be programmed to show up 1/20 of the time, while another might be programmed to show up 1/5 of the time.
You have no way of knowing or estimating what the probability is, either.
To make things even more interesting, 2 identical slot machines might have different programming “under the hood.”
You might be playing The Price Is Right slot machines at a casino and be facing a 95% payback percentage.
You might switch to the same game at the same stakes at the machine next to it and be facing a payback percentage of 85%. There’s no way to tell the difference.
This change in the way the games work enables casinos to offer larger jackpots than they would be able to offer otherwise.
But you trade transparency for that.
I prefer to play games where I can figure out how much of a mathematical disadvantage I have.
That’s impossible with most modern slot machine games.
Random Number Generator Programs and Why Slot Machines Don’t Cheat
The computer program that powers these results is called a random number generator. That’s almost always referred to by an acronym of “RNG.”
It’s a simple enough computer program. It’s just a program that continually thinks of numbers—thousands of them per second. When you press the spin or stop button on a slot machine, the computer program stops on one of those numbers.
That number corresponds to a combination on the reels of the machine.
The outcome has been determined by the computer program before the reels stop spinning.
This doesn’t mean that the machine is cheating. You’re not more likely to lose after a winning streak, and you’re not more likely to win after a losing streak. Every spin of the reels is an independent event.
The difference between the odds of winning and the payout odds for each bet is what creates an edge for the house. Cheating isn’t necessary for the casinos or the slot machine designers.
The math takes care of that for them.
I have a paranoid friend who literally believes the world is flat. He also thinks slot machines are rigged.
He’s wrong about both, but he’s less wrong about the slot machines.
They ARE rigged, mathematically, by providing payouts that are lower than the odds of winning.
But they work honestly in terms of providing completely random results and independent trials. In fact, in any jurisdiction where such games are legal, they’re heavily regulated, inspected, and audited.
Casinos make more money from slot machines than they’d probably make with a printing press that printed new money in that same amount of floor space.
The Difference between Short Term Results and Long Term Expectations
The mathematical examples I’ve used assume you’re interested in predicting results in the long run. That’s the entire point of gambling math as it relates to probability.
But long term expectations have little to do with what happens in the short run.
The long run can be defined as an infinite number of bets. Every bet you place brings you closer to the long run, but you’ll never get there.
The Law of Large Numbers is a mathematical principle that says the more independent trials you run, the closer you’ll get to the theoretical expectation.
In the short term, though, you’re possibly going to win. I’ve seen surveys that showed that roughly 20% of the gamblers at a casino leave with some winnings in their pocket on any given visit. The casinos don’t mind. In fact, they’re counting on it.
If no one ever won, people wouldn’t play. And without gamblers, casinos make no money and can’t stay in business.
My best advice to someone who’s playing slot machines is to not spend much time in front of them. If you get a reasonable sized win when you sit down, be willing to quit and walk away.
The longer you play, the more likely you are to see results that mirror the long term expectation.
Your goal should be to take advantage of those short term aberrations called luck or deviation. You can’t count on that in any given situation,
The longer you play, the more your results are going to resemble the mathematically expected results.
And with a negative expectation game like a slot machine, you’re going to lose all your money if you play long enough. That’s how a negative expectation gambling game works.
LOUISIANA SLOT MACHINE PAYBACK STATISTICS Gaming regulations require that gaming machines in casinos be programmed to pay back no less than 80% and no more than 99.9%. For video gaming machines at locations other than casinos, the law. /slot-machine-payout-rules.html.
What about the Other Bells and Whistles on Modern Slot Machine Games?
When I use the expression “bells and whistles,” I’m talking about features of slot machine games other than the standard 3 spinning reels. Some of these additions and changes are complicated, but some of them are simplicity itself to understand.
One example of a bell and whistle is the number of reels on a slot machine game. Traditional slot machines just had 3 reels, and one of the reasons for that was the size of the reels and the machine that housed them.
The number of symbols also used to depend on the size of the reels—the smaller the reels, the fewer symbols you can print on them.
Additional paylines are another bell and whistle on most modern slot machines. The traditional machine just has a payline horizontally across the center, but modern slot machines have various patterns similar to the various patterns you might use on bingo cards.
They might run diagonally, or they might run in a zig zag pattern.
To activate multiple paylines, you must make multiple bets. Each payline gets activated by a wager, and the payout is based on the combination that appears on that line and the wager on that line only.
On larger machines with lots of paylines, you can win on multiple paylines but still be a net loser. For example, if you bet a nickel on each of 20 paylines, you’ll have put an entire dollar in action. If one of those paylines wins for 50 cents, you’ve still lost 50 cents on the game.
But the slot machine still lights up and shows you the payout as if you were a net winner.
Wild symbols are another example of a bell and whistle on a modern slot machine. If you’ve played cards, especially poker, you are probably already familiar with the concept of a wild symbol.
It’s a symbol that can be used to complete any winning combination. It acts as a replacement for the symbol that you needed to make that combination.
Scatter symbols are a little more confusing, but they’re similar to wild symbols. A scatter symbol is one that doesn’t have to be on a payline to trigger a payoff. You just need enough of those scatter symbols to show up somewhere on the screen at once.
Many times, on a 5-reel machine, you’ll get a payoff if 3 scatter symbols or more show up from left to right. They don’t need to be along a payline or anything like that. They can literally be “scattered” across the screen.
Sometimes scatter symbols and/or wild symbols trigger bonus games or free spins. Free spins are a simple enough concept to understand—they’re just extra spins on the reels that you don’t have to pay for.
On some machines, they’re always winning spins—the only thing in question is how much you’re going to win on each spin.
Bonus games can be more interesting, but they’re almost always entirely random. Often the bonus games involve choosing from a video display of multiple boxes or treasure chests. Depending on which one you choose, you get a prize amount.
There’s no skill involved in these kinds of bonus games.
Slot machine designers are now experimenting with design elements that borrow from video games like Space Invaders, though. If you get a certain number of symbols, you can trigger a bonus game, and the amount you win from that bonus game might depend on how many aliens you can shoot from the skies overhead.
Slot Machine Strategies and Systems Don’t Work, So Don’t Even Bother
If I could teach you only one thing about slot machine games, it’s this:
They’re entirely random. Each spin is an independent event. This means that what’s happened on previous spins has no effect on what’s going to happen on a subsequent spin. Most strategies and systems assume that the previous spins have some relationship to subsequent spins.
I once read an entire book of slot machine systems that were supposed to help you win at slots. The guy who wrote it was a total cornball. I’m not even going to mention the name of the book or the author here.
I will describe what he suggested, though. His first piece of advice was to track how many “naked pulls” you’ve had in a row.
A naked pull on a slot machine is one that results in no winnings at all.
His advice was to switch machines any time you get 5 or 7 naked pulls in a row. (I don’t remember the exact number, but it was something arbitrary like that.)
The idea behind this advice is that any machine which hasn’t paid out in the last 5 or 7 spins must be running cold, so you should find a machine that’s NOT running cold.
He also offered advice about setting loss limits and win goals. This idea has some merit, but not much.
A loss limit is the amount of your session bankroll that you’re willing to lose before walking away from a game. 20% is a commonly suggested number. So if you put $100 in a slot machine game and lost $20, you’d cash out and walk away for that session.
A win goal is just the opposite. It’s an amount that you will win which will signal that it’s time to quit playing. You might have a 20% win goal, too, which means that once you’re up to $120, you’ll call it a day for that playing session.
This can help you avoid having huge losing sessions. It can also help you have book occasional winning sessions.
What it doesn’t do is change the odds in your favor in any way. In the long run, you should think of playing slot machine games as one long game that lasts for the rest of your life.
Eventually the odds are going to even out to a point where you see the kind of results the math would predict, regardless of what happens during those individual sessions.
I’ll confess that when I play slot machines, I do use a variation of this strategy. My loss limit, though, is always 100% of the amount I put in the machine. I either want to hit my win goal or lose all my money trying.
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That’s as effective as any other loss limit, but people never suggest that.
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Raising and lowering the sizes of your bets don’t change the odds on the machines, either. Don’t pay attention to any advice which suggests otherwise.
Other Lame Pieces of Slot Machine Strategy Advice You’ve Probably Heard (Or Will Hear)
One of my favorite pieces of advice from slot machine gurus is to try to find loose slot machines on the ends of the rows of slots at the casinos.
The idea is that the casino managers put the loose machines there to attract more customers.
You’ll find superstitious types who believe that playing with you slot machine card inserted is also a mistake. They think having the card inserted makes it impossible to win.
They don’t understand how the computer programs in question work at all. They’re not connected. The random number generator determines the results of each spin. The card reader just tracks how much money you’ve put into action.
The 2 have no relation to each other.
In fact, it makes no sense that a casino would want to discourage you from using the card reader. They have a slots club for a reason—they want to encourage people to play at their casino.
In the long run, the math behind their games ensures them a healthy profit. They count on a percentage of their gamblers going home a winner.
They also want their gamblers to take advantage of the free stuff they’re earning with their slot machine club cards, because that means it’s working. It’s motivating them to play more.
Why Almost Every Other Game in the Casino Is Better than Slot Machines
The traditional way that gambling experts measure one casino game against the other is by comparing the house edge. The higher the house edge, the more the casino expects to win over time on average for each bet you place.
Slot machines generally have the highest house edge in the casino. Some of them might be exceptional, but you have no means of comparing them, because a slot machine is like a black box. You put money in and get money back.
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Compare that to a video poker game, where you can calculate the payback percentage based on the probability of getting specific poker hands against the payout for those hands.
Since those games use a 52-card deck to determine your probabilities, it’s a simple enough matter to compare one video poker game to another.
Table games make it even easier to compare house edge figures.
But even if a slot machine had the same house edge as all the other games (or lower), it’s still one of the fastest-playing games in the casino. An average slot machine gambler makes 600 spins per hour.
This means slots players are putting more money into action and losing more money over time as a result.
Finally, slot machines are proven to have an addictive effect on the human brain. Addiction is bad. Alcohol can be fun. Some drugs can be fun, too.
But addiction takes something that would otherwise be fun and turns it into something that’s NOT fun.
Look for progressive slot machines with the highest possible existing jackpot. While statistically your odds of striking said jackpot remain the same, as all today’s online slot machines use random number generators that make each spin a statistically unique event – in other words completely independent from any of the countless spins that. Slot machines work like this, you place your bet, spin the reels, and win an amount based on what the paytable shows. Progressive slot machines are different. They do have the paytable, but there is an additional jackpot that grows until a winner is chosen. What does a progressive slot machine look like. First let’s take a look at the basic of progressive machines. The big progressive jackpot is made by taking a percentage of all the money played into the machine. This means that the jackpot continues to grow as more people play the machine until somebody hits the winning symbols for the top award. First on the list is IGT Interactive's Megabucks. The first wide-area progressive machine. For example, many slot machines use the traditional slot symbols like ‘cherries‘ ‘bars‘ and the ‘big 7‘. A jackpot on this type of machine might be 5,000 coins for three 7’s (7-7-7). Most of the time—but not always—slot machines with non-progressive jackpots are of a more traditional design.
Slot machines are the most popular games in the casinos, but that’s only because most gamblers are stunningly ignorant of how they work. You don’t have that excuse any more.