Math Of Slot Machines
- Math Behind Slot Machines
- The Math Behind Slot Machines
- Math Of Slot Machines Machine
- Math Of Slot Machines Jackpots
- Math Of Slot Machines Games
Modern slot machines are more complicated it’s much more difficult to mathematically predict the odds, because the numbers are theoretical and are essentially developed from a pool of infinite spins. Modern slot machines use a Random Number Generator (RNG). The RNG electronically generates a random value from millions of combinations. Coin-in, simply speaking, is the total amount of bets made. Let’s say you pick a slot machine and bet $1 per spin and do 100 spins. Your total coin-in is $100. Coin-in is not a count of how much currency you’ve inserted into the machine, but instead a cumulative total of wagers made. There was a question presented to you on 'mathematics in the slot machines'. Forget it, the slot machines are run by computers and can be tightened or loosened at the casino's whim. Best regards, Larry and Alice. Dear Larry and Alice, And Earth is flat and the center of the universe. Best of luck in and out of the casinos, John.
Remember the movie National Lampoon’s Vegas Vacation, when gambling fever consumes Chevy Chase’s character, Clark W. Griswold? He goes on a losing streak to beat all losing streaks while his son, Rusty, wins four cars by playing the slot machines. Maybe Clark would have done better if he had read Probability For Dummies! In this article, you discover the basic ideas behind slot machines and how they work, so that you can get past the myths and develop a strategy based on sound probability.
Understanding average payout
Slot Tutorials Slot Machine Math: Hit Frequency. Written by Joshua. Today’s post probably could double as a slot volatility. 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. M athematicians first got interested in randomness by studying games of chance.
When casinos advertise that their slot machines pay out an average of 90 percent, the fine print they don’t want you to read says that you lose 10 cents from each dollar you put into the machines in the long term. (In probability terms, this advertisement means that your expected winnings are minus 10 cents on every dollar you spend every time the money goes through the machines.)
Suppose you start with $100 and bet a dollar at a time, for example. After inserting all $100 into the slot, 100 pulls later you’ll end up on average with $90, because you lose 10 percent of your money. If you run the $90 back through the machine, you’ll end up with 90 percent of it back, which is 0.90 x 90 = $81. If you run that amount through in 81 pulls, you’ll have $72.90 afterward (0.90 x 81 = 72.90). If you keep going for 44 rounds, on average, the money will be gone, unless you have the luck of Rusty Griswold!
How many pulls on the machine does your $100 give you at this rate? Each time you have less money to run through the machine, so you have fewer pulls left. If you insert $1 at a time, you can expect 972 total pulls in the long term with these average payouts (that’s the total pulls in 44 rounds). But keep in mind that casinos are designing slot machines to go faster and faster between spins. Some are even doing away with the handles and tokens by using digital readouts on gaming cards that you put into the machines. The faster machines can play up to 25 spins per hour, and 972 spins divided by 25 spins per minute is 38.88 minutes. You don’t have a very long time to enjoy your $100 before it’s gone!
The worst part? Casinos often advertise that their “average payouts” are even as high as 95 percent. But beware: That number applies only to certain machines, and the casinos don’t rush to tell you which ones. You really need to read or ask about the fine print before playing. You can also try to check the information on the machine to see if it lists its payouts. (Don’t expect this information to be front and center.)
Implementing a simple strategy for slots
Math Behind Slot Machines
Advice varies regarding whether you should play nickel, quarter, or dollar slot machines and whether you should max out the number of coins you bet or not (you usually get to choose between one and five coins to bet on a standard slot machine). In this section, you’ll find a few tips for getting the most bang for your buck (or nickel) when playing slot machines.
Basically, when it comes to slot machines, strategy boils down to this: Know the rules, your probability of winning, and the expected payouts; dispel any myths; and quit while you’re ahead. If you win $100, cash out $50 and play with the rest, for example. After you lose a certain amount (determined by you in advance), don’t hesitate to quit. Go to the all-you-can-eat buffet and try your luck with the casino food; odds are it’s pretty good!
Choosing among nickel, quarter, and dollar machines
The machines that have the higher denominations usually give the best payouts. So, between the nickel and quarter slots, for example, the quarter slots generally give better payouts. However, you run the risk of getting in way over your head in a hurry, so don’t bet more than you can afford to lose. The bottom line: Always choose a level that you have fun playing at and that allows you to play for your full set time limit.
Deciding how many coins to play at a time
When deciding on the number of coins you should play per spin, keep in mind that more is sometimes better. If the slot machine gives you more than two times the payout when you put in two times the number of coins, for example, you should max it out instead of playing single coins because you increase your chances of winning a bigger pot, and the expected value is higher. If the machine just gives you k times the payout for k coins, it doesn’t matter if you use the maximum number of coins. You may as well play one at a time until you can make some money and leave so your money lasts a little longer.
For example, say a quarter machine pays 10 credits for the outcome 777 when you play only a single quarter, but if you play two quarters, it gives you 25 credits for the same outcome. And if you play the maximum number of quarters (say, four), a 777 results in 1,000 credits. You can see that playing four quarters at a time gives you a better chance of winning a bigger pot in the long run (if you win, that is) compared to playing a single quarter at a time for four consecutive tries.
The latest slot machine sweeping the nation is the so-called “penny slot machine.” Although it professes to require only a penny for a spin, you get this rate only if you want to bet one penny at a time. The machines entice you to bet way more than one penny at a time; in fact, on some machines, you can bet more than 1,000 coins (called lines) on each spin — $10 a shot here, folks. Because these machines take any denomination of paper bill, as well as credit cards, your money can go faster on penny machines than on dollar machines because you can quickly lose track of your spendings. Pinching pennies may not be worth it after all!
Slot machines – and, in fact, any gambling machine – pays back a percentage of bets in such a way that the casino generates a profit. That payback percentage varies from casino to casino and from machine to machine.
The attraction that slot games have is that they sometimes produce profits in the short term.
But in the long run, the math ensures that the casino will profit.
The Math Behind Slot Machines
In this post, I look at some of the math behind how slot machines and payback percentages work.
It’s not complicated, but you should understand it before putting your money into one of these games.
Odds, Probability, and Slot Machines
The first thing you should understand is that the outcome of any given spin on a slot machine is random. It’s also an “independent event.” This means that what happened on the previous spin has no effect on the probability of getting a result on the next spin.
An event’s probability if always a number between 0 and 1. An event that can’t possibly happen has a probability of 0. An event that will happen every time has a probability of 100%. And when you add the probability of something happening with the probability of it not happening, the total is always 1.
You probably already know this, but any number between 0 and 1 can be expressed in multiple ways:
- As a fraction
- As a decimal
- As a percentage
Something that will happen as often or not has a probability of 1/2, which can also be expressed as 0.5 or as 50%.
Most people understand exactly what that means, too – it means that this event will happen half the time.
Another important thing to understand about probabilities is that when you’re trying to determine the probability that event A will happen AND event B will happen, you multiply.
Here’s an example:
If you have a standard deck of cards, you have a 50% probability of drawing a red card when you draw a random card from the deck.
If you want to calculate the probability of drawing 2 red cards in a row, you’re looking at the probability of getting a red card on the first draw AND getting a red card on the 2nd draw.
This means your probability is 50% X 50%, or 25%.
An Example of a Slot Machine Probability Problem
Suppose you have a slot machine with 10 symbols on it and 3 reels. Each symbol has an equal probability of coming up.
You want to calculate the probability of getting 3 cherries.
The probability of getting a cherry on reel #1 is 1/10. That’s the same for reel #2 and reel #3.
So 1/10 X 1/10 X 1/10 = 1/1000.
How the Payouts for the Prizes Determine the Profitability of the Machine
With 10 symbols on this slot machine, you have 1000s different possible outcomes.
When you add up the prize amounts for every possible winning outcome, you will inevitably come up with a number less than 1000, because that’s how the casino makes its profit.
You can see this by assuming that you make 1000 spins and get every possible combination. Add up how much money you put into those spins. Then look at how much money you’re left with.
The percentage is always less than 100%.
For example, if you add up all the potential prizes and get 900 coins on a slot machine with 1000 different outcomes, the payback percentage for that game is 90%.
The casino, on average, over time, makes 10% for every bet you place.
This number will go up and down over time because of the nature of random events.
But the Law of Large Numbers suggests that as you make more spins, the closer your actual results will get to the theoretical expectation.
And when you talk about the long run with gambling games, you’re usually talking about thousands of tens of thousands of spins.
The average slots player makes 600 spins per hour, but I’ve clocked players who were making 900 spins per hour.
I average about 450 spins per hour, because I intentionally play slowly to keep my average loss per hour down.
Your Average Hourly Loss Rate
The casinos are interested in your average hourly loss rate. Luckily for them, it’s easy to calculate. All they need is the total amount of your hourly action on a machine and the payback percentage for that machine.
Your total hourly action is easy to calculate. It’s the number of bets you’re making per hour multiplied by the size of those bets.
For example, if you’re playing Megabucks slots, you’re making a $3 average bet. At 600 spins per hour, that’s $1800 per hour in action.
If the payback percentage for that machine is 85%, you’ll get back $1530, which means you’ll lose $270.
The more time you spend on the machine, the likelier the casino is to see you lose the expected amount. Also, over a large number of customers, the more time spent on the machines, the more money they make.
The Relationship between the House Edge and the Payback Percentage
When you talk about table games, you talk about the “house edge,” which is the amount of each bet that the casino expects to win from you over the long run. Payouts for table games are expressed in terms of odds, and the odds for table games are expressed as “x to y.”
For example, you might place a casino bet where the payout is 2 to 1. The 1 represents your bet, and the 2 represents the payout if you win.
If you lose, the 1 unit goes to the casino. If you win, you get the 1 unit back along with 2 units in winnings. The payout is 2 to 1.
Math Of Slot Machines Machine
Gambling machines, though, handle their payout odds differently. They pay out on an “x for y” basis.
In this case, you lose your original bet no matter what the outcome is – you’re trading your bet for the payout instead of getting the payout and the bet back.
If you’re getting paid 2 to 1, you show a profit of 2 units.
If you’re getting paid 2 for 1, you only show a profit of 1 unit.
The unit you initially wagered is gone.
This is why payback percentage is the standard for gambling machines and house edge is the standard for table games.
But it doesn’t have to be that way.
You could talk about the house edge on a slot machine, for example. And the same thing is true for gambling machine odds as is true of probability – when you add the payback percentage and the house edge together, the sum is always 100%.
The Problem with Gambling Machines and Math
The reason that gambling machines are so profitable for the casino is the same reason that it’s so damaging to your pocketbook:
You make more bets per hour playing slot machines or video poker than you would at any other casino game by a factor of at least 3.
If you’re playing real money blackjack with a fast dealer and no other players, you’re only getting 200 hands per hour.
Put another 2 players at the table with you, and the number of hands you get per hour drops dramatically – maybe to 60 bets per hour.
Anytime you reduce one of the factors in a multiplication problem by that big a factor, the other factors don’t matter as much.
For example, someone betting $3 per spin on a slot machine is putting $1800 per hour into action. Even if you find a rare unicorn of a slot machine with a 1% house edge, you’re still losing $18 per hour.
Contrast that with a blackjack player betting $5 per hand against the same 1% house edge. You’re looking at $1000 per hour in total action, so your expected loss per hour is only $10.
And guess what.
You won’t find a slot machine with a 1% house edge, but you can and will face a 1% house edge if you master basic strategy in blackjack.
Does the Math Mean I Shouldn’t Play Slot Machines?
If the only thing you’re interested in is minimizing how much money you’re going to lose at the casino, you shouldn’t play ANY of the casino games. That way you won’t lose any money at all, which is the definite minimum amount to lose in a casino.
After that, you have to start weighing in how much you enjoy the games.
Do you really find slot machines 3, 4, or 5 times as entertaining as blackjack?
The answer might well be yes, and if that’s the case, great – spin those reels.
On the other hand, if the answer is no, you probably shouldn’t fool with the slot machines.
Conclusion
The gambling math behind slot machine odds and probability isn’t much different from the math of other casino games.
Math Of Slot Machines Jackpots
But you should have a basic understanding of what’s happening to your money when you gamble.
Math Of Slot Machines Games
The only way to do that with slot machines is to understand the math behind the games’ proba