On page 193 in Slot Machines: A Pictorial History of the First 100 Years by Marshall Fey, there’s a great picture of Bally’s casino floor in Atlantic City that illustrates my point. The picture shows hundreds of slot machines all lined up in perfect rows like little soldiers. Atlantic City’s Best Casino Slots are at Resorts AC Over 800 New Slot Machines! With more than 800 slot games and a reputation as the “luckiest casino” for slots in Atlantic City, there’s no better place to play the slots.

Some people might want to know how to find the payout percentage on a slot machine. Sadly, it’s not something that’s printed on most games — at least not here in the United States.

This post is for them.

Understanding this topic involves some rudimentary understanding of probability as it relates to casino gambling. You’ll need to understand three separate concepts thoroughly:

Payback percentage
House edge
Return to player

This post explains each of those in enough detail that even a beginner should understand what they mean.

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Some Basic Facts Related to Probability, the House Edge, Payback Percentage, and Return to Player

Probability is the branch of mathematics that deals with how likely an event is to happen. If you want to measure how likely you are to win a jackpot on a slot machine, probability is the way to figure that out.

But the word also refers directly to that likelihood.

In other words, if I say the probability of getting heads when I flip a coin is 50%, I’m not talking about that branch of mathematics. I’m talking about the actual statistical likelihood of that event.

You should understand a few things about probability in general.

Probability is always a number between 0 and 1. An event with a probability of 0 will never happen, and an event with a probability of 1 will always happen. The closer to 1 the probability is, the more likely the event is to happen.

Probability can be expressed multiple ways. It can be expressed as a fraction, a decimal, a percentage, or as odds. The probability of getting heads on a coin flip can be expressed as 1/2, 0.5, 50%, or 1 to 1.

An event’s probability is the number of ways it can happen divided by the total number of possible outcomes. When you’re discussing a coin toss, you have two possible outcomes. Only one of those is heads. That makes the probability 1/2.

The probability that an event will occur added to the probability that an event won’t occur always equals 1. Therefore, if you know the probability that something will happen, you also automatically know the probability that it won’t happen, and vice versa.

The house edge is a statistical measure of how much the house expects to win (on average, over the long run) from every bet you make on a game. The house edge is a theoretical number that accounts for the probability of winning versus the probability of losing AND the payout if you win.

All casino games carry a house edge. In the short run, it doesn’t matter much, but in the long run, it’s the most important thing.

If I say a game has a house edge of 4%, this means that over time, you should average a loss of $4 for every $100 you bet on the game. This is a long run statistical average, though. In the short run, you’re unlikely to see results that mirror the house edge.

The return to player and the payback percentage are the same thing. Some writers use one to refer to the statistical expectation and the other to refer to the actual results, but most writers use these terms interchangeably.

The payback percentage added to the house edge always equals 100%. The payback percentage is the amount of each bet that you get back, and the house edge is the amount of each bet that the casino wins. Again, these numbers are on average over the long run.

A game with a 4% house edge has a 96% payback percentage.

In the United States, slot machine payback percentages are impossible to calculate and not posted on gambling machines. To calculate the house edge or the payback percentage for a casino game, you need two pieces of data:

The probability of winning
The amount of money you’ll win (the payoff)

Slot machines include their payouts on their pay tables, but they don’t include the probability of achieving any of the winning outcomes.

In some countries, the payback percentage is posted on the machines, but not in the United States.

To make things even worse for a slot machine player, the random number generator program can be set differently even if the slot machine is identical to the one next to it. You could be playing The Big Lebowski slots at Choctaw Casino in Durant, Oklahoma, and your buddy could be playing the identical machine right next to you.

The payback percentage on his machine might be 94%, and the payback percentage on your machine might only be 88%.

The difference comes from how the probabilities are weighted for each symbol. On one game, the bars might show up 1/4 of the time, but on the next, they might only come up 1/8 of the time.

This has an obvious effect on the payback percentage.

The payback percentage would be easy to calculate if you knew the probabilities. The payback percentage is just the total expected value of all the possible outcomes on the machine.

Let’s assume you have 1000 possible reel combinations. Let’s also assume that if you got each of those in order, from 1 to 1000, you’d win 900 coins.

The payback percentage for that game would be 90%.

You’d put 1000 coins in, and you’d have 900 coins left after a statistically perfect sampling of 1000 spins.

If you knew the payback percentage and house edge for a slot machine game, you could predict your theoretical cost of playing that game per hour in the long run. You’d only need to multiply the numbers of bets you made per hour by the size of those bets. Then you’d multiply that by the house edge to get your predicted loss.

Most slots players make 600 spins per hour. Let’s assume you’re playing on a dollar machine and betting three coins on every spin, or $3 per spin. You’re putting $1,800 per hour into action.

If the slot machine had a 90% payback percentage, you’d lose $180 per hour on that machine. You’d have $1,800 at the start of the hour and $1,620 at the end of the hour — assuming you saw statistically predicted results.

In the real world, though, where you’d be seeing short-term results, you’d see some hours where you won and some hours where you lost. If you played long enough, the Law of Large Numbers would ensure that you’d eventually see the statistically predicted results.

This is how the casinos make their money. In the short run, you’ll win some of the time. That will keep you playing.

But in the long run, the math will ensure that the casino will win a net profit.

How You Could Calculate a Payback Percentage Based on Actual Results

Of course, you have some data that you can directly observe when you’re playing slot machines.

But tracking this data and calculating the payback percentage on a specific session can add to your enjoyment of any slot machine game. It can make you more mindful because you’ll be paying more attention to what’s happening.

Here’s how to do it.

Start by tracking how many spins you’re making per hour. This is easy to do, but it takes more effort than you might think. It might help to get one of those clicky things people use to count stuff with. You will probably also need a stopwatch of some kind. I just use the timer function on my phone.

Make a note (mental is fine) of how much you’re betting per spin. It helps to bet the same amount.

Also note how much money you started with so that you can calculate how much you’ve won or lost. The slot machine will convert your money into credits. The easiest thing to do is to keep up with how many credits you had at the beginning of the session and again at the end of the session.

Now, let’s do the math using a hypothetical 45-minute session.

I made 300 spins in 45 minutes. I was betting $3 per spin, and I started with $600.

After my playing session, I had $500 left. At times I was up, and at times I was down.

But my net loss was $100. (My starting bankroll was $600, and I finished with $500.)<