- Actual Hold Percentage Slot Machine
- Hold Percentage Slot Machines
- Slot Machine Percentage Sheet
- Payout Percentages Of Slot Machines
In 2008 when gaming was introduced the average slot machine hold was a relatively high 8.7 percent. In 2009 average hold was 8.8 percent and average coin-in was $1.2 million. By 2014 average hold was at 9.9 percent and average coin-in decreased to $883,832. In order to calculate payout percentage on a slot machine with completely random RNG (Random Number Generator), you need to know 2 things beforehand: occurrence of all symbols on each reel and paytable. In a very simplistic example suppose we have a slot machine with 3 reels and with only 2.
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.
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.
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.)
Over 300 spins, that means I lost an average per spin of 33 cents. $100 in losses divided by 300 spins is 33.33 cents per spin.
How much was I betting per spin?
Since I was playing a $1 machine, and my max bet was three coins, I was risking $3 per spin.
33 cents is 11% of $3, which means my actual loss was 11%. The machine paid back 89% for the session.
Does this mean that the payback percentage for the machine is 89%?
Probably not.
In the scheme of things, 450 spins is a small sample size. To have any confidence in your statistics, you really need to have at least 5,000 spins under your belt.
Even then, depending on how volatile the game is, your actual results might be wildly different from the mathematically expected payback percentage.
Here’s another example that will prove that point.
My friend Leo went to the Winstar last weekend and played the $5 slots. He started with $3,000, and when he left, he had $4,800, which means he had an $1,800 profit for the day.
He played for seven hours.
I’ve watched Leo play. He’s slow, but not much slower than average. He makes about 500 spins per hour.
This means that he made about 3,500 spins.
$1,800 in winnings divided by 3,500 spins is an average win of 51 cents per spin.
Since he was betting $5 per spin, his return was 10.3%.
His actual return for the trip on that slot machine was 110.3%.
I have friends who design slot machines for a living — more than one, in fact. They’ll be happy to tell anyone who asks that the algorithm is never set up to have a payback percentage of more than 100%.
What About the Casinos That Advertise a Specific Payback Percentage?
Some casinos advertise a specific payback percentage. This is almost always stated as an “up to” number.
So you might see an ad for a casino that says, “Payback percentages up to 98%!”
They’re almost certainly telling the truth, too. They probably have one slot machine in their casino that has a payback percentage of 98%. Of course, it isn’t labeled, so you don’t know which one it is.
And in the short run, which is what you’re going to be playing in as an individual gambler, there’s not much difference between a 98% payback percentage and a 92% payback percentage. You could walk away a winner or a loser at either setting.
Also, keep in mind that the games aren’t designed to tighten up after a win and loosen up after a lot of losing spins. That’s not how it works at all.
The machines are designed to allow you to win a certain specific percentage of the time because of the probability. Then there’s an average amount that you’ll win based on the payout for the specific combination of symbols that you hit.
But every spin of the reels on a slot machine is an independent event. You can hit a jackpot on a spin, and your probability of hitting the jackpot on the next spin hasn’t changed at all.
What About the Denominations and Location Reports I See Advertised on the Internet?
You’ll find websites like Strictly Slots and American Casino Guide which post payback percentages for specific denominations and specific casinos. These are AVERAGES.
These averages have little bearing on the machine that you’re sitting in front of.
For example,
you might be looking at a casino that reports an average payback percentage of 94% on its dollar slot machines. That casino might have half their machines paying off at 90% and the other half paying off at 98%.
And you won’t be able to differentiate between the two because the hit ratio might be the same from one of those machines to another.
What Do Hit Ratio and Volatility Have to Do With It?
The hit ratio is the percentage of time that you can expect to hit a winning combination on a slot machine. Something like 30% isn’t unusual, but it can vary 10% or more in either direction. The casinos want you to a hit a winning combination often enough that you won’t lose interest in playing the game.
But hit ratio is only part of the equation. The average size of the prize amounts is also important. Volatility takes this into account. A game that hits less often but has higher average prize amounts might have the same payback percentage as a game that hits more often but with lower payouts.
Either way, in the short run, it will be all but impossible to discover this number, too.
If you wanted to, you could track how many spins resulted in wins for you and calculate the percentage, but you’re facing the same obstacle you are with the overall payback percentage of the machine.
You just don’t know what it’s programmed to accomplish in the long run.
Online Slot Machines
Some online casinos post the payback percentages for their slot machine games. I think this information is of limited use, but I also think it’s fairer to the gambler than not providing them with that information.
After all, table games are transparent. You can calculate the house edge for any casino table game there is because they all use random number generators with known quantities — cards, dice, and wheels.
There’s been a push to label food, both at the grocery store and at restaurants, with nutritional information that includes caloric amounts.
Requiring casinos to provide similar information about their gambling machines only makes sense.
We’ll see if it ever happens, though.
Conclusion
You can’t find the payout percentage on a slot machine — at least not in the United States.
I’ve heard that you can get this information on slot machines in Europe, but I’ve never seen an actual photograph of this kind of labeling.
You can, though, have some fun calculating actual payback percentages in the short run. This at least gives you something to keep track of while you’re playing slots, which is honestly one of the more mindless activities in the casino.
Tommy, who is one of my blog readers asked how to calculate payout percentage of any given slot machine after reading this slot strategies article. I started writing a reply to his question in the comment, but the answer turned out much longer than I had initially planned so I decided to dedicate the answer a full post I believe it deserves.
Please note that the payout percentage can only be calculated this way if each spin is completely random. The only way you can be sure it’s completely random is if you play in a casino, which is licensed by a jurisdiction dictating the outcome of each slot spin must NOT be predetermined, it has to be completely random. Casinos bound by this restriction are all legally operating casinos in Las Vegas and Atlantic City as well as most licensed online casinos.
In order to calculate payout percentage on a slot machine with completely random RNG (Random Number Generator), you need to know 2 things beforehand: occurrence of all symbols on each reel and paytable. In a very simplistic example suppose we have a slot machine with 3 reels and with only 2 symbols
and
Total number of symbols on each reel is 3: 2xBAR and 1xSeven
Payout table shows 2 winning combinations for each $1 bet as follows:
wins $1
wins $15
First we need calculate the probability of each combination:
For 3xBAR the probability is 2/3 * 2/3 * 2/3 = 0.3
For 3xSeven the probability is 1/3 * 1/3 * 1/3 = 0.037
Note that the probability to get BAR on 1 reel is 2 out of 3 times, hence 2/3 in the formula and for Seven it’s 1 out of 3 (1/3)
We multiplied probabilities 3 times because the combination is made up from 3 times the symbol.
Now we can calculate the payout of each combination:
For 3xBAR the payout is $1 * 0.3 = $0.3
For 3xSeven the payout is $15 * 0.037 = $0.56
Finally we add the payouts of each combination together to get the total payout:
$0.3 + $0.56 = $0.86
Since we payout we just calculated is for $1 nomination (according to the paytable) then the payout for this nomination is $0.86 (each time we bet $1, on average we win back $0.86) or in other words the payout for $1 nomination is 86% (without bonus game or progressive jackpot)
Note that payout percentage can vary depending on the nomination. Higher nominations often offer better payback.
If the slot game has a bonus round, we also need to take that into account and start by calculating the probability of getting into the bonus round. Then multiply it with the average amount you can win at the bonus round and add the result to the total payout.
Suppose in our example 3xSeven puts us into a bonus round where we are given a choice of 3 pots of gold. If we choose the right one, we win additional $3
On average we would win 1 out of 3 times in the bonus round. Since the win amount is $3, then the total amount we would win on average is 1/3 * $3 = $1 each time we get to the bonus round.
Since we have already calculated the probability to get to the bonus round (3xSeven = 0.037), then we can add another $1 * 0.037 = $0.037 to the total payout which now stands at $0.86 + $0.037 = $0.90. Now that we have taken the bonus round into account, the total payout is 90%.
If it’s a progressive slot, we need to multiply the probability to hit the jackpot with the jackpot amount and add the result to the total payout as well.
Suppose the probability to hit the progressive is one in a million and the jackpot is $10 000
1/1 000 000 * $10 000 = $0.01
After adding it to the total payout, we get $0.9 + $0.01 = $0.91 or 91% payout.
Suppose the progressive jackpot is $100 000 instead
1/1 000 000 * $100 000 = $0.1
Actual Hold Percentage Slot Machine
After adding it to the total payout, we get $0.9 + $0.1 = $1 or in other words 100% payout.
If you were an advantage gambler who has done the homework like we just did here, you would know that whenever the progressive on this slot machine reaches $100 000, the total payout percentage reaches 100%, at which point playing on that slot machines becomes profitable in the long run. ‘A long run’ in this case would probably mean a few million spins, but you would be guaranteed to make profit if you had a sufficient bankroll and a lot of patience (or an army of apes pulling levers).
As you can see the math behind calculating the slot machine payout is quite simple. The most difficult part of the whole process is probably finding the information regarding the occurrence of each symbol on the reel as casinos don’t tend to publish this simply because an average gambler has no need for this type of information.
If you have any questions, feel free to post them as comments and I’ll try answer them as best as I can.
UPDATE: Tommy asked how to calculate the keno video slot payout percentage, so I figured I’d throw it in here as well.
I have to admit I’m not a big fan of keno video slotmachines myself, but I believe I have a fairly good understanding how they work.
Hold Percentage Slot Machines
Suppose we mark 3 spots. First we need to calculate the total number of ways possible to draw 3 balls out of 80.
80/1* 79/2 * 78/3 = 82 160
Notice we substract 1 after each draw. That’s because the ball we just drew cannot be drawn again, it’s now out of the “bubble”.
Since the game draws 20 winning balls, we have to calculate the total number of ways 3 spots can be amongst the winning 20.
Slot Machine Percentage Sheet
20/1 * 19/2 * 18/3 = 1140
The probability to hit all 3 spots is therefore 1140/82160 = 0.0139 or 1.39%
Suppose the paytable shows $40 prize for hitting all 3 on a $1 bet. The payout for hitting 3 spots out of 3 is then $40 * 0.0139 = $0.56
Suppose paytable is generous enough to award us $2 should we hit 2 spots out of 3 with every $1 bet.
The total number of ways to hit 2 spots out of the winning 20 is 20/1 * 19/2 = 190 and the total number of ways possible, that 1 ball remains amongst the 60 that don’t get drawn, is 60/1 = 60. This means there are a total of 190*60 = 11 400 different possible ways to draw 2 winning balls and 1 losing ball.
Payout Percentages Of Slot Machines
We already calculated there are 82 160 possible ways to draw 3 balls, therefore probability to draw 2 winning + 1 losing ball is 11400/82160 = 0.14
This adds another $2 * 0.14 = $0.28 to the total payout which is now at $0.56 + $0.28 = $0.84. That means the total payout is 84% for $1 card played with 3 spots.
If the paytable is the same for both 1- and 20-card version, the payout percentage remains unaffected so whether you play 1-card keno 20 times or 20-card keno once, it doesn’t really matter.