# Whats Maryland Law Slot Machine Return

Slot Machine RTP Return to player (RTP) is a measure of how much a slot machine pays back to its players for each unit wagered over time. It is most commonly expressed as a percentage value and is almost always below 100%. Understanding slot machine math can be daunt ing for even the most seasoned individual. You do not hav e to be an accountant, analyst, or even a statistician to understand the fundamentals of slot math. The take-away is to know why this math is so important in monitoring performance and compliance at your property.

- Appendices
- Slots Analysis
- Miscellaneous

## Winning at Slots - What Are The Odds?

Law: Most players don't know, but chances of hitting a jackpot go back to a 300-year- old mathematical principle.

Medicine & Science

Imagine this scenario: Jack plunks down a cup of quarters in front of a Pimlico slot machine, loses 50 times in a row and quits in disgust. As he stalks away, Jane spies his machine, drops a quarter in the slot, then laughs as she wins 100 coins.

Jack, of course, is convinced he cheated himself by quitting too early - and furious at the woman for taking 'his' winnings. Now Jane drops 99 of her new-found quarters into the same machine, losing every time. But as she prepares to play her 100th quarter, she is convinced her odds are better than when she started. 'That's a common fallacy, and it's completely wrong,' says Michael Shackleford, a former Social Security actuary who runs a casino advice Web site called the Wizard of Odds.

According to Shackleford and other math Wizards, millions of players are ignorant of the 300-year-old mathematical principle that governs slot machines.

But that very ignorance will guarantee millions for Maryland and the racing industry - if Gov. Robert L. Ehrlich Jr. succeeds with a plan to put one-armed bandits at the tracks.

Discovered by Swiss mathematician Jacob Bernoulli in 1689, the principle is known as the Law of Large Numbers, and it has two parts.

First, it says, random outcomes such as a coin flip or tug on a slot machine lever are unaffected by previous flips and tugs. Each has the same odds as the one before it and the one after.

Second, the overall result of random outcomes generally becomes more predictable as the number of outcomes increase. This is known as the Law of Averages: It means that flipping a coin 10 times may yield nine heads and a tail, but flipping it a million times will yield close to 500,000 of each. 'The key is that things that are unpredictable on a small scale are predictable on a large scale,' said James Fill, a professor of mathematics at the Johns Hopkins University.

No one can say with precision just when the Law of Large Numbers kicks in. But Shackleford gave it a try two years ago when he dropped 4,000 quarters into the same Reno slot machine over 10 hours and recorded the results. At times winning and losing in the course of the day, he wound up short about $50 at the end.

'It really didn't take that long,' he said. 'I wanted to document the actual results.'

If the General Assembly approves slots, the state will ultimately determine the results for Maryland's bettors by deciding what percentage of the cash gambled must be returned in jackpots. Typically, that would be about 80 percent.

The rest of the money, known as the hold or the take, would be split among the track owners, the horse racing industry and state and local governments. Once they know the ultimate return to bettors, casino operators can calculate their odds and jackpots - knowing that the outcome of millions of slot machine plays can be predicted with reasonable certainty.

So what about the odds on an individual machine?

That depends on the design. Slots have been around since the 1890s, and many still show bettors a display of three or more reels covered with symbols, such as cherries, lemons, bars and numbers.

The odds of winning vary with the number of reels, the number of symbols on each reel and the variety of combinations that win jackpots.

The math works this way: For a traditional three-reel, $1 machine with 20 symbols on each reel, if the casino wants only one winning combination - say three cherries - the probability of winning will be 1 in 8,000 plays. Theoretically, the house can make a $1 profit by offering a $7,999 jackpot on three cherries. That's not likely to be enough to keep a casino in business, though. If the house wants to keep 5 percent of the money wagered, it will make the jackpot $7,600 and keep $400, or 5 percent of the $8,000 wagered.

The odds could get longer if the machine has more reels or more symbols. For example, a machine with four reels and 250 symbols on each reel - and only one winning combination - would produce odds of 3.8 million to 1. Nobody would stick around for such a rare combination to come up, so casinos sweeten the deal by providing smaller jackpots for different combinations of symbols. It is the same as the Maryland Lottery paying lesser sums for hitting four or five numbers in the Lotto's six-digit winner.

So if the three-reel machine with 20 symbols had a lesser payout of $10 for one cherry on any reel, the odds of winning would improve to about 1 in 7. The computer-driven slot machines that have been popular since the 1980s offer a variety of games and winning combinations. Calculating their jackpots requires sophisticated mathematical analysis and, in many cases, computer simulations.

But experts say the same general rule applies to all slots. 'The player has to understand that the casino has the edge,' says Robert C. Hannum, a math professor at the University of Denver and consultant for slot machine manufacturers.

He said people often play slots knowing the odds are against them, but they chalk up their losses as the cost of entertainment. 'It's like watching a sporting event, only there's a chance for them to win something,' Hannum said.

Casinos order machines with the size and types of payouts they want. But that can vary with the state, casino and machine. Nevada, for example, allows casinos to hold up to 25 percent of the amount gambled, while New Jersey allows 17 percent. Proposed Maryland legislation specifies holds of 17 and 13 percent.

The actual odds and the house advantage are not posted on slot machines or provided to players. But according to results reported to state regulators, most casinos pay out more than the minimum percentage - the result of competitive pressure.

Shackleford said his research shows that Nevada slots pay out $85 to $98 of every $100 bet. But there's still a healthy profit because a busy machine can generate 800 spins per hour.

'They make money because of the huge volume of bets,' he said. Because casinos are permitted to average the hold among their machines, they will set a few machines with 'looser' or more frequent payouts to encourage playing, while others are set 'tighter.' While gamblers often talk about 'lucky' machines, Shackleford said, the loose machines are paying out only slightly more.

Since the 1980s, manufacturers have produced video-based slot machines with sound and animation. Some allow multiple simultaneous games, while others are hooked up to networks, so a number of players playing the same game can build up 'progressive jackpots' that top $1 million.

Unlike the system of wheels, cogs and gears that governed their forebears, today's machines rely on a computerized random number generator that determines where each reel stops. It selects stops for every reel the instant the lever is pulled - the image of spinning reels coming slowly to a stop is strictly for effect.

'These generators are spinning out numbers at the rate of thousands per second, so it's a case of pulling the lever at exactly the right instant, no matter who is playing,' Hannum says.

So if Jane wins on her first pull, right after a man has lost 50 times at the same machine, her jackpot is strictly a random occurrence.

But try telling that to Jack.

Playing the game

## Slot lingo

- House advantage: The percentage of money wagered by gamblers that's retained by the casino.
- Loose machine: A slot machine that returns a higher percentage of money to players than the house average, it does not mean a machine is ready to return a large jackpot.
- Tight machine: A machine that returns a lower percentage to players than the house average.
- Progressive jackpot: A system that places a fraction of each wager into extra-large jackpot pool that increases until someone wins. Can operate across multiple machines or even several casinos.

## Typical house advantage

- Keno (average) 27%
- Slots 5-10%
- Roulette (double zero) 5.3%
- Caribbean stud 5.2%
- Blackjack (avg. player) 2.0%
- Craps (pass/come) 1.4%
- Video poker 0.5-3%

Written by: Michael Shackleford

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.

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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.

### Whats Maryland Law Slot Machine Return Policy

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.

### Whats Maryland Law Slot Machine Returns

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.