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One of the most common questions you’ll see about anything in the casino gambling industry relates to “honesty”. You’ll see this question asked about every casino game under the sun. You’ll also see it asked about every casino, especially the online gambling sites.

The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning 30 times. Use the normal approximation to the binomial distribution. Find the area under the normal curve over the interval (29.5,30.5). Mathematical probability says it'll be right on 88 percent. Each slot machine is programmed with thousands of combinations of symbols. 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.

In this post, I want to address this specific question:

The numbers are slightly misleading. The truth is, this means that you will lose 5% from every dollar you put into a slot machine. This is of course an average. You could always hit the jackpot on that first dollar and turn everything on its head. You aren’t guaranteed to lose that each time. The number is a probability figure for a long-term. First, suppose each window of the machine has one jackpot position. Second, imagine each window has an equal likelihood of displaying any of 32 positions. If these assumptions were strictly true, you could find the exact probability of a jackpot by multiplying 32 by itself as many times as there are reels on the machine.

Are slot machines honest?

How Do You Define Honest?

When I use Google to look for a definition of honesty, I see some of the following definitions listed:

• “Free of deceit and untruthfulness”
• “Sincere”
• “Morally correct or virtuous”
• “Fairly earned, through hard work”

I think most people are thinking of the first definition when they ask whether slots games are honest. They want to make sure they’re not being cheated. In this context, the answer is yes, slot machines are honest. I’ll explain why in detail in the rest of this post.

In the second context, where “honest” means “sincere”—I’m less sure. Are the casinos sincere when they want you to think you’re able to win money? I think so, but they know in the long run, anyone who plays slots long enough will lose all their money.

In the third and fourth contexts, I’d have to say that slot machines are NOT honest. Slot machines are closer to morally neutral than they are to sinful, but you might have a different belief system about such things. It’s hard to say that slots don’t appeal to one of the seven deadly sins, though (greed).

I’m not sure anyone could (or would) consider money won on a slot machine “earned” or to have anything to do with “hard work”. It’s a game of luck. If you win, then you got lucky—it has nothing to do with working hard or being smart.

I’ll explain more about that later in this post, too.

How a Slot Machine Works Mathematically

Answering the question “are slot machines honest?” begins with learning how the games work mathematically. The math behind the games is easier to understand than most people probably think.

The first concept to understand is basic probability. When someone says “probability”, they’re talking about the mathematical likelihood that something is going to happen. That “something” is called an event.

The probability of an event is always represented as a number between 0 and 1. An event that will always occur no matter what has a probability of 1. An event that will never occur has a probability of 0. An event that will occur half the time has a probability of 0.5.

For simplicity’s sake, and to make understanding the concept easier, I just used whole numbers and decimals in the previous paragraph. But probabilities are almost always expressed as percentages or fractions.

How to Express Probability as a Percentage

You’re watching the evening news, and the meteorologist says there’s a 50% chance of rain tomorrow.

That means it’s just about as likely to rain as it is to not rain.

Here’s another example:

You flip a coin. You have a 50% chance of it landing on heads. You also have a 50% chance of it landing on tails.

If you add the probabilities of all possible events together, you always get a total of 1 (or 100%).

Probability is the mathematical engine that makes gambling games possible.

How to Calculate a Probability

Here’s how you calculate a probability:

You take the number of ways an event can happen. You divide that by all the total events possible (including what can happen and what happens if it doesn’t.)

You’re rolling a single six-sided die. You want to know the probability of getting a 6.

There are 6 possible outcomes. Only one of them is a 6.

The probability of getting a 6 is 1/6.

Another way to express that is using odds, which can be useful when calculating whether a bet is expected to be mathematically profitable or not.

Odds expresses the number of ways something can’t happen versus the number of ways it can happen.

In the six-sided die example, the odds of getting a 6 are 5 to 1. You have 5 ways of NOT rolling a 1, and only 1 way of rolling a 1.

If you want to calculate a probability that includes the word “or”, you add the probabilities of the events together.

If you want to calculate a probability that includes the word “and”, you multiply the probabilities by each other.

You want to know the probability of getting a 1 or a 2 on a roll of a six-sided die. The probability of each is 1/6.

1/6 + 1/6 = 2/6

You can reduce that to 1/3.

Here’s another example:

You roll 2 dice. You want to know the probability of getting a 6 on both dice. The probability of each is 1/6.

1/6 X 1/6 = 1/36

Applying Probability to a Simple Hypothetical Slot Machine Game

But how does all this apply to the honesty of slot machines?

I’ll use a super simple hypothetical slot machine game to explain how this probability affects the integrity of the game.

This super simple game has 3 symbols on each reel—an orange, a lemon, and a cherry.

The probability of getting a lemon on the first reel is 1/3.

The probability of getting a lemon on the second reel is also 1/3.

In fact, it’s the same on each reel.

But the game only pays off if you get 3 of the same symbol on each reel.

The probability of that is 1/3 X 1/3 X 1/3, or 1/9.

Let’s suppose the payoff for getting 3 lemons is 4 for 1.

And let’s suppose the payoff for getting 3 cherries is 3 for 1.

Finally, we’ll suppose the payoff for getting 3 oranges is even money.

• The probability of winning 4 coins is 1/9.
• The probability of winning 3 coins is also 1/9.
• The probability of winning 1 coin is also 1/9.
• The probability of winning nothing is 6/9, or 2/3.

Now let’s suppose you’re putting $1 in on every spin, and you play 9 spins, getting every possible result once.

You win 4 coins once. You win 3 coins once. You win 1 coin once. That’s a total of 8 coins you’ve won.

But you’ve inserted 9 coins into the game.

Where did the extra coin go?

In the pockets of the casino, that’s where.

By setting up the payoffs so that they’re lower than the odds of winning, the casino sets up a situation where it’s guaranteed a mathematical profit over the long run.

Of course, most modern slot machines aren’t quite this simple. They have more symbols on each reel, for one thing. For another, the probability of getting a particular symbol might be different from the probability of getting another symbol.

For example, you might have a 2/3 probability of getting a pear, and only a 1/24 probability of getting a cherry.

What Happens in the Long Run vs. the Short Term?

By manipulating the payoffs and the probabilities of the symbols, the casino can guarantee that over a long period and many spins, they’ll profit.

But in the short run, a player might win a big jackpot or lose several times in a row.

That’s the nature of random events. In the short run, anything can happen. In the long run, the numbers get closer to the theoretical probability.

This is obvious when you look at it with an extreme example.

On an infinite number of spins, your average loss per spin will mirror the mathematical expectation.

The closer you get to an infinite number of spins, the closer you’ll get to the mathematical expectation.

Do Slot Machines Cheat?

The casinos don’t need to cheat to make a healthy profit.

The slot machine designers and manufacturers don’t need to cheat to make a healthy profit.

In fact, in well-regulated jurisdictions (like Nevada), games are thoroughly audited for fairness. When they’re auditing a game for fairness, one of the things they check is whether a game has a jackpot that’s impossible to win.

That’s the main concern many players have when they ask if slot machines cheat.

Does the game have jackpots that are impossible to win?

The short answer in almost every case is no, they don’t.

But you have no way of knowing what the probability of winning that jackpot is. Slot machine games have opaque odds and probabilities. The results are generated by a computer program called a random number generator (RNG).

The only people who know the exact settings for that RNG are the designers and the casino managers.

In fact, you could be playing two identical slot machines located right next to each on the casino floor and have different odds of winning. Not only is this legal, it’s common.

Does that sound like cheating?

By the strict letter of the law, it’s not.

Is it honest?

I’d say yes. Having two games next to each other offering different odds is intentionally misleading. It’s legal, but it’s not sincere in any way.

Online slot machines are no different, except that in some cases, these games HAVE been known to cheat. But not reputable casinos and not reputable software providers.

How do they cheat?

They set up games which are impossible to win.

The reasons baffle me. You stand to make far more money in the long run if you offer an honest game.

Even an idiot can tell after a while that he’s never going to win a rigged casino game on the Internet.

But otherwise smart people will continue to deposit money and wager it at a breakneck pace if they’re winning something every now and then, even if they’re showing a net loss over time.

That’s how gambling works.

What About Video Poker Games?

You need to understand immediately that video poker games are NOT the same thing as slot machine games. They look similar on the surface, but the math and the gameplay couldn’t be more different. And the philosophy behind these games is different, too.

Here’s why:

A video poker machine uses a random number generator that duplicates the odds found in a 52-card deck of cards. You know the probability of getting a specific symbol. Any specific card has a 1/52 probability of appearing.

A card of a specific suit has a ¼ probability of appearing. A card of a specific rank has a 1/13 probability of appearing.

Payback Percentages and the House Edge

Knowing this enables mathematicians and computer programs to calculate the actual payback percentage for these games.

What’s a payback percentage?

It’s the percentage of each bet that’s paid back to the player on average in the long run. It’s the opposite of the house edge.

On a slot machine, you have no way of calculating a game’s payback percentage. It’s impossible, because you have no way of knowing the probability of getting a specific symbol.

But on a video poker game, you can calculate all the possibilities. And since you know how much the game pays out for various combinations, you can add the expected value of each to get an overall payback percentage for the game.

And you know what’s even better than this?

The payback percentages for video poker games are significantly higher than the payback percentages on slot machines in almost every case.

Even the worst video poker game usually has a payback percentage of 95% or so. But the better games offer payback percentages in the 98%+ range. Some (rare) games have pay tables which offer a slightly positive game for the player, like 100.2%. But those numbers assume perfect strategy on your part.

But even the best slot machine games usually have a payback percentage in the 95% range. The more common games slip down into the lower 92% or so range.

Expected Hourly Loss Rates in Slot Machine Games vs. Video Poker Games

What does this mean to your bankroll?

Let’s look at how much money you can mathematically expect to lose playing 2 different games:

We’ll start with an average slot machine game with a 94% payback percentage. You’re playing for $1 per spin, and you’re making 600 spins per hour. You expect to win 94% of each bet back, which means you expect to lose 6% of each bet.

6% of $600 is $36, which is the amount the casino expects you to lose on this game on average over time.

Then we’ll consider a 9/6 Jacks or Better game which you’re playing with perfect strategy. The payback percentage for this game is 99.54%, which means the house edge is 0.46%.

We’ll assume you’re playing a quarter machine and betting 5 coins per hand. You’re putting a little more money into action on each bet–$1.25. Most video poker players are as fast as slot machine players; they play 600 hands per hour. That’s $750/hour in action.

But with a house edge of 0.54%, your expected loss on that kind of action is only $3.77.

That’s right.

Playing slots costs you 10 times as much as playing video poker.

Video poker offers other advantages over slots, too. One of these is the skill element. You might not want to think about what you’re doing when you’re gambling.

But if you’re anything like me, you want to be able to at least exert a little bit of control over your destiny.

In video poker, you get to do that. The decisions you make playing each hand have a direct effect on your bottom line.

Play your hands well, and you’ll be playing one of the best gambling games in the house.

Should You Play Slot Machines at All?

This is a legitimate question. Should you play slot machines at all?

Here are some pros and cons of playing slots:

Pros:

• You can win bigger jackpots on slot machine games than any other gambling game except maybe keno. If you’re looking for a life-changing jackpot, like you’d see if you won a lotto drawing, slots are the way to go.
• They require little in the way of attention or effort on the part of the player. This suits some temperaments just fine. Relaxing in front of the spinning reels seems like a good deal for a lot of people.
• They’re available in an endless variety. You can find a slot machine game with any theme you can imagine. Love Elvis Presley? You’ll find a slot machine for it. Play Dungeons & Dragons when you were 12? There’s a slot for that, too. The themes and games are almost endless.

Cons:

• They offer some of the worst odds in the house. The house edge for slot machines vary widely. Some of them might offer good odds, but most of them have a house edge of between 5% and 10%. This isn’t awful. After all, roulette has a house edge of 5.26%. The problem is that slots play so fast that you can easily put more money into an action than you thought you could.
• You can’t figure out what the odds are. I have a philosophical problem with slot machine games. No other casino game is opaque about your odds. You can calculate the house edge for any table game in the casino. You can calculate it for video poker, too. But you’re never given the information you need to figure out the house edge on a slot machine. This is unacceptable to me.
• They’re designed to be addictive. Slot machine manufacturers spend millions doing research into what kinds of stimuli are going to put most people into the “flow” state. Flow is great if you’re interested in personal productivity at work, but if you’re playing a gambling game, it’s awful. No other casino game is as addictive as a slot machine.

Conclusion

Yes, slot machines are honest—in a manner of speaking, anyway. Casinos don’t make claims about slot machines that are blatantly untrue. If a game has a maximum jackpot of $1 million, you do have a chance of winning that much money.

What you don’t know is how likely or unlikely it is to win that amount.

Is this disingenuous on the part of the casinos?

I think it is, at least to some extent.

But all casino games have math behind them that puts the odds in the casino’s favor. That’s just the nature of the games. Slots are no different in that respect.

No matter which casino game you play, if you stick with it long enough, you’ll eventually lose all your money.

The only exceptions are certain games that can be played with advantage techniques, but that’s another subject entirely.

The only way for you to get an edge against a slot machine game is to cheat.

Probability Of Winning Slot Machine Jackpot

In most jurisdictions, cheating is blatantly illegal. You’re better off learning to play poker at an expert level, or learning how to count cards in blackjack.

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

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!

Slot Machine Jackpot Probability Calculator

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.)

Slot Machine Jackpot Probability Numbers

Implementing a simple strategy for slots

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

Slot Machine Jackpot Probability Games

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.

Slot Machine Jackpot Probability Jackpot

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!