Probability Theory Basics and Applications - Slots Odds. On a 3-reel 2 x 3- or 3 x 3-display slot machine, any two paylines are linked; therefore we cannot estimate the probabilities of the winning events related to several lines. 16-reel slot machines The 16-reel slot machines usually have the 4 x. 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) when the mean =np=500.0.05 and the standard deviation = sqrt(500.0.05.0.95). A slot machine house edge is known by casino managers as the “hold”, and hold percentages vary a great deal, and do tend to be smaller at more expensive slots, frequently found to be around 1- 3% at the five dollar slots.

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.

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

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.

For free online casino battle creek. 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?

Slot Machine Odds

Here are some pros and cons of playing slots:

Pros:

Probability Slot Machines

• 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.

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.

Please enable JavaScript to view the comments powered by Disqus.

The gaming industry is big business in the U.S., contributing an estimated US$240 billion to the economy each year, while generating $38 billion in tax revenues and supporting 17 million jobs.

What people may not realize is that slot machines, video poker machines and other electronic gaming devices make up the bulk of all that economic activity. At casinos in Iowa and South Dakota, for example, such devices have contributed up to 89 percent of annual gaming revenue.

Spinning-reel slots in particular are profit juggernauts for most casinos, outperforming table games like blackjack, video poker machines and other forms of gambling.

What about slot machines makes them such reliable money makers? In part, it has something to do with casinos’ ability to hide their true price from even the savviest of gamblers.

The price of a slot

An important economic theory holds that when the price of something goes up, demand for it tends to fall.

But that depends on price transparency, which exists for most of the day-to-day purchases we make. That is, other than visits to the doctor’s office and possibly the auto mechanic, we know the price of most products and services before we decide to pay for them.

Slots may be even worse than the doctor’s office, in that most of us will never know the true price of our wagers. Which means the law of supply and demand breaks down.

Bonus Code No code required. Read Review Play Casino. Casino name: Casino RedKings Amount: 25 Free Spins Valid for: Existing Bonus type: Free Spins Wagering: 60xB Valid for Games: Wild Crystal Arrows Expires on: 2020-11-28. This offer is For depositing only. More bonuses for Casino RedKings. Casino redkings no deposit bonus codes 2015. RedKings Promo Code Claim the no deposit bonus from RedKings - check below promo code for RedKings and use when creating your account to receive any no deposit bonuses or free spins available with them. New users only, 18+. Bonus T&C apply.

Casino operators usually think of price in terms of what is known as the average or expected house advantage on each bet placed by players. Basically, it’s the long-term edge that is built into the game. For an individual player, his or her limited interaction with the game will result in a “price” that looks a lot different.

For example, consider a game with a 10 percent house advantage – which is fairly typical. This means that over the long run, the game will return 10 percent of all wagers it accepts to the casino that owns it. So if it accepts $1 million in wagers over 2 million spins, it would be expected to pay out $900,000, resulting in a casino gain of $100,000. Thus from the management’s perspective, the “price” it charges is the 10 percent it expects to collect from gamblers over time.

Individual players, however, will likely define price as the cost of the spin. For example, if a player bets $1, spins the reels and receives no payout, that’ll be the price – not 10 cents.

So who is correct? Both, in a way. While the game has certainly collected $1 from the player, management knows that eventually 90 cents of that will be dispensed to other players.

A player could never know this, however, given he will only be playing for an hour or two, during which he may hope a large payout will make up for his many losses and then some. And at this rate of play it could take years of playing a single slot machine for the casino’s long-term advantage to become evident.

Short-term vs. long-term

This difference in price perspective is rooted in the gap between the short-term view of the players and the long-term view of management. This is one of the lessons I’ve learned in my more than three decades in the gambling industry analyzing the performance of casino games and as a researcher studying them.

Let’s consider George, who just got his paycheck and heads to the casino with $80 to spend over an hour on a Tuesday night. There are basically three outcomes: He loses everything, hits a considerable jackpot and wins big, or makes or loses a little but manages to walk away before the odds turn decidedly against him.

Of course, the first outcome is far more common than the other two – it has to be for the casino to maintain its house advantage. The funds to pay big jackpots come from frequent losers (who get wiped out). Without all these losers, there can be no big winners – which is why so many people play in the first place.

Specifically, the sum of all the individual losses is used to fund the big jackpots. Therefore, to provide enticing jackpots, many players must lose all of their Tuesday night bankroll.

What is less obvious to many is that the long-term experience rarely occurs at the player level. That is, players rarely lose their $80 in a uniform manner (that is, a rate of 10 percent per spin). If this were the typical slot experience, it would be predictably disappointing. But it would make it very easy for a player to identify the price he’s paying.

Raising the price

Ultimately, the casino is selling excitement, which is comprised of hope and variance. Even though a slot may have a modest house advantage from management’s perspective, such as 4 percent, it can and often does win all of George’s Tuesday night bankroll in short order.

This is primarily due to the variance in the slot machine’s pay table – which lists all the winning symbol combinations and the number of credits awarded for each one. While the pay table is visible to the player, the probability of producing each winning symbol combination remains hidden. Of course, these probabilities are a critical determinant of the house advantage – that is, the long-term price of the wager.

This rare ability to hide the price of a good or service offers an opportunity for casino management to raise the price without notifying the players – if they can get away with it.

Casino managers are under tremendous pressure to maximize their all-important slot revenue, but they do not want to kill the golden goose by raising the “price” too much. If players are able to detect these concealed price increases simply by playing the games, then they may choose to play at another casino.

This terrifies casino operators, as it is difficult and expensive to recover from perceptions of a high-priced slot product.

Getting away with it

Consequently, many operators resist increasing the house advantages of their slot machines, believing that players can detect these price shocks.

Our new research, however, has found that increases in the casino advantage have produced significant gains in revenue with no signs of detection even by savvy players. In multiple comparisons of two otherwise identical reel games, the high-priced games produced significantly greater revenue for the casino. These findings were confirmed in a second study.

Further analysis revealed no evidence of play migration from the high-priced games, despite the fact their low-priced counterparts were located a mere 3 feet away.

Importantly, these results occurred in spite of the egregious economic disincentive to play the high-priced games. That is, the visible pay tables were identical on both the high- and low-priced games, within each of the two-game pairings. The only difference was the concealed probabilities of each payout.

Armed with this knowledge, management may be more willing to increase prices. And for price-sensitive gamblers, reel slot machines may become something to avoid.