The Probability Of Slot Machines

• Appendices
• Slots Analysis
• Miscellaneous

1. Best Odds On Slots
2. The Probability Of Slot Machines Dispense

A slot machine has three slots; each will show a cherry, a lemon, a star, or a bar when spun. The player wins if all three slots show the same three items. If each of the four items is equally likely to appear on a given spin, what is your probability of winning? (Enter an exact number as an integer, fraction, or decimal.) I have tried 1/64, 1/12, 1/4. What am i doing wrong.

Introduction

When it comes to gambling, the easier a game is to understand the worse the odds usually are. This is certainly the case with slot machines. Playing them is as easy as pressing a button. However, between the high house edge and fast rate of play, there is no quicker way to lose your money in a casino.

Before going further, let me make clear that this page addresses the way slot machines work in most parts of the United States and the world. However, some parts of this page do not apply everywhere. For example, I state that slot machines have a memory-less property, where the odds of every spin are the same. In some places, like the UK, some machines in bars, called 'fruit machines,' have a mechanism that guarantees a certain profit over the short run, which causes the game to go through loose and tight cycles. These games do not have the usual independence property of the major slot makers.

How They Work

Whether you're playing a 3-reel single-line game or a 5-reel 25-line game, the outcome of every bet is ultimately determined by random numbers. The game will choose one random number for each reel, map that number onto a position on the reel, stop the reel in the appointed place, and score whatever the outcome is. In other words, the outcome is predestined the moment you press the button; the rest is just for show. There are no hot and cold cycles; your odds are the same for every spin on a given machine.

Slot machines are just about the only game in the casino where the odds are not quantifiable. In other words, the player doesn't know how the game was designed, so it is difficult to look at an actual game to use as an example. So, to help explain how they work, I created the Atkins Diet slot machine (link). It is a simple, five-reel game with a free spin bonus round, much like IGT's Cleopatra game.

For information on how it works and all the odds, please visit my Atkins Diet par sheet.

For a more complicated example, featuring sticky wilds in the bonus, please try my Vamos a Las Vegas slot machine.

For information on how it works and all the odds, please visit my Vamos a Las Vegas par sheet (PDF).

Odds

The following table shows the casino win for Clark County Nevada (where Las Vegas is) for all slots for calendar year 2012. They define 'slot' as any electronic game, including video poker and video keno. I've found video keno to be about equally as tight as reeled slots, but video poker has a much higher return. So, the return for reeled slots should be higher than these figures.

Clark County Slot Win 2012

Source: Nevada Gaming Control Board, Gaming Revenue Report for December 2012 (PDF, see page 6).

Most players play penny video slots. Based on past research, I find the house edge on those to usually be set from 6% to 15%. In general, the nicer the casino, the tighter the slots.

Advice

While there is no skill to playing slots, there is some skill in selecting which machine to play and ways you can maximize your return. What follows is my advice, if you must play slots at all.

• Always use a player card. Slots may be a lousy bet, but the casinos treat slot players very well. A $1 slot player will probably get comped better than a $100 blackjack player. Of course, don't play for the reason of getting comps. You'll give them a lot more than they'll give you.
• The simpler the game, the better the odds. The fancy games with big signs and video screens tend to not pay as well as the simple games. However, slot players always tell me the fancy games are more fun.
• The higher the denomination, the better the odds. For that reason, it is better to play one coin per line on a 5-cent game than five coins per line on a 1-cent game.
• Don't forget to cash out and take your ticket when you leave. It is easy to forget after hitting a jackpot.
• Try to play slowly and as little as possible to get your fix.
• In some games there is a skill feature, like Top Dollar. In such games, advice is usually offered, which you should take.

Myths and Facts

Just about everything that players believe about slots is untrue. Here are the most common myths and facts. As a reminder, this page is based on slot machines commonly found in the United States. Some machines, like 'fruit machines' found in the United Kingdom work differently.

• Myth: Slot machines are programmed to go through a cycle of payoffs. Although the cycle can span thousands of spins, once it reaches the end the outcomes will repeat themselves in exactly the same order as the last cycle.

  Fact: This is not true at all. Every spin is random and independent of all past spins.

• Myth: Slot machines are programmed to pay off a particular percentage of money bet. Thus, after a jackpot is hit the machine will tighten up to get back in balance. On the other hand, when a jackpot has not been hit for a long time it is overdue and more likely to hit.

  Fact: As just mentioned, each spin is independent of all past spins. That means that for a given machine game, the odds are always the same. It makes no difference when the last jackpot was hit or how much the game paid out in the last hour, day, week, or any period of time.

• Myth: Machines pay more if a player card is not used.

  Fact: The mechanism that determines the outcome of each play does not consider whether a card is used or not. The odds are the same with or without one.

• Myth: Using a player card enables the casino to report my winnings to the IRS.

  Fact: That makes no difference. If you win $1,200 or more they will report it either way. If you have a net losing year, which you probably will, at least the casino will have evidence of it. Such annual win/loss statements may be used as evidence to declare offsetting loses to jackpot wins.

• Myth: The slot department can tighten my game with the press of a button remotely. Thus, you better be nice to the staff and tip them well, or they will use a remote control to have the machine take you down in a hurry.

  Fact: There is now some truth to the myth that the odds of a machine can be changed remotely. Such 'server-based slots' are still experimental and in a minority. Even with server-based slots, there are regulations in place to protect the player from the perceived abuses that could accompany them. For example, in Nevada a machine can not be altered remotely unless it has been idle for at least four minutes. Even then, the game will display a notice that it is being serviced during such changes. (source) Meanwhile, for the vast majority of slots, somebody would physically need to open the machine and change a computer chip, known as an EPROM chip, to make any changes.

• Myth: The machines by the doors and heavy traffic flow areas tend to be loose while those hidden in quiet corners tend to be tight.

  Fact: I've studied the relationship between slot placement and return and found no correlation. Every slot director I've asked about this laughs it off as just another player myth.

• Myth: Slots tend to be looser during slow hours on slow days of the week. However, when the casino is busy they tighten them up.

  Fact: Nobody would take the trouble to do this, even if he could. The fact of the matter is the casinos are trying to find a good balance between winning some money while letting the player leave happy. That is best achieved by slots loose enough to give the player a sufficiently long 'time on device,' as they call it in the industry, with a reasonable chance of winning so he will return to the same casino next time. If the slots are too tight, the players will sense it and be unlikely to return.

  The kind of place you're likely to find tight slots are those with a captive audience, like the Las Vegas airport. So, if the slot manager feels that 92% is the right return for a penny game, for example, he is likely to set every penny game all that way, and keep them that way for years.

Play

Reviews

• Dazzle Me (NetEnt)
• Mr. Vegas (Betsoft)
• Sparks (NetEnt)

Internal Links

• Appendix 1 shows the details and analysis of almost 4000 actual spins on a Reno slot machine.
• Appendix 2 shows an example of the virtual reels behind a hypothetical slot machine and how the average return is calculated.
• Appendix 3A: 2003 Las Vegas slot machine rankings.
• Appendix 3B: 2002 Jean/Primm slot machine rankings.
• Appendix 3C: 2002 Tunica slot machine rankings.
• Appendix 3D: 2002 Henderson/Lake Mead slot machine rankings.
• Appendix 3E: 2002 Quarter and dollar returns for Las Vegas slots
• Appendix 4 shows how the return is calculated for my Wizard's Fruit Slot Machine.
• Appendix 5 analysis of the 21 Bell Slot Machine.
• Appendix 6 Analysis of Red, White, & Blue Slot Machine.
• Lock and Roll analysis of the skill-based slot machine found in North Carolina.
• Deconstructing Jackpot Party analysis of the video slot machine.
• Deconstructing Lion's Share analysis of the classic MGM progressive game.
• Deconstructing Cleopatra analysis of the popular IGT game.
• Deconstructing Lionfish analysis of the slot game found on many Game Maker machines.
• Deconstructing Megabucks.
• Deconstructing the Atkins Diet slot machine.
• Deconstructing Lucky Larry's Lobstermania.
• Deconstructing Hexbreaker.
• Deconstructing Blazing Sevens.
• Deconstructing Hot Roll.
• Mystery progressives on Ainsworth slots.
• Mystery progressives on WMS slots.
• Baltimore Sun article, in which I am quoted.
• 100% Rebate on Slot Losses Promotions: When to quit playing when all losses are refunded.

External Links

• For a simplified explanation of slots, please see my companion site Wizard of Vegas
• German translation of this page is available at richtigspielen.com
• Another decent overview of how slots work and some practical advice for playing them is How Slot Machines Work at VegasClick.com.
• PAR Sheets, probabilities, and slot machine play: Implications for problem and non-problem gambling by Kevin A. Harrigan and Mike Dixon, University of Waterloo, Waterloo, Ontario, Canada. This is an outstanding academic paper that details how some popular slot machines were designed.
• PAR Sheets, probabilities, and slot machine play: Implications for problem and non-problem gambling - Academic paper based on the par sheets for some modern slot machines

Slot machines are the most exciting casino games in the world. The combination of simplicity and huge jackpots - along with plenty of psychological factors designed in the game (best explained in Addiction by Design: Machine Gambling in Las Vegas by Natasha Dow Schull) ensure that Americans keep pouring billions of dollars a year into slots. The downside for customers? You'll lose by a wide margin in the long run, and in general the bigger the jackpot, the more of an edge the slot machine has over you.

You can increase your chances in the long run, though, by choosing the right games at the right casinos -- it's not unheard of that you will lose five times the amount on average that you would have lost if you chose the best slot machines and played at the best online casinos.

The intention of this slot machine guide is to explain everything you need to know about slot machines in order to minimize your losses and give yourself the best chances to win money. If you're just looking for a high-quality, reliable slots online casino to play at, here are my top recommendations:

• Bonus: 100% up to $5,000.
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• Ran by the team behind 'Bodog' brand.

How Real-Money Slots Work - The Basics

A slot machine has no feelings. The amount of winnings it pays are dictated by the EPROM chip and the random number generator ('RNG') inside the machine. It doesn't consider whether someone has recently won or lost -- every spin of the reels is random.

It's possible to influence your chances of winning at slots. When you press Spin, the RNG generates a random number (between one and a billion, for example) for each reel of the machine. Every number represents one of the symbols (the more numbers represent a symbol, the more it is 'weighted' in the machine).

The EPROM chip then determines whether you've won with the combination of symbols or not; the more winning combinations there are, and the more the player wins per winning combination, the higher the odds of winning and the payback of the machine.

Suggesting you have all the information available, calculating your chances of winning at slots is simple: multiply the probability of each outcome with what those outcomes pay, and then sum the results. It's always under 100% (otherwise casinos would make no profit) and often near 90% (casinos make a lot of money from slots).

Here's an example of an imaginary slot machine (let's call it King of Cats) with three winning combinations -- a real-life slot machine works the same way, but likely with more ways of winning at slots:

The slot machine above would return 97.5% to players in the long run. However, we rarely know the odds of slot machines. We do know the paytable - how much each winning combination pays to players - but we have no idea of the probability of getting that winning combination.

To calculate the probability of a winning combination, we need to know is how many stops there are for each symbol. For example, in the machine above there could be 45 stops and one of them would be a Lion symbol. By calculating (1/45)*(1/45)*(1/45) we get 0.001%, or the probability of hitting three Lion symbols in a row.

In real world, those symbols would have been weighed differently so that they're more likely to come on the first two reels and much less likely to come on the last reel, resulting in a near-miss situation.

I advise you not to play at all because slot machine odds are never good, but if you're going to play anyway, here's how you can find the slot machines that likely have better odds than others.

Why We Lose At Slots

We lose at slot machines because they're set to give back less than they take on average. It's impossible to play slot machines better; you can just press spin and hope for the best. With that said, though, you can improve your odds of winning at slot machines greatly by making good decisions before playing and having a good strategy when entering a casino - more about that lower on this page.

Generally, the more decisions you can make in a casino game, the lower the house edge is (with optimal play). Since there's almost no room for decisions when playing slots machines - again, your only decision is to press spin - the house edge is high at slots when compared to other popular casino games. And since you play slot machines for real money so fast (400-800 spins an hour), you lose more at slots than at any other casino game. (Read how slots work to understand them better.)

Like most casino games, a slot machine is a game of independent trials (the previous game has no influence on the next game). Your chances of winning with each spin are the same regardless of whether you've lost or won. So, there's absolutely no room for in-play slot machine strategy.

How Much Do Slot Machines Pay Back?

A slot machine's payback percentage could be anywhere from 75% to almost 100%, but of course, always lower than 100% (otherwise, the casino would make no profit). You can calculate a casino game's house edge by subtracting its payback percentage from 100% - this is how much the casino makes per bet in the long run. For example, with a 5% house edge, casinos make $5 per every $100 bet.

Calculating a slot machine's payback percentage is easy if you have all the information available: multiply the probability of each outcome with what they pay, and the sum is how much the slot machine returns in the long run, also known as its 'payback.'

But most of the time we don't have that information. We're in the dark -- sure, casinos can claim certain payback or payout percentages but how do we know they're truthful? Some online casinos get their payouts reviewed by private auditors, but how do we know if the auditors are honest?

It's a different situation with games like blackjack or roulette; in both cases we can calculate the house edge because the rules are known. If you care enough to make the calculations (and you should), you'll know exactly how much you stand to lose or win in the long run.

You could argue that casinos make so much money from slot machines that they have no reason to cheat. I agree, but you can still get a raw deal even if they are honest (setting a low payback percentage is not cheating). I want to have an idea of what kind of a return I get for my money regardless of the honesty of the casino. (See how to pick slot machines to find the best slots to play.)

Not only do casinos keep slot machine players in the dark about payback percentages, they have also weighed slot machine reels differently, resulting in as many near-miss moments as possible, which encourage future play. The first reel is the likeliest to hit something, the second reel is less likely to hit and the third reel is even less likely to hit.

NOTE: Some casinos are tested by auditors that publish monthly payout percentages for everyone to see online - now, 'payout' is different from 'payback.' The actual money that the casino has returned to players through their games is 'payouts' and the theoretical money that the slot machines are set to return is 'payback.' Payouts can be influenced by huge jackpot wins, for example, in which case a month's payout would look much better than the games have been set to pay back.

How You Can Win More

Here's the truth: the best thing you can do is to stay far away from slot machines (and stay clear from myths). Losing less is winning more and you can lose the least by never playing slots, even if you knew how to play slot machines the optimal way.

But you came here to learn how to play slots for real money, so I have to assume that you will play them at some point. Good news: you can win more (or, in fact, lose less) by playing the right slot machines at the right casinos.

The main consideration is always payback but you should also pay attention to casino comps and other benefits (such as cashback) that come along with playing at casinos.

Why to Play Slots

Some of you may wonder why to play slot machines at all. Exactly. They're a terrible investment -- think of a machine that you put $1 in and receive $0.95 back. That is basically a slot machine, except for all the sounds and animations, and of course a chance to win a lot of money, perhaps even millions of dollars.

The odds are heavily against you winning that money though. Meanwhile, in the long run, the casino takes your dollar bills and gives you back less. So if you agree to participate in this weird transaction, the least you can do is to find the casinos and slot machines that give you back the most money.

How to Find the Best Casino Slots to Play

If you're going to play in Las Vegas or some other popular gambling destination, take a look at this survey. It'll give you a good idea of how the location of the casino affects the general payback percentage of its slot machines; the best Las Vegas casinos are located mainly in North Las Vegas, not on the Strip. You can use the same logic in other places where there are many casinos around, although if you're 'stuck' with only a few, I'm not sure if location makes much of a difference.

After selecting a casino that potentially has a high payback percentage on average, an important part of a good slot machine strategy is to immediately join the casino's Slot Club (could be called 'Player's Club' as well). Contrary to popular myths, Slot Club members have the same house edge in their games as other players; the difference is, casinos can track Slot Club members (you have to insert a Club membership card to the slot machine when you play) and it helps them to give you comps when you deserve them (otherwise you may miss-out on them). You'll likely receive something extra just for signing up - free money to play with or a free drink, for example.

Additionally, most casinos give Slot Club members cashback (0.5% per bet, for example) and that is almost like playing against less house edge, although not literally. You don't win more likely but you receive a portion of your bets back.

Now, look around the casino. I bet you feel the temptation to head over to the flashiest slot machines with the biggest jackpots. That's what most slot players do and it's exactly the opposite of the best way to play slots. Unless your only goal is to win a million dollars (regardless of how unrealistic it is), playing progressive jackpot slots is the worst slot machine strategy you can choose. Many make that mistake and it's no wonder why US casinos get 70% of their revenues from slot machines.

Odds in Progressive Jackpot Slots

Best Odds On Slots

The only way you can win a million dollars playing slots is to play slot machines with progressive jackpots, however, you get even worse odds to win than you would get if you played flat-top slots.

The odds of winning a jackpot are usually way better on the first reel of the machine than on the last one. The casino wants to create as many 'near-miss' moments as possible -- it is a psychological trick, designed to make the player want to to play more.

It's easy to see why near-misses work: if you're one symbol away from winning a jackpot, it'll leave you with a different feeling than if the jackpot wasn't close at all.

In reality, it only seemed to be close.

In Nevada, the regulations state that one stop on the reel can't be weighted more than six times the stops before and after it (many have adopted this rule).

Progressive slot machine odds could be weighed like above; the first reel hits a jackpot symbol once out of five times while the third reel only hits once out of 13 times, often resulting in mentioned 'near-miss' situations.

But that was a simplified example. Hitting a progressive jackpot usually has more symbols, of course, and way worse odds. The chances of winning the biggest of them all, Megabucks, are somewhere in the 1:50,000,000, according to John Robinson at Casino City Times.

Progressive slot machine odds are worse than flat-top machines (the ones without a progressive jackpot) -- this is because a part of the bet goes to the jackpot while the casino takes its own cut. Unless the size of the jackpot is huge - in which case playing jackpot slots could be worth it - it always makes sense to choose a simple fixed jackpot slot machine.

So which slot machine types are best for you?

The simplest slot machines, also known as 'straight' or 'flat-top' slots, are your best choice financially. No, you can't win a million dollars playing those machines, and yes, they're less flashy than other slots, but they're the best slot games to play at a casino. For every dollar you bet, you may have to lose 10 cents more to flashier machines with progressive jackpots - that's a huge difference in the long run.

So now that you've chosen a simple machine, let's think about your betting strategy for slot machines (I'm not referring to progression betting systems; they don't work):

The Probability Of Slot Machines Dispense

• Choose the highest denomination. The higher the denomination, the lower the house edge. For example, nickel slots have a higher house edge than dollar slots.
• Bet the maximum amount of coins. There's usually an incentive to bet maximum coins. For example, the jackpot becomes bigger relative to the bet, giving you a better return from the machine (odds stay the same but payout increases relatively more than bet size).
• Bet slowly. Not because pressing the Spin button fast or slow would impact your odds of winning at slot machines, but because it's a viable slot machine strategy because you have more time to play with your money and the longer you stay at a casino, the more comps you'll probably receive.