Understanding slot machines is easy. They’re basically just a giant math equation. Casinos are so open about slot machines, they publish their own payback percentages in industry publications, and they often brag about the percentage that their machines pay back in a given month or year.
The most important odds to understand in slot machine gambling are a machine’s hit frequency and payback percentage. It’s impossible to ascertain the specific odds of winning on a given slot machine in today’s casinos, though. Gone are the days of 3 reels with 10 symbols per reel, when calculating the odds of hitting a given jackpot took little more than some back of the napkin multiplication. Still, hit frequency and percentage are easy to understand, and that information is easy to find.
- Placing a $1 bet has the best odds of winning, with only an 11 Percent edge for the house, but also the worst payout. The Joker offers a 36x payout but has a 24 percent edge for the house. Odds of Winning Slots: Around 1 in 49,836,032.
- In a modern slot machine, the odds of hitting a particular symbol or combination of symbols depends on how the virtual reel is set up. As we saw in the last section, each stop on the actual reel may correspond to more than one stop on the virtual.
Basic Slot Machine Odds
Casinos are designed to make money just like any business. The slot machines are a big piece of the profit puzzle so the casinos do everything they can to make them more profitable. Now that you know these 15 slot machine secrets the casinos don’t want you to know you can gamble as an informed player.
Now that random number generators power slot machines, the odds are more complicated. In the old days, figuring out your odds of winning on a slot machine meant dividing the total number of symbols by 1. If a slot has 3 reels and 10 symbols on each reel, the odds of one particular symbol appearing on the machine would be 9 to 1, or 9 losing symbols and 1 winning symbol. To figure out the odds of hitting 3 particular symbols (for a jackpot), multiply your chances of landing one symbol three times by itself. You have a 1/10 chance of pulling up a particular symbol. The odds of pulling up a given 3 reel combination are 1/1000. That can also be expressed as 999 to 1.
Back to the random number generator: you just can’t use simple multiplication to figure slot machine odds any more. Modern slot machines contain so many different symbols, reels, and winning combinations, that a purely mathematical approach is out of most people’s reach. Understanding a slot machine’s hit frequency and payback percentage are important because we can’t just sit there and figure out our odds by looking at the machine.
For example, with a modern slot machine, one symbol might appear one out of every twenty spins. A second symbol might appear one out of every ten spins. And a third symbol might be set to appear one out of every fifty spins. But there’s no way to determine the settings unless you have access to the slot machine’s PAR sheet, which is what sets these specifications in the random number generator program.
Slot Machine Hit Frequency
The term hit frequency applied to slot machines means an informed estimate of the ratio of losses to wins on a given machine. As the number of wins in the ratio increases, so does the slot’s hit frequency rate. Because of the variety of ways to win on modern machines, figuring out a slot’s hit frequency is somewhere between taking a mathematical average and making a guess.
One way to estimate a slot machine’s hit frequency is to play the machine 100 times and track the results. The cheapest way to do this is to find a nickel machine, pull the lever 100 times, and work out the ratio the hard way. Make a mark for every time during those 100 spins that you win, any win big or small.
What’s a good hit frequency? That depends on how much you’re looking to win and what kind of machine you’re playing, but most slot gamers consider any machine that pays out less than 10% of the time a bad machine.
To further complicate hit frequency, and to get a better overall idea of a machine’s odds, you can factor in the amount of winnings. Slot machines are often designed to pay out a lot of small winnings, so a hit frequency of 50% may seem like a loose slot machine, but if you’re only winning tiny amounts, you may want to move on down the line. On the other side of the coin, if a slot machine pays out only 9 or 10 times per 100 spins, but you win a ton of credits, you may be tempted to stay and press your luck for the big jackpots.
Slot Machine Returns
When you hear people talk about a slot machine’s return, they are referring to the percentage of money paid out by the machine compared to the amount of cash a gambler put into it. People who play slots at the tournament level keep track of these numbers and form strategies based on which machines to play at a given casino property.
To work out a return, you just need to do a little simple math. If you pumped $100 into a slot machine and at the end you’ve won $90 back, you just got a slot machine return of 90%. The casino kept $10 of your money for your troubles, but if that $100 kept you playing for an hour, you just had an hour’s entertainment for $10. That’s cheaper than going to the movies.
If you’re just a casual slot gamer, you don’t really need to keep track of slot machine returns. Casinos report their slot machine returns to local governments in most gambling jurisdictions, and those details and other figures are available to the general public. An easy way to stay on top of machine returns is to subscribe to Casino Player magazine or Strictly Slots magazine, where these numbers are published.
Slot Machine Payback Percentage
A final note on slot machine odds: don’t get too hung up on a slot machine’s payback percentage. Payback percentages are essentially made-up numbers, theoretical figures that make a guess about how much a particular machine will pay back to a gambler over time.
The trouble with payback percentage figures is that they’re developed from a pool of infinite spins. Think of payback percentage as slot machine returns in a vacuum. These numbers are used by game designers and casino managers and are not meant to inform gambling.
These numbers come from game manufacturers, who program a machine to return a theoretical amount to the customer. If a game designer advertises a slot’s payback at 95%, all that means is that over an infinite amount of time, the slot will pay back 95 cents for every dollar that is put in.
If you finished this article more confused than when you started, you’re in good company. Slot machines are straightforward gambling devices, little more than random numbers activated by a gambler. Still, modern technology has muddied the waters of actual slot machine probabilities, placing an emphasis on a game’s design and features rather than advertising it as a particularly player friendly machine.
Just because a game designer produces a machine that is programmed to pay back 90% of money put in doesn’t mean that you will always make $90 for every $100 gambled. At the same time, understanding slot machine odds and hit frequency can inform your choice of casinos.
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Introduction
The following table ranks the Las Vegas casinos according to the looseness of their video display reeled nickel slot machines. The returns are based on a sampling of five different types of machines. The data collected goes back as far as October 2001 so the information is a bit dated.
Las Vegas 5 Cent Slot Survey
| Rank | Casino | Average Return |
|---|---|---|
| 1 | Palms | 93.42% |
| 2 | Gold Coast | 92.84% |
| 3 | Sahara | 92.81% |
| 4 (tie) | Bourbon Street | 92.63% |
| 4 (tie) | Imperial Palace | 92.63% |
| 4 (tie) | Slots a Fun | 92.63% |
| 7 | Key Largo | 92.60% |
| 8 | Western | 92.57% |
| 9 | Ellis Island | 92.56% |
| 10 | El Cortez | 92.56% |
| 11 | Orleans | 92.56% |
| 12 | Circus Circus | 92.56% |
| 13 | Gold Spike | 92.55% |
| 14 | Fitzgeralds | 92.54% |
| 15 | Fiesta - Rancho | 92.53% |
| 16 | Arizona Charlie's East | 92.51% |
| 17 | Barbary Coast | 92.50% |
| 18 | Terrible's | 92.49% |
| 19 | Arizona Charlie's | 92.49% |
| 20 | Hard Rock | 92.47% |
| 21 | Town Hall | 92.47% |
| 22 | Longhorn | 92.47% |
| 23 | Riviera | 92.23% |
| 24 | California | 92.14% |
| 25 | Lady Luck | 92.10% |
| 26 | Nevada Palace | 92.06% |
| 27 | Plaza | 91.94% |
| 28 | Luxor | 91.92% |
| 29 | Paris | 91.92% |
| 30 | San Remo | 91.88% |
| 31 | Excalibur | 91.84% |
| 32 | Palace Station | 91.84% |
| 33 | Ballys | 91.82% |
| 34 | Las Vegas Club | 91.76% |
| 35 | Four Queens | 91.75% |
| 36 | Texas Station | 91.71% |
| 37 | Casino Royale | 91.67% |
| 38 | Boulder Station | 91.55% |
| 39 | Aladdin | 91.5% |
| 40 | O'sheas | 91.48% |
| 41 | Hilton | 91.40% |
| 42 | Boardwalk | 91.28% |
| 43 | New York New York | 90.99% |
| 44 | Horseshoe | 90.96% |
| 45 | Sam's Town | 90.89% |
| 46 | Santa Fe Station | 90.87% |
| 47 | Flamingo | 90.86% |
| 48 | Golden Nugget | 90.85% |
| 49 | Stratosphere | 90.8% |
| 50 | Tropicana | 90.71% |
| 51 | Golden Gate | 90.64% |
| 52 | Silverton | 90.57% |
| 53 | Main Street Station | 90.56% |
| 54 | Westward Ho | 90.40% |
| 55 | Fremont | 90.37% |
| 56 | Castaways | 90.36% |
| 57 | Monte Carlo | 90.24% |
| 58 | Stardust | 89.97% |
| 59 | Frontier | 89.91% |
| 60 | MGM Grand | 89.81% |
| 61 | Harrahs | 89.32% |
| 62 | Treasure Island | 89.32% |
| 63 | Mirage | 89.3% |
| 64 | Caesars Palace | 89.05% |
| 65 | Mandalay Bay | 88.87% |
| 66 | Rio | 88.72% |
| 67 | La Bayou | 88.26% |
| 68 | Mermaids | 88.26% |
| 69 | Bellagio | 87.42% |
| 70 | Venetian | 86.66% |
| 71 | Airport | 85.02% |
Excluded Casinos
The Suncoast and Rampart Casino in Summerlin do not allow playing slots and taking notes at the same time. I can not include any casino that prohibits the method in which I gather data.
How To Beat The Slots Every Time
Location Averages
The next table shows the average return by location.
Returns by Region
| Location | Average Return |
|---|---|
| Off strip | 92.07% |
| Downtown | 91.66% |
| Strip | 91.47% |
| Total | 91.74% |
The above sign can be found across the street from the Palms. Although I did the study Anthony Curtis published it in the LasVegas Advisor, which is how it become well known. The'...' in the sign encompases quite a bit of information,which was conveniently left off the sign. Actually the study only says that the Palms had the lowest nickel video slotsof the casinos surveyed in Las Vegas. The small print at thebottom says, 'Independent study conducted between November2001-February 2002 on Austin Powers, Fortune Cookie, Reel'em In, and Wheel of Fortune games. They left off LeopardSpots, and the study began in October.
Observations
There seemed to be no truth behind slot placement myths. Machines on the end of a bank did no better on average than those in the middle. There was also no correlation between return and proximity to such things as the main door, table game pit, high traffic areas, and low traffic areas.
Most casinos were very consistent in their slot returns.If one nickel machine had a return of x% then all others like it also returned x%. However some casinos did mix up loose and tight machines, most notably Treasure Island and the California casinos.
Methodology
A kind and anonymous source provided me with par sheets for the games in question. The EPROM (Erasable Programmable Read Only Memory) chip is what tells the machine the order of the symbols on the reel, in some cases how the stops are weighted, how much each winning combination pays, and any other pertinent information about how much the machine pays.It is up to the slot manager to select which EPROM chip to order according to the return percentage desired. On atypical game there might be about 8 different possible return percentages, ranging from about 85% to 98%.
Each of the different par sheets has five sets of distinct reels. On video display slots the stops are not weighted; in other words all stops are equally likely. The distribution of each symbol on each reel is what determines the theoretical return of the machine. For example a higher paying machine may have more of the higher paying symbols.
On the machine itself three consecutive symbols arevisible on five different reels. By comparing actualobservations of results to the par sheets it is possible todetermine which reels the machine uses, and thus which par sheet and which return. There are various three-symbol combinations that appear in at least one but not all par sheets. So if one of these combinations occurs on an actualmachine it narrows down the possible par sheets. By playingenough the player can narrow down the possible par sheets tojust one.
To help identify the unique combinations I wrote a computer program for each game, which had the exact reel order of all 5 reels of all the par sheets. The program then counted the number of par sheets with each possible three-symbol combination. If the number was greater than 0 and less than the maximum then that combination was identified along with the associated par sheets it belonged to.
It is then a matter of simply playing the game and comparing the outcomes to the list of partially unique combinations. It only takes about 5-10 plays per machine to narrow down the possibilities to just one par sheet.
Best Casino Slot Machine Odds Game
The averages in the table are actually an average of averages. For each kind of machine at each casino I took an average return. Then I took the average of these averages over the five kinds of machines I tested for.
Slot Machine Definition
Best Casino Slot Machine Odds
Best Casino Slot Machine Odds Chart
There is some confusion about what constitutes a 'slot machine' or 'slot.' My definition, and that of most gamblers, is a gambling machine with either actual spinning reels or video representations of the them.
People in the gaming business and regulators generally refer to a slot machine as any gambling machine, including reeled slots, video poker, video keno, video blackjack,etc.. For purposes of statistics both casino managers and regulators combine all the electronic gambling machines together. For example, the Slot Chart in Casino Player magazine and reports by the Nevada Gaming Control Board do not isolate just reeled slots but consider all electronic games a 'slot.' Therefore my return percentages should not be expected to agree with those reported by the casinos or regulators. As far as I know mine is the only source to isolate just the return of reeled slots.
Acknowledgements
I would like to thank Rob Feldheim for helping with the slot play and record keeping. Rob helped me with most of the casinos on the east side of town and part of downtown. I would also like to thank par Sheet Pete (not his real name)for providing the par sheets, without which this project would not have been possible.
Internal Links
Best Casino Slot Machine Odds
Go to slot machine appendix3B (Jean/Primm slot returns).
Go to slot machine appendix 3D(Henderson slot returns).
Go to slot machine appendix 3E(Las Vegas quarter and dollar slot returns).
Go to slot machine appendix 3F(Montreal slot return).
Go back to slot machines.
External Links
The main-stream media has covered this study in depth. Here are links to some articles.
- Turning'em loose, an article that appeared in the Las VegasReview Journal on May 19, 2002, about the possible effectsof this study.
- One-Armed Bandit or Robin Hood? , an article by myself for Contingencies Magazine explaining the methodology, results, and weaknesses of the study.
- Play by the rules and the one-armed bandits will still win. Boston Globe article about slot machines, in which my Las Vegas survey is mentioned and my advice quoted. (cache)
Written by: Michael Shackleford
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