Casino Slot Odds
Slots odds are the probabilities of getting a winning combination on the reels. They depend on the type of slot machine you play. Originally the odds were very easy to calculate as the only thing the players had to consider were the number of reels and the symbols used on each of the reels. As a result, the 3-reel slot machines are traditionally believed to be better for player's winning chances, and thus the more reels and symbols on them, the lower a player's advantage.
How to Calculate Odds
- As an example, if you play a slot machine that has a 10% theo, then the casino would expect to keep about 10% of all the money you play through that machine. So, if you played $1,000 through that slot machine, the casino would calculate its theoretical win as $100 because 10% of $1,000 is $100.
- The odds that you would hit three lion symbols in a row on a 3-wheel slot would be (1/45).(1/45).(1/45), which is equal to 0.001%. However, in the real world, the symbols are weighted. Therefore, the lion symbol on the first wheel may have a greater probability of showing than say that on the second or third wheel.
The odds of getting any combination on the slot reels are easy to calculate if you know the number of symbols used on each reel. Let's take a closer look at the odds and consider an example:
If you have to make a line of 3 diamonds on one payline to win the jackpot, it is most likely that each reel has only one diamond symbol on it. If the machine is a 3-reel one and there are 20 symbols on the reels, the chances of hitting this combination are:
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%.
Possible combinations on the reels: 20 x 20 x 20 = 8000. The odds of getting this combination are 1 in 8000. For a 5-reel slot machine the chances are even less: 20 x 20 x 20 x 20 x 20 = 1/ 3,200,000 (1 in 3,200,000). The slots probabilities are usually shown as a percentage, so for 3-reel and 5-reel slot machine with 20 symbols on each reel we have these probabilities:
However, the number of symbols on the reels can differ from machine to machine, and that is why the slots odds are different. Here we look at some more examples of slot machines containing 3 and 5 reels each with different number of symbols on them - for these examples: 20, 22 and 25.
| Slot Machine Type | Number of Symbols | Number of Combinations | Odds | Probabilities |
| 3-reel | 20 | 8,000 | 1 in 8,000 | 0.0125% |
| 22 | 10,648 | 1 in 10,648 | 0.0093% | |
| 25 | 15,625 | 1 in 15,625 | 0.0064% | |
| 5-reel | 20 | 3,200,000 | 1 in 3,200,000 | 0.0003125% |
| 22 | 5,153,632 | 1 in 5,153,632 | 0.0000194% | |
| 25 | 9,765,625 | 1 in 9,765,625 | 0.00001025% |
Slots Payback Percentages
The slots payback or return is the amount of money the slot machine pays out as winnings, against the total number of credits wagered by players. The payback is always shown in percentage.
The main idea behind counting the odds in slot machines lies in understanding how the machine pays out money. Unlike what many people believe, not everything is random in a slot machine. Slots are programmed to pay out a certain percent of the money put in with each play.
For example, one machine may pay back 80% of bets while another one may pay back 91% and even 100%. This means that for every dollar put in the machine the casino takes 9 cents and pays out 91 cents. But it does not do it for every dollar put in, it just pays out explosively and this is what makes the game so great.
You must remember that there are two basic types of slot machines. These are:
- Loose slots are slot machines that are programmed to return 82-98% of the wagered money, or even more if you play slots online. As a rule, high-denomination slots pay out more than those offering, for example, $0.05 or $0.25 bets. For more about typical paybacks on different slot machines please read the strategies page.
- Tight slots are machines that pay out less than 80% and sometimes down to 50% of the wagered money. To avoid playing at these slot machines try not to gamble in motels, airports, bars, gas stations, etc. The payback percentages vary from casino to casino and that is why it may be difficult to find the best machine in the gambling hall.
As you understand, one of the best slots tips on how to win at slots is always to look for the loose machines. It can be easy if the gambling hall shares this information with the visitors. In any case you can gamble on the Internet as most online casinos provide the statistic data about their slots games. So, when choosing one of the casinos recommended by SlotsDoc.com you can expect such paybacks:
- Appendices
- Slots Analysis
- Miscellaneous
Introduction
Indian Casino Slot Machine Odds
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.
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.
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
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
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)