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Ask the Wizard: Slot Machines

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Progressive slot machines

First, love the site, very informative! Background: When using a Random Number Generator (RNG) to determine certain payouts for a finite set, such as 1 million lottery scratch off cards, the RNG can be programmed to drop non-pay or add pay selections so as to keep a more even distribution of winners throughout the finite set of cards created. The goal is to maintain a more even distribution in the cards along with the payout percentage as required. Is this, or can this programming be done in Nevada? The law of averages would indicate no need for this, but is it not theoretically possible for a signed 97% slot machine to payout 95% one year and 99% the next year unless some control on the RNG was made? — Jonathan from Ft. Lauderdale
Thanks for the kind words. Scratch cards and pull tabs can indeed be printed in batches. These batches will have a specified number for each win, and the return of the overall batch will be exactly as the maker intended. In some jurisdictions, where only pull tabs are legal, the outcome can be displayed to the player on a video monitor, in the form of a slot or video poker machine. However, in Nevada, that is not how slots work. Each play is completely independent of the past. A machine programmed to average a 97% return, could indeed pay under 95% or over 99% over a year, especially if not heavily played. July 11, 2008
Hiya Wizard, I'm hoping you can settle a bet between me and my wife. Do the odds of hitting the Station Casinos Jumbo Jackpot get better as the jackpot increases? My wife believes that it doesn't matter when you play, because it's equally likely to hit at any time. I believe that this means it's better to play later, because it's an equal distribution over all the numbers but you're playing against a subset so it's an increased likelihood of hitting. Who is correct? — Nick from San Diego
As usual, the person asking the question is right. For the benefit of other readers, I indicate the rules in my March 4, 2008, column. The probability of the jackpot hitting is inversely proportional to the how far the jackpot is from the guaranteed hit point of $100,000. The closer you get to $100,000 there is a smaller range where the jackpot can hit, so the odds of hitting at any given moment go up. If the current jackpot is j, the probability it will hit before the jackpot goes up $1 (for j<=$99,999) is 1/(100,000-j). At a jackpot of $50,000 the probability of hitting before going up $1 is 0.002%. At a jackpot of $99,999, the probability of hittng before going up $1 is 100%. So, you win the bet. June 16, 2008
Hello Wizard, thanks for the great site. Do you have any insight or knowledge of how the Jumbo Jackpot works at Station Casinos? Is it more likely to hit as the jackpot increases simply due to more chances being drawn, or are there other considerations? Dan from Las Vegas, NV

You’re welcome. I don’t guarantee this as fact, but here is how I believe it works. First, the point at which the jackpot hits is randomly chosen between $100,000 and $150,000. I think each hit point is equally likely, but I could be wrong. It has been known to hit under $102,000 and over $147,000.

When the meter crosses the predestined hit point, everybody with a slot card in and playing will win $50 in fee play. To be considered “playing” the player must have his player card inserted, and have made a bet within the last 30 seconds. It is not clear if using free play counts as "playing." Then, somehow, a machine is chosen at random from all those being played to win the Jumbo Jackpot. It does not appear that the amount bet matters, so all qualifying machines have the same probability of being chosen. Players have been known to monopolize entire banks of penny machines, betting a penny at least once every 30 seconds, when the jackpot gets close to $150,000. This, indeed, would be a good strategy. However, I’m told once a player was doing this at the Palace Station, and was limited to playing only two machines.

I would like to thank Bob Dancer for his help with this question. March 4, 2008

Foxwoods casino had progressive slots that I played. The Jackpot was well over $225,000 and when I went back to play 2 days later, all of the Progressive Slots were removed and replaced with Video Slots. When I went to the casino's web site, I did not see anyone listed as winning this Jackpot. I wrote to the Casino and never got a satisfactory response - very evasive to my questions. I therefore wrote to the DA's office and a State Senator as to my concerns. Basically, I was told that they had no control and that it was up to the Tribunal Commission -- they could do what they want. I'm sure this is not fair to all those who played these slot machines. Are there any Industry rules on this? Thanks - Norman Cote, Nashua NH
Here in Nevada the casino would have to roll the progressive jackpot into another game, per Nevada Gaming Control Board regulation 5.110.5(c). If there is any such policy at Foxwoods I am unaware of it. If Foxwoods would like to express their version in this forum I would be happy to accept their statement. March 18, 2007
A long time ago, I asked you about progressives on slot machines where they decide to pull that slot. And I asked if the amount over the base minimum for the progressive is just kept or if it is redistributed to players in some other way. You weren't entirely sure. Well something interesting happened over Christmas. I follow jackpot amounts at the IGT website. The jackpot for $0.25 Wheel of Fortune jumped unexplainably from about 3-400,000 to over $5 Million literally overnight. At the same time, I noticed that they had pulled the Quartermania machines, which had a jackpot of over $2 Million at the time. There were some other brands that had disappeared as well. If you click on the link for the $0.25 Wheel of Fortune, you'll see that it shows the last win at over $5 Million at Caesars. So my question is, do you have the resources to figure out what happened here? Is it just a typo or error, or did they really roll other discontinued jackpots into this one? Thanks in advance. – Roger S. from Dallas, Texas
I agree with your hypothesis, that they pulled out the Quartermania machines and rolled the progressive jackpot into Wheel of Fortune. It can't be a coincidence. March 5, 2007

What happens with accrued money in a progressive slot jackpot that is not won at the time that the progressive is discontinued? Seems to me that the accrued amount over the base should be allocated back to the players in some way since it was part of the return. - Roger from Dallas, Texas

According to Nevada Gaming Control Board regulation 5.110.5(c) the casino licensee must add the progressive jackpot to a similar game at the same establishment. Nov. 2, 2005
What is your opinion of online progressive slots, such as the Dazzler at Unified Gaming casinos? The jackpot starts at $15,000. If the jackpot gets large (> $75,000), do you think the player has an edge? - Mark from Allston, Massachusetts

I don't have any information on the odds of that game so I can't tell you at what point the meter is high enough to give the player an edge. However, keeping an eye on the meter and only playing when it is high is a good idea. March 11, 2001

I'm told the casinos don't pay jackpots for progressives, they're paid by the game vendor. Is this true and if so, does this apply to other slot jackpots as well?

That is true only of the super-big jackpots like Megabucks and Wheel of Fortune. When somebody wins, a representative of IGT (the slot-maker) verifies the win is legitimate and then pays the winner. A portion of each bet made goes to a fund to pay the progressive. Aug. 23, 2004

Is there some way of telling when a progressive slot has reached a level where the house edge is zero? For example, what would the Major Millions jackpot have to be?

Although this is easy with video poker, with slots there is no way to tell without knowing how the machine was programmed. Aug. 25, 2003

This is a great website!. FYI - A guy missed the Megabucks jackpot (7.9M) yesterday because he had just two coins in. To the best of your knowledge, when does the RNG stop and determine your outcome? If it stops on the first coin, then he blew it. If it is on the last coin, he could have had an entirely different outcome. My guess that the stop time is set by the individual manufacturer, and there is no regulation telling him when to do so. Just wondering if you knew different. - Andy Zachar from Bloomfield, USA

Thanks for the compliment. I'm sworn to secrecy on whom, but I know of one major manufacturer who chooses the random number at the moment the player spins the reels. Assuming IGT does this, then the player who hit the jackpot with two coins would almost certainly not have hit it with the maximum coins because the player would hit "spin" at a later time. April 15, 2001

Your site is definitely the best one I've ever seen regarding gambling, and I commend you for providing some light and truth in a seemingly endless sea of "winning gambling strategies, tips & tricks." My question is this. I'm no slot player, but obviously when a progressive jackpot reaches a certain point, the edge would shift from the house to the player. I was wondering if there are any 'groups' or 'clubs' that go out into the casinos when this happens, (virtually) monopolize the machines, capitalize on the opportunity, and split the winnings? I have never heard of any, but they've got to be out there. ñ Bryan Mitchell from Palmdale, USA

Thanks for the kind words. I have never heard of teams of slot players doing this. However, this is very common with progressive video poker players. There are many teams of these professional players who routinely check the meters and when they find one high enough they call their teammates in an attempt to monopolize the machines until somebody hits the jackpot. The problem with slots is that it is not clear to the player what the odds are of hitting the jackpot are. Hence, it is not obvious what the jackpot size has to reach for the machine to become profitable. Plus, it probably rarely happens that a meter gets high enough to overcome the house edge. Dec. 10, 2000

Concerning the Cash Splash progressive slot game played on Microgaming sites... Is the jackpot paid by all participating casinos? If so, does each casino have the same payout percentage set for these machines or is it set by each casino individually? What about mid level payouts on these Cash Splash machines? Thank you very much. -- Helen from Memphis, U.S.

I would assume that the odds are the same at all Microgaming casinos. All casinos probably contribute money to the same account from which the jackpot is paid. This way the individual casino from which the jackpot was hit does not have to reach into their own pocket when somebody wins. Mid level payouts are probably paid by the casino itself. Sept. 3, 2000

Payback percentages

Is there a statistical test to check that a slot machine's payout is correct? For example, the casino claims 93% payout, but a test shows 91% payout in 10,000 games. I think statistically, this may be okay, but I don't know how the math would work. – Mary Jo from Calgary
Let’s assume 10.8 for the standard deviation, which I get from the Red, White, and Blue game described in my slot machine page. The standard deviation of the mean over n spins is standard deviation per bet divided by the square root of n. In this case, 10.8/10,0000.5 = 0.108. The difference between 93% and 91% over 10,000 spins is just 18.5% of one standard deviation. To get the standard deviation of the mean to just 2% you would need a sample size of 291,600 spins. The standard deviation in slots will vary substantially, so take these figures with a grain of salt. November 23, 2007
If a bank slot machines has signage that says "97.4% Return" what does that mean?
According to the Nevada Gaming Control Boards that means that every slot machine in that bank must be set to a theoretical return of at least 97.4%. Popular opinion has it that only one machine must be set to 97.4%, or that the overall average must be 97.4%. However, I am taking a firm stand that both notions are wrong, at least here in Nevada. July 22, 2006

How does the RNG logic interact with the hold %? I believe that most machine are set to hold X% and that over time that number will be reached. It would seem that that "hold" number must have some influence on the odds a machine will pay or not. I realize that a newly installed machine that has never been played can hit the royal on the first play, however, it is my belief that over time, the hold % will met by that machine. I have also heard the term "cycle". I slot tech at a casino told me that a machine was on a 365-day cycle. What does that mean?

First, lets clear up what the term "hold" means. For purposes of electronic games, it is the theoretical return the game is set to. In both video poker and slots, each play is random and independent of all past plays. The laws of mathematics dictate that even with independent trials, as the sample size gets larger the actual return will tend to get closer to the theoretical mean, or the hold. So contrary to popular belief a machine never goes hot or cold to get back in balance. Never mind the term "cycle". It is a poorly named industry term for the number of possible outcomes of the random number generators inside the machine. Unfortunately the term has trickled down only to confuse low level employees and players alike. Contrary to popular myth there are no cycles and again each play is equally random and independent of all other plays. July 28, 2004

When a local gaming authority sets a minimum payout for slots does that minimum apply to each individual machine or a casino average payout? I know some games are set from the manufacturer higher than other and some lower. For example if the minimum is lets say 87% can one machine be set to 60% and another set to 120% for and average of 90% thus exceeding the minimum or does each machine must pay atlease 87%. -- Jim from the U.S.

The minimum applies to every machine. Someone with the Gaming Control Board in Carson City, Nevada, told me that every machine in the state must meet minimum payback percentages. The only exception, he said, are on some antique machines in Virginia City. Sept. 3, 2000

Lets say you have a slot machine like sizzling seven's that pays a top prize of 60 coins for one coin played 500 for 2 coins and the progressive for the 3rd coin. Let's say the machine is played only by one coin players receiving only 60 coins max prize. In other words they excluded themselves from the progressive and 500 coin hits. How does a manufacturer program the machine to satisfy local gaming regulations if this machine will never pay out a jackpot higher than 60 coins. Obviously the machine doesn't return the same amount to one coin players as it does for three coin players. Doesn't this violate the minimum payout requirement or does the machine compensate for this? - Jim from the USA

I'm not sure but I think that for purposes of meeting minimum return requirements the gaming authorities assume that the players are playing optimal strategy. In the case of slots this would mean the player is playing the maximum coins for the maximum return. However, I think the return is only about 1% less if the player does not play the maximum coins. Due to the competitive nature of most gambling jurisdictions the slots pay out much more than 1% above the minimum requirements. Sept. 10, 2000

Casinos setting & changing the payouts

How often do Las Vegas or Reno (Nevada as a whole if easier) change their slot machines? Better stated perhaps as what is the average life cycle of a slot machine before it is worn out, out of fashion, unsecure, etc.? How does that average compare to smaller markets such as Deadwood, South Dakota? – Justin from Rapid City

I forwarded your question to Brian, a former regulator and current casino manager. Here is what he said.

There are two types of changes. The first would involve completely swapping out the machine and the second would consist of simply changing the game, but keeping the existing cabinet. As you can imagine, changing the software is much cheaper which is why there is so much hype around downloadable games. How often games are swapped out depends on a casino's capital expenditures budget. Participation machines are turned over much more rapidly because the manufacturer has a vested interest in keeping the best product on the floor. In many instances, they will handle the scheduling for software and new machine replacements. Participation machines are those that are on lease to the property by the manufacturer. Usually, the manufacturer gets 20% of the revenue, less taxes. From an accounting perspective, the useful life of a slot machine is 5 years and then the asset is fully depreciated (no longer has a book value). The final consideration is popularity. How often do you go into a casino and see a section of slot machines that are the old IGT three reel Red White and Blue machines? If the machines are performing well, why spend $10,000+ to replace each unit? September 13, 2006

Wizard, what do you think about the new "server based" slot machines currently being tested at Barona Valley Ranch? Apparently this technology allows the casino to instantly change the machines from their back offices - including the games offered, denominations, and.....the payouts! I think this is going a bit far. I mean what's to stop the house from targeting certain players (like the drunk high roller) and making it tougher for that player to win? We all know the casinos can pretty much keep an eye on any player they want any time. Between the surveillance and now this technology it seems to give the house too much of an edge. Suppose a table player has a heated disagreement with a dealer or pit boss over a hand (which occasionally happens); now this same player goes to the slots and the house can extract revenge by making his machine pay out less??!! Of course they could "favor" certain players too...which could be just as dangerous. I'm all for allowing the games and denominations to be changed, but shouldn't the regulators be involved when it comes to payout percentages??? - Gary from Charlotte, NC

From what I hear anything you can configure at the machine you can configure remotely through the server. This would include the theoretical return percentage. However most casinos report that changing the theoretical return of a slot machine necessitates a lot of paperwork.

I asked a source of mine who works at one of the casinos that utilize this technology. Besides the Treasure Island, this technology is also used at casinos in California, Michigan, and Mississippi. Here is what he said,

"Nothing can be changed if there are credits on the game. The slot machine will always reject any changes sent when there are credits on the meter. In Nevada, the machine also has to be idle for four minutes prior to and following any changes. It's also not completely transparent to anyone standing in front of the slot machine. A black window pops up that says 'Remote Configuration In Progress' (or something like that).

We mainly use ours to change the available denominations on our games. Similar to how table games will raise minimum bets on when the casino is busier, we will remove lower denominations on Friday morning and return them on Monday morning."

So, rest assured, that the slot manager can not tighten up a game on you just because he doesn’t like you. As long as you have credit in the game, nothing can be changed.

Even if it were effortless to move the slot machine return up and down, it strikes me as a conspiracy theory to think the casinos would do that on a player by player basis. Living here in Vegas, I hear all kinds of theories about the lengths the casinos go to in order to win, like pumping in oxygen and playing a subsonic mantra that says "lose lose lose." These are just urban legends. Most casinos correctly believe that if you give the player a good experience and a fair gamble then he will keep coming back. As they say, you can only slaughter a sheep only once, but you can shear it many times. (My webmaster, Michael Bluejay, who is a vegetarian, tried to get me to use this analogy instead: "You can seize all of a sheep's money only once, but you can force it to take you bowling many times.") May 10, 2006

Many of your responses to questions about slots refer to e-prom which you say is regulated and requires approval by a state agency prior to changing. However, in California I know of no regulatory agency that requires Indian casinos to submit changes for approval prior to changing any EPROMs. I assume Indian casinos can make the changes whenever they desire (yes/no?). - Fred from Bonita

When I write about government regulations I almost always am talking about Nevada. Many other jurisdictions more or less mirror Nevada laws. However, Indian casinos are largely self-regulating. As far as I know, they can change EPROM chips at will and not answer to anybody about it. Nov. 2, 2005
How often does a casino change the percentage on a slot machine? - Nathan from Marquette, Michigan

Not often. Contrary to popular myth, the casinos don't tighten the machines on weekends or whenever it is busy. Here, in Las Vegas, the casinos have to fill out a form on each game every time they change the percentage. Most slot managers I have spoken with have a policy on what coinage is set to what return. I tend to think the most likely reason to change the percentage would be a change in ownership and/or management, neither of which happens often. Aug. 21, 2005

Do casinos have the ability to change the slot payout percent (or really take percentage) at any time after receiving the machine? I always thought that was set at the manufacturer and that the RNG was not changeable. - Jarin Satterlee from San Diego, CA

Physically all you have to do to change the return of the slot machine is change the EPROM chip inside. Assuming the casino manager had all the EPROM chips, which I think they sometimes do, they could make the change themselves. However, in a major jurisdiction the change would have to be reported to the gaming authorities, not to mention internal paperwork. The random number generator is constant, it is what the program does with the random numbers that determines the return. Mar. 24, 2002

How is it possible for casinos to program their slot machines to pay out a regulated percentage if the slot machines run off a random number generator? It would seem there is no way to know what number or combination (winning or losing) is next. ñ Steve from Milton, U.S.

The casinos don't actually program the slot machines to pay a certain percentage but rather determine the weighting of the reels so that the theoretical return is whatever they wish. In the short run the actual return can be either much higher or lower than the theoretical return. However, the laws of mathematics dictate that the actual return will approach the theoretical return as the number of trials increases. Sept. 26, 2000

Do casinos have the right to change minor prize odds on multi-casino progressive linked games such as megabucks or wheel of fortune or are the odds set the same for all casinos. The prizes I'm refering to are the bar, double bar Tripple bar hits. Also do the video poker games such as triply play poker the same odds for all casinos or does each casino have the right to vary their own odds for the game. - James from Cherry Hill

In general the casino can choose its own payback percentages from the manufacturer. The casino is still confined to certain minimums determined by the gaming authorities but most are well above those limits anyway. I speculate that there is no exception for linked progressive machines on the smaller prizes but that the probability on the jackpot may be constant. The odds on video poker can be calculated based on the payoff table which vary from place to place. April 22, 2000

When are the odds chips changed in a slot machine? Do casinos tighten machines on weekend? - James of Cherry Hill, USA

I think the proper term for what determines the odds is an "e-prom" and they are very seldom changed. If a casino wants to tighten or loosen a machine it must first seek approval from the gaming authorities. The machines are equally as tight on the weekends as during the week. Feb. 19, 2000

Questions related to denominations

Do multi-denomination video slot machines have only one payback percentage for the physical machine, or does each denomination have its own par sheet and payback percentage characteristics?

Each denomination can be set to its own payback percentage. On many IGT machines you can tell if they change the return percentage by whether or not the symbols on the screen change when you change the denomination. Sept. 14, 2004

Do the five ten and twenty-five dollar machines pay off just a little better i seem to have a little better luck on them rather than the quarter machines which seem to swallow up a twenty fast? - Mario Dinovo from Troy, New York

In general, the higher the coinage the better the rate of return is. However, in my own research I have seen plenty of exceptions, notably dollar machines that paid less than quarters. April 22, 2002

Great site! Is it better to go max three quarters on a quarter machine or drop one dollar in a dollar machine?

Thanks. This is a good question and I wish I had a firm answer. The exact answer depends on the theoretical return of both machines, and nobody ever reveals this information. Yes, you do get a better return, in general, on dollar machines than quarters but you are giving up the max coin bonus. I think the house edge will go down about 2% making the jump from quarters to dollars. However, without reel weightings I can't tell you the cost of not playing max coins. Personally, I would look at the paytable. If there is a big incentive to play max coins then I'd stick with the quarter machine, otherwise I'd play the dollar one. May 1, 2001

The myth of "cycles", and spontaneous loosening/tightening

Considering that a slot machines random number generator is fixed to supply the selected numbers to the virtual reel stops and in turn are tied to the actual reel stops, is it not possible for the casino computers to swap non winning stops to win stops thus increasing the win percentage. This would maybe explain why all machines on some carousels seem to get hot at the same time, then all revert back after drawing a crowd of players...just wondering...your site is a great information site...thanks

No, this does not happen. How much the casino pays is determined by a microchip called an e-prom which is generally left alone. To change it the casino would have to get permission from the gaming authorities. Even without permission the casino would have to open up each machine and change them by hand.

I speculate that the reason for what you observed about all the machines on a carosel getting hot at the same time is due partially to chance and partially to a snowball effect where players will gravitate to an area where they hear a lot of winning and simply add to the number of wins because of more players. June 25, 2000

I play a Machine in Atlantic city Called "Reel Detectives". I have read your informative article on how slot machines work and I have a good understanding of the programing behind them. what I don't understand is how on some days these machines will pay almost an exclusive combination of 7 wins with no jackpots all day and yet other days it will pay Jackpots all day with little to no 7 wins. If the machine is truly picking random combinations wouldn't the prize distribution be more random. It's as if IGT programmed the machine to have "Planned Cycles" to make the game more interesting to play. I know your going to say that these are just ramdom events, but it is extreamly unprobable that a machine will only pay mid and lower tier prizes all day and omit the Jackpot and vice versa and do this over and over again. HOW are these WEIGHTED cycles explained? Also if you could point me to any books you recommend on the programming of slot machines I would appreciate it. - James from Cherry Hill, U.S.

These are just random events. The laws of probability dictate that some days will be dry with a few big winners and others will have a lot of lower payouts. Most days will have a balanced mix and these days are always the first forgotten by the player. There is no switch the casino is throwing to alter the mood of its machines. To change the payout distribution, the casino would have to get authorization from the local gaming authority and then replace the program chip in the machine. March 11, 2000

In "how slot machines works" you mention that the Random numbers (1 to 2+ billion) are drawn in a cycle to ensure each number is chosen once per cycle. Are you saying that the slot has a 2+ billion-element table that gets filled with all the possible numbers (over time)? Is this why a slot machine will sometimes hesitate (as if it's "thinking" for a few seconds before allowing you to initiate a play... because it's filled the "random number table" and is re-initializing it for another round? I have always wondered about these periodic (after maybe around 30-50 pulls) "hesitations" that slot machines exhibit; because my observations are that the pay/take characteristics of a slot machine seem to change between these "hesitations". Frequently I have seen a slot that was in a "pay cycle" (for lack of better words) go suddenly cold after going through this hesitation. Conversely, I have seen cold machines suddenly start paying more after this hesitation occurs. Whatever! The exact reason for this "pause" it seems clear the machine is re-initializing or re-loading something... I just don't know what it is. - Scott Harris of Leawood, USA

No, the machine does not have a huge element table of over two billion elements. The random number generators choose each number once in the cycle using mathematical algorithms and do not need to keep track of which numbers were already chosen. Regarding the pause, I'm quite sure that has nothing to do with how much it is going to pay. I speculate it is doing some internal test. There is no such thing as hot and cold cycles with slot machines. If a machine is paying off well, that just means you are lucky, there is nothing premeditated about it. Feb. 19, 2000

When the RNG fires

Hey Shack I hadn't been to the site in awhile and I just wanted to compliment you on the new sleek look. I know you initially wanted to stay away from the banners but they do help pay the bills eh? Congratulations also on the new gig with Casino Player, I enjoy it the site and your occasional posts on bj21. As someone who works in the industry, admittedly not slots, I was under the impression that the more recent slots have the RNG stop the moment the first coin drops, so it really doesn't matter if you play 1,2, or 3 coins the symbols will line up the same. Have I been misinformed? According to your previous answer I apparently have. Keep up the good work and I'll stay in touch, thanks and best wishes. - Dave Simon

Thanks for the kind words Dave. You're right that it was the money that finally made me accept the banners. Different makers use different events on what event determines when the random number is selected which is directly related to the outcome. However, I believe that most manufacturers either use the random number when the last coin was inserted or the reels are spun. So, in general, the number of coins you play does affect the outcome. Feb. 19, 2000

You are playing a three-coin slot machine. You only are playing two coins at the time. The jackpot is hit. If you had been playing one coin, or if you had been playing three coins, would it still have gone off at that point? -Ronald Bennett of Maryland, USA

If you had put in one or three coins the outcome would likely have been entirely different. The machine is constantly drawing random numbers and the numbers that were drawn at the moment you spin the reels determine the outcome. So, if you had played fewer or more coins you would have spun the reels at a different moment and thus the outcome would have been different. circa Jan. 2000

Slot strategies

The Wynn invited me to a slot tournament with the following prize structure.

1st place: $1,000,000
2nd place: $150,000
3rd-6th place: $25,000
7th-8th place: $20,000
9th-50th place: $5,000

The cost is $25,000, and the tournament is limited to 50 players. It is easy to see the expected win is $30,000. However, it is a huge long-shot. What would be the required bankroll for entry to be a sound bet under the Kelly Criterion? — Anonymous

The Kelly Approximation is the advantage divided by the variance. The possible outcomes are a win of 39, 5, 0, -0.2, and -0.8 times the bet amount. The advantage is (1/50)×39 + (1/50)×5 + (4/50)×0 + (2/50)× -0.2 + (42/50)×-0.8 = 0.2.

The variance is Expected(win2) - (Expected(win))2 = (1/50)×392 + (1/50)×52 + (4/50)×02 + (2/50)× -0.22 + (42/50)×-0.82 – 0.22 = 31.4192

So, the approximate optimal Kelly bet is 0.2/31.492 = 0.0063655 times the bankroll. For a full entry of $25,000, the required bankroll would have to be 25,000/0.0063655 = $3,927,400.

However, for large bets like this, I think it is worth the time to find the exact optimal Kelly bet. Next, find the bet size b, which maximizes the expected log of the bankroll after the tournament, as follows.

Log of bankroll after tournament = (1/50)*log(1+39×b) + (1/50)*log(1+5×b) + (4/50)*log(1) + (2/50)*log(1-0.2×b) + (42/50)*log(1-0.8×b)

There is no easy way to solve for b. Personally, I recommend the "Goal Seek" feature in Excel. The answer will come out to 0.0083418. So, the exact Kelly bet should be 0.0083418 times your bankroll. To justify the $25,000 entry fee, your bankroll should be $25,000/0.0083418 = $2,996,937. May 13, 2008

If you are playing Slots at an online casino, but have only a limited amount of money to spend, (ex. $100), is it wiser to play for instance, 25cent slots 1 coin at a time?-or-would it be wiser to play the MAX on one machine even if you seem to be losing it faster? - Lori Galgon from Allentown, USA

I believe that most online slots have a fixed return, regardless of the coinage. This is unlike slots in real casinos, which return more the greater the coinage. What you should do depends on your priorities. If you want playing longevity then you should play as little as possible per spin. If you want hope for a big win then you should play as much as possible per spin. However, the house edge is likely the same either way. July 18, 2001

Do you feel it's better to play one slot machine or many and how much should I feed before walking away. If given a touch screen to stop tumblers should I stop them. - Gene Franceschini from Laguna, USA

None of these factors matter. Walk away when you're not having fun any longer. March 11, 2001

Is there a particular time of the day or night that's better to play [slots] and a time that's best to avoid? -Mrs. Mary R. Cook of San Gabriel, California

No, any given machine pays equally at all times. Feb. 12, 2000

Which are the best slots to play and is it better to play 3 coins all the time or rotate from 2-3 coins. - Fran Gray from Geulph, Canada

Most slot machines offer an incentive to play the maximum coins. For example, 2 coins may pay 2,000 on the jackpot but 3 coins will pay 5,000. On a jackpot per coin basis, maximum coins is usually the best bet. So, if there a maximum coin incentive then it is better to always play the maximum coins. I'm afraid I can't answer the question on which slot machines are the best to play, the casinos don't usually tell you what their payback percent is for any given machine. March 11, 2000

Finding loose & winning slot machines

While it is widely reported that casinos put their better paying machines in high traffic areas, do they also put the highest paying machine in these areas as well? I envision the following scenario: for a casino to have a sign saying payouts up to XX% (usually 97%+) only one machine needs to pay that percentage, and that machine will be tucked into a low traffic area (or frequently moved) to keep the amount of winnings on that machine low. While the machines paying significantly lower (though still better paying than the rest of the casino) say 90% are kept in the high traffic area, with the low paying 85% machines throughout the remaining areas. Is there any reason to believe this is how casinos operate? From your review of slots how often do you see different payout % for machines of the same type in the same casino? Sorry for the lengthy questions, love the site and the absence of silly cant lose strategies/advice. - Mitch from Hopkins, USA

Based on my own research I have found that the theory about the correlation between return and slot placement to be untrue. I do believe that oversized novelty machines in high visibility areas are set lower, but that is as far as I'll go. Most casinos are very consistent and all slots of a particular kind and coinage will be set to the same percentage. Those that do mix up loose and tight machines seem to do so randomly. You are right that if a casino advertises "Our machines pay up to 99%" then only one in the entire casino has to be set that high. However, some casinos will have certain carousels or banks that they claim are all set to a certain percentage. Wherever me or my associates have seen such claims, and tested them, we found the claim to be true. So my advice to slot players is to look for particular machines that are guaranteed to pay a high return, and don't pay any heed to the guessing games. Feb. 11, 2002

Is there any way to spot a would-be winning slot machine? - Dave from Yale, USA

No. Feb. 18, 2001

Where is the best place to find loose slots in casinos, if there is any? - Bill Giessregen Jr. from Austin, U.S.

According to my research there are no good or bad areas. Either the casinos are consistent across the same coinage or the mix up loose and tight machines apparently randomly. Sept. 3, 2000

Could you please tell me what are some of the better paying slot machine to play? And also the placement of the machines that pay off the best? any help would be appreciated. i like slots but never win!!!! - Denises Montmarquet of Lowell, USA

There is no way to tell whether a slot pays well by looking it. Most likely, the only one who knows is the slot manager and perhaps a few other casino executives. The kind of machine is not a major factor. While it's "common knowledge" that casinos put higher-paying slots in the higher-traffic areas I'm skeptical that that is really the case and I intend to conduct some research into this soon Aug. 13, 2000

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