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Best of John Robison

Gaming Guru

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Still more "truth" about slots

4 August 2008

Dear John,

Thank you for your time. I am glad you are an expert so you can help us to "see in the dark."

Yes, you are right. Someone can hit the jackpot at the very first pull, but unfortunately just theoretically. The probability of such event is like probability that I will be President of USA. It is very close to zero.

From your description of the USA slot machines someone can get impression that they are fair. Are they?

Let's split a complete machine program into two parts: RNG module and rest of the software which calculates the outcome and let's call it Outcome Calculator. If we want to make fair Outcome Calculator, it supposes to give same outcomes with any RNG module. Is that possible? To my understanding of the math the answer is NO. Additionally, the slot machine guarantees specified payback requested by the buyer. So how can you guarantee different paybacks from 60% up to 95%? Without controlling either RNG or Outcome Calculator. It is impossible. If you say YES, let's create "fair slot machine" and prove it. It is not so complicated and we can create it in the MS Excel, so everyone can check it. We will see if anyone can achieve 90% payback. Probably you would say "in a long term." What does "long term" mean? One day, one year, 10 years, 100 years? Can the manufacturer of the slot machine guarantee that machine will work for 10 years with no failure? Of course not. So, there is no guarantee that the machine will ever give specified payback. Will machine continue from exact point after the technician fixes it? Of course no. Who can block the machine owner from removing the machine from the floor? Gambling regulatory agencies are not publishing "long terms." Why? You were testing different machines so you can tell us what the average "long term" is. I mean results from the tests you performed. Instead using that term we should use "number of spins which guarantees 95% payback" What is that number?

Are the tests valid?

Due to the fact that "random numbers are cycling," there is no formula to mathematically determine the probability of the projected payback. To be able to calculate the probability you have to know total number of "random numbers," speed of cycling and samples have to be taken after equal periods of time. So only way to determine the payback and at same time to check "fairness" of the machine is through a statistical experiments.

You said the RNG generator stores pulled numbers in the memory locations. That memory location is a shift register. If you "sync" with the register you can see and save all "random numbers." Once you have all numbers you can check the Outcome Calculator if it is producing expected outcomes. Then you have to perform the statistical experiment to check the payback. Of course that is accelerated mod when you are pulling numbers at equal periods of time between the pulls. That is not a case in casinos, and due to the fact that "random numbers" are cycling, from statistical point of view there is a high probability that the machine will never achieve projected payback. But do not worry; someone had invented a term "long term." Everything is projected in a long term, but nobody is telling you what the "long term" actually is. "You did not play enough, play again." So, are they fair? Is it fair to offer a game to someone, where his chances to win are almost zero?

In your explanation about the payback calculations you did some calculations based on the winning combinations. But, I am telling you: RNG pattern is mayor factor in the payback determination. Without knowing the pattern all calculations are in domain of the theory. In other words, the payback is valid only and only on just one RNG pattern. To determine the payback you do not have to check the source code at all. The source code has to be checked on the "backdoors" only.

To be honest I did not understand how you can determine 32 virtual stops on the machine with 22 physical stops. I would appreciate your detailed explanation. Let's talk about one of the most popular slot machine. I do not want to mention name, but I think you will recognize it easily, it is very popular. That machine has 3 reels, each with 22 physical stops. Each reel has 11 empty fields, one cherry, 2 single bars, 2 double bars, 2 triple bars and 2 diamonds. So, in total 22 stops. Why should be MODed with 32 and what are the 32 virtual stops? Is that fair? Just one more question: are the jumps in the RNG generator allowed in the US slot machines?

I mentioned England because there are several companies from England specialized in the software development for the gambling machines. One of them has developed software for several IGT machines. You can find IGT machines almost everywhere in the world.

Best regards and tank you for posting our discussion.

Mike

Dear Mike,

I'll respond to some of your statements.

"Someone can hit the jackpot at the very first pull, but unfortunately just theoretically. The probability of such event is like probability that I will be President of USA. It is very close to zero."

The probability of hitting the jackpot on a machine on its first pull is the probability of hitting the jackpot on the machine. It's no more theoretical than hitting the jackpot on any other spin.

"From your description of the USA slot machines someone can get impression that they are fair. Are they?"

It depends on what your definition of "fair" is. A mathematically fair game is game that is not biased toward any player. Slot machines are not mathematically fair because they favor the casino.

The games are fair, however, as compared with carnival games, which use optical illusions and other tricks to make the games appear easier to win than they actually are. On a U.S. slot machine, it is possible to hit every combination displayed on the pay table on every spin and the machine will pay you the proper amount for a winning combination based on your bet. In this sense they are fair.

"Make a fair Outcome Calculator"

One makes a slot machine mathematically fair by altering the game so the amounts you get paid for the winning combinations are related to the probabilities of hitting those combinations. There are two ways to do this. One way by adjusting the pay tables. Using roulette as an example, the chance of hitting a straight number bet on a double-zero wheel is 1 out of 38. If the game were fair, the bet would pay 38 units instead of 35. The other way to make a slot machine mathematically fair is to alter the probabilities of hitting the winning combinations by changing the layout of the virtual reels.

In the United States, Class III slot machines (machines with RNGs) must display the outcome as determined by the number(s) polled from the RNG. No alteration of that outcome is allowed.

"Long term"

Time on a slot machine is measured in spins. Given that pay table and virtual reel layout for a machine, we can calculate the volatility of the pay table. Given the volatility, we can calculate the volatility index. With the volatility index, we can calculate confidence intervals, which tell us the range around the machine's long-term payback we expect the machine's actual payback to fall after a certain number of spins with a given level of confidence. You can see the calculations in Kilby and Fox's Casino Operations Management.

As the number of spins increases, the range decreases. After we've done the calculations, we can say something like "we can be 90% sure that this 95% long-term payback machine's actual payback to be between 94% and 96% after 10,000,000 spins."

Here's the 90% confidence values table for a particular Double Diamond machine:

PullsRange
1,000   64.96% - 131.07%   
10,00087.56% - 108.47%
100,00094.71% - 101.32%
1,000,00096.97% - 99.06%
   10,000,000   97.69% - 98.35%

"How can you guarantee different paybacks from 60% up to 95% without controlling either RNG or Outcome Calculator?"

It's called Random Sampling with Replacement. Look it up. Given enough plays, a machine's actual payback percentage will be very close to its calculated long-term payback percentage.

"Is it fair to offer a game to someone, where his chances to win are almost zero?"

Every casino does it every day. As long as the game isn't biased except for the house edge, and the rules of the game are well known and followed, players know what they are getting and are getting what they are paying for. Is it fair? Yes, players know there is a house edge. In addition, they don't have to play.

"But, I am telling you: RNG pattern is mayor factor in the payback determination."

Nonsense. The RNG is nothing more than a mechanism to draw a sample. (Have you read anything about Random Sampling with Replacement yet?)

A machine's long-term payback is calculated using the pay table and the layout of the symbols on the virtual reels. The RNG is irrelevant.

"To be honest I did not understand how you can determine 32 virtual stops on the machine with 22 physical stops."

It's just an example. Look for my articles and articles by others about virtual reels, expanded reel listing and Telnaes maps. You can even download the Telnaes patent.

Briefly, most modern slot machines use a virtual reel table to expand the 22 physical stops on the physical reels to 32 or more virtual stops on a virtual reel. Slot designers do this to be able to lower the probability of a stop landing on the payline below 1/22. Slot designers do that so the machine can have a larger jackpot than could otherwise be offered if the probability of landing the least likely combination was 1 over 22-cubed.

I would be happy to keep this conversation going, but no more epic e-mails, please. Limit them to one or two questions related to the same topic.

You'll also have to do your homework. I've been involved in too many exchanges in which the other people are only interested in arguing their beliefs about the way slot machines operate and are unwilling to do any research and investigation on their own.

Your homework is to read articles about Random Sampling with Replacement and virtual reels.

John


Send your slot and video poker questions to John Robison, Slot Expert, at slotexpert@comcast.net. Because of the volume of mail I receive, I regret that I can't reply to every question.

John Robison

John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

You may hear John give his slot and video poker tips live on The Good Times Show, hosted by Rudi Schiffer and Mike Schiffer, which is broadcast from Memphis on KXIQ 1180AM Friday afternoon from from 2PM to 5PM Central Time. John is on the show from 4:30 to 5. You can listen to archives of the show on the web anytime.

Books by John Robison:

The Slot Expert's Guide to Playing Slots
John Robison
John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

You may hear John give his slot and video poker tips live on The Good Times Show, hosted by Rudi Schiffer and Mike Schiffer, which is broadcast from Memphis on KXIQ 1180AM Friday afternoon from from 2PM to 5PM Central Time. John is on the show from 4:30 to 5. You can listen to archives of the show on the web anytime.

Books by John Robison:

The Slot Expert's Guide to Playing Slots