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21 July 2008

Dear John,

Thank you for posting my comments and accepting the discussion.

My evidence? Let's first define what the evidence is? To me, real evidence is the court evidence. In other words, have you ever developed any firmware for the slot machines? If the answer is "yes" then your evidences are much stronger than mine. Otherwise both of us are guessing. I had a chance to analyze some firmware and I had a chance to monitor several machines with complete reports from the machines every single day for many months. And guess what, I was able to predict which machine is ready to give very good payoff. The books that I have had in my hands are for me useless. Simply they are presenting mathematical models and nothing else.

When I said I analyzed firmware I meant did some statistical experiments and reset electronics to perform "cold boot." My conclusion and conclusion of guy who is PhD in Electronics is: Nobody can cheat gambling machines externally. If you know statistics of the machine yes, you can predict high payoffs. The design of the "motherboard" allows you to cheat everyone including the government commission. Sealing EEPROM does not mean anything. By adding a few shift registers or flip-flops you can completely change logic of the EEPROM. But anyway, let's discuss your comments.

To be honest I could not make conclusion about your vision of generating random numbers. In one sentence you said they are cycling, than in other sentence they are not cycling until the player starts the game. English is my second language so may be I did not catch your idea. I would appreciate your opinion about cycling. I do not need to throw the dice to see that number 1 appears in 16.67%. Each book about The Probability says that all 6 numbers on the dice have equal probability to appear and the probability is 1/6. You just confirmed that fact in the percentage. If you do the same tests for number 2 and above you will find same probability.

Let's go back to the slot machines. As you said there are 4.3 billions of random numbers (that just confirmed my statement that they are using 32-bit machines). Probability that each number will appear is: 1 divided by 4.3 billions! The machine has, let's say, 10 winning combinations (numbers). With such a low probability you cannot guarantee any payout for a year and casinos and manufacturers are talking about 95% payback? Logically impossible. If you think it is possible I really appreciate your mathematical explanation. (BTW I've read several articles from you and I did not see your mathematical model of the slot machine, I mean detailed. If you did it, please post the link.) To increase probability of the winning combinations you have to assign many random numbers to each winning combination. How many? 10, 1,000, 10,000…? I do no mean physically assign numbers, much easier way is to use dividing techniques and residuals. To my understanding "Hit frequency" is determined by the "number of assigned numbers" for each winning combination. That is explanation for you question about fact that hit frequency of double bars is much higher than three of sevens. Simply the programmer is selecting which combination will appear more frequently. Yes, you are right. There is no need for two RNG tables. I did not elaborate that properly. There is just one primary RNG generator. Two tables I am talking about are "losing table" and "winning table" or tables. The easiest way to create those tables is to switch from 32 to 16 bit, or 8 bit RNG numbers, or you can increase "number of assigned numbers." So the machines are cheating.

You can guarantee based on the probability and randomness? Yes you can guarantee but the question is what? But let me challenge your opinion. Let's make "true RNG" with 90% payback, with only one winning: \$100,000.00! We will determine number of "random numbers" with just one table. Once we create the "slot machine" I will pay you for each spin on that "machine" amount that corresponds to the number of the random numbers. If I win you have to pay me \$100,000.00.

You said that many of those random numbers do not give any outcome. Sorry, but I did not understand that. Can you explain it to me?

In one of the next e-mails I will send you a link to the website where group of enthusiasts in England proved that many machines are cheating.

Best regards,
Mike

Dear Mike:

It is rare in life that two people can make opposing statements and both be right. In your last statement you mention machines in England.

In what country were the machines that you analyzed? I'm writing strictly about games in the United States and not about games in any other country. Other countries may have rules that differ from those here in the United States. For example, a former co-worker told me he had a friend who develops a particular piece of software for fruit machines in England. This particular piece of software was designed to keep a machine's actual payback within a specific range. If the firmware you analyzed and reports you monitored were for non-U.S. machines, we can both be right.

Let me further clarify my position by stating that most of my articles describe Class III slot machines. The piece of software I described in the preceding paragraph is illegal in a Class III slot machine in the United States.

I have not developed any slot firmware myself, but I have acted as an expert witness in patent disputes. As an expert witness, I've had access to source code, depositions and testimony.

How can you have a "true RNG" with 90% payback? RNGs do not have paybacks. They just generate a stream of numbers.

Here is how a Class III slot machine operates in the U.S.:

Let's assume we have a 3-reel machine with 32 virtual stops and 22 physical stops on each reel.

Hundreds, if not thousands, of times each second, the slot's operating system calls the RNG function to generate another number. This occurs all the time, even when the machine is not being played. Thus the vast majority of the numbers produced by the RNG are never used to determine the outcome of the spinning reels. The RNG stores the number it generates in a specific memory location.

When the player initiates a game by pressing the Spin button, the program "polls the RNG" to find out the most recently generated number. It reads the number stored in that specific memory location.

Most machines poll the RNG for each reel, so this number will be used to determine where only the first reel will stop. The range of the numbers produced by the RNG is probably larger than the number of virtual stops on the virtual reel, so we have to MOD the number down to the proper range. In this case we'll MOD 32 to get a number from 0 to 31. That's the virtual stop chosen on the first reel.

Now that we know the virtual stop, we have to look at the virtual reel layout to see which physical stop is mapped to this virtual stop. The program then stops the stepper motor on the first reel on that physical stop.

The RNG has continued to generate numbers while this was going on. Now it's time to poll the RNG to get a result for the second reel. The number we get from this poll is again MODded to the proper range. The program checks the virtual reel layout for the second reel to find out which physical stop should land on the payline. It then stops the stepper motor on the second reel on that physical stop.

The process is repeated for the third reel.

The RNG generated hundreds of numbers while this spin was playing out. Only three of them were used to determine the outcome of the spin.

We calculate a machine's hit frequency by looking at each winning combination and seeing how many ways we can make the combination based on the layout of the symbols on the virtual reels. For example, if there are three triple bars on the first and second reels, and only two on the third, there are 3 x 3 x 2 or 18 ways to hit triple bars. Add up all the ways to make all the winning combinations and divide by the total number of combinations on the virtual reels to get the hit frequency.

To find the one-coin long-term payback, we build on the work we did calculating the hit frequency. Take the number of ways to hit each winning combination and multiply it by the value of the combination when playing one coin. Add up all those products and divide by the total number of combinations to get the one-coin long term payback.

To find the payback when playing other than one coin, the value used in the multiplication is the value used when playing that number of coins. We also have to divide by the number of coins played too.

U.S. machines do not have two virtual reel layouts, a losing layout and a winning layout. The RNGs do not change their "bitedness" based on past spins.

U.S. machines rely on nothing but the principles of Random Sampling with Replacement to guarantee that in the long run a machine's actual payback will be very close to the payback calculated from the layout of the symbols on the virtual reels. Slot regulations in the U.S. require that the outcome determined by the RNG must be displayed.

It's possible that a machine can show a loss for a while after it is put on the casino floor. It's even possible for a machine to hit the jackpot on the very first pull after it's put on the slot floor. As the machine gets more play, its actual payback will tend to get closer and closer to its calculated payback.

Best of luck in and out of the casinos,
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