Monday, July 14, 2008

The Truth About Slot Machines

I came across an interesting analysis of slot machine technology that includes cheating and rigging possibilites by John Robison, who writes a column for Casino City Times. Some of your questions about random number generators (RNG) and their true randomness might be answered here in this exchange between Robison and a person named Mike seeking knowledge about slot cheating and technology.

Dear John,

I've read many articles about slot machines on the internet and almost all of those are offering: "the truth about slot machines". With full respect to your educational level and your experience I would like to discuss certain questions regarding the slot machines.

1. RNG or random numbers generation?

To my knowledge and experience with the electronics, there is no such thing. There are simulators and algorithms for "random number generation" but in fact they are predetermined numbers and they will come in the same order after the first cycle ends. There are more sophisticated generators but I doubt the gambling industry is using them for the slot machines. How long would be just one cycle of the predetermined RNG engine? Let us say, that slot machines are using 32-bit technology, knowing that 64-bit technology is just lately introduced, but the mathematics will prove that even if they are using 64 or 128 bit technology the one cycle will be relatively very short. Today's microprocessors are making millions of iterations per second. Let's assume that slot machine has the processor running at 2 millions of iterations per second, which will give us 178800 millions of iterations per day. With 32-bit technology we can generate almost 4,3 billion numbers. Obviously the cycle of the RNG will end with in a day, or if they use 64 or 128 bit technology we are talking about a few days, in worst case a week. So, as per my math, the RNG is cycling very often, but there is no jackpot yet. Why? You would say randomness and probability?

2. Probability?

Winning spin and all other spins have absolutely equal probability to appear on the slot machine. Casinos and slot machine owners are not happy with that fact simply because it does not guarantee them a profit from the machine, even the probability is very low. All slot machine manufacturers guarantee the profit with predetermined percentage. Pure randomness and probability cannot guarantee that. Additionally the manufacturers offer machines with different percentage of the payoffs. If you can guarantee percentage that simply means you are controlling either "randomness" or "probability" or both. Logically the best and most reliable controller is pays in and pays off. Otherwise the owners would be exposed to the risk. If you guarantee something you cannot relay on probability and randomness. Everything has to be under full control!

Slot machines work with at least two or more predetermined tables of "random numbers". Pay in and pay off are controlling which table will be active. That is the truth of the slot machines. There is possibility to use the same table if you assign more numbers to the symbol on the reel, but again the number of assigned numbers will be controlled by the machine.

John, I hope you will post my opinion and I appreciate your detailed comments about my statements.

Best regards,

Dear Mike:

You are correct that the RNGs in slot machines are more properly called Pseudo-Random Number Generators because the algorithms use deterministic functions. This fact is well documented. It would be cumbersome for slot writers to point out the the RNGs are really P-RNGs in every article, so we just call them RNGs and make the point that they're not truly random only when relevant to the article. In any case, labs test the stream of numbers produced by the P-RNGs and the stream passes many of the tests for randomness. The P-RNGs are good enough for the purpose of determining outcomes on a slot machine.

According to Casino Operations Management, the P-RNG used by IGT has a cycle of 4.3 billion numbers. The clock speed of the CPU is really irrelevant. Slots are not required to poll the RNG so many times per second. Slots poll the P-RNG only a few hundred or thousand times a second. The speed changes to make RNG cheating more difficult. The P-RNG will also be reseeded at various times, also to thwart RNG cheats.

There's another factor you have to keep in mind. The P-RNG isn't polled until the player initiates a game. The human factor adds another dimension. If you looked at the stream of numbers actually used to generate outcomes, the randomness of when a player hits the spin button combined with the P-RNG may produce a stream of numbers that are truly random.

Let's say that the P-RNG does cycle at least once a day. Why don't we see a jackpot every day? Because not every iteration of the P-RNG is used to generate an outcome. Nearly all of the iterations are ignored.

You wrote, "Winning spin and all other spins have absolutely equal probability to appear on the slot machine." Complete and utter BS. Do you hit three Double Diamonds as frequenly as you hit three mixed bars on a Double Diamond machine?

Machines have different hit frequencies. Do you hit as frequently on a Blazing 7s as on a Wild Cherry? Combinations, winning or losing, have different probabilities of landing on the payline.

It is true however that each virtual stop has an equal probability of being chosen.

"If you can guarantee percentage that simply means you are controlling either 'randomness' or 'probability' or both." More nonsense. Throw a die. Many times. I can guarantee you that the percentage of times you threw a 1 is very close to 16.67%. "If you guarantee something you cannot rely on probability and randomness." On the contrary, I can guarantee something because I relied on probability and randomness.

"Slot machines work with at least two or more predetermined tables of 'random numbers'." Congratulations! Hat trick. More nonsense. There's only one P-RNG algorithm in a slot machine.

I suggest you search for articles on Random Selection with Replacement. The principles behind this method of random sampling explain why a machine's actual payback will be very close to that calculated from the layout of the symbols on its virtual reels in the long run. The program doesn't need two tables of numbers, pay cycles and take cycles or anything else. Randomness alone is enough to ensure that a machine's actual payback will approach its calculated payback.

"That is the truth of the slot machines." I can point you to numerous books, web pages and statutes that confirm my description of how slot machines operate. Where's your evidence?

Best of luck in and out of the casinos,