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Ask the Slot Expert: Are slot machine results really random?13 January 2016
I was originally going to start by saying that the controlling logic you surmise exists not only does not exist, but is illegal in most (if not all) jurisdictions in the United States. But, in a sense, some sort of controlling logic does exist, just not in the program running the slot machine.
Let me address your statements. First, random results means the casino cannot control the payback percentage. What's happening inside the slot machine is that the output of the RNG is used to choose a result at random from the pool of possible results. Each combination of symbols on the reels appears one or more times in the pool. If we knew the number of times a combination, say bar-bar-bar, appeared in the pool and the total number of combinations in the pool, we could divide the former by the latter to get the probability of landing three bars on the payline.
If we sat down and played the machine and noted how many times we hit three bars, we'd find that the ratio of the number of times we hit three bars to the number of spins we played would get closer and closer to the probability we calculated from looking at the pool. This occurs as a result of Random Sampling with Replacement, which means that we select an outcome at random and the probability of each outcome does not change from trial to trial.
Consider throwing two fair dice. If we chart the number of times we throw each possible roll, we'd get a figure that looks more and more like the pyramid of craps as we continue to throw. Where is the controlling logic in the pair of dice that causes the pyramid of craps to be produced every time?
This is where I would normally say that there is no controlling logic. Producing the pyramid of craps, and the fact that a slot machine's actual payback percentage will approach its calculated payback percentage as the machine gets more play, is just a consequence of Random Sampling with Replacement. But I suppose we could consider Random Sampling with Replacement to be the controlling logic, although there really is no control.
The probability of throwing a six on a fair die is 1/6. If we tossed this die and tracked the numbers thrown, the ratio of the number of times we threw a six over the total number of throws would get closer and closer to 1/6. I was once a spectator to the start of an email exchange discussing the metaphysics of why this always occurs. The exchange went nowhere. We don't know why. It's just the way the world works.
Now, it's true that the actual payback percentage from a machine may be quite far from its calculated percentage when the machine has had little play. Many PAR sheets include confidence intervals, which tell the operator the expected range of payback after a certain number of spins. This calculation is possible because each result is random.
As the number of spins increases, the payback range in the interval decreases. As a machine gets more and more play, its actual payback percentage gets closer and closer to its calculated payback percentage. Happens every time. It's Random Sampling with Replacement.
I once attended a seminar given by one of the guys who helped develop the Blazing 7s slot machine. It was first tried out in, I believe, Reno, where the machines were a smashing success. Players loved them and they were profitable for the casino.
If I remember correctly, the next casino to try the machines was the Tropicana in Las Vegas. Players really loved the machines there -- the machines were hitting 7s combinations right and left. The Trop initially hated the machines because it was losing money on them. The speaker told the folks at the Trop to be patient. As the machines got more play, the actual payback percentages from the machines closed in on the calculated payback percentage. Players still loved the machines because they liked the frequent mini-jackpots and now the casino loved the machines too.
Again, no controlling logic. Just Random Sampling with Replacement.
Moving on, you can't necessarily equate the outcome of a coin flip to landing three bars. The probability of landing heads or tails with a fair coin is 0.5. The pool of outcomes for a coin is short -- heads or tails.
The probability of landing three bars depends on the number of times the three-bar combination appears in the pool of outcomes and the total number of possible outcomes. As we all know from playing Double Diamonds, landing three bars happens far less than 50% of our spins. Similarly, the probabilities of landing the other paying symbols depends on the number of times they appear in the pool of possible outcomes.
Now is a good time to say that there really isn't a pool of possible outcomes in the programming of the slot machine. There are virtual reel layouts. Each symbol on the physical reel appears one or more times on the virtual reel. The virtual reel layout is like putting Silly Putty on the physical reel and stretching some of the symbols so they take up more than one stop.
The program running the slot machine gets a number for each reel from the RNG. This number tells the program which virtual stop was chosen for that reel. The program maps the virtual stop to the physical stop on the reel. The program spins the reel and stops it on that physical stop. It then looks at the symbols that landed on the payline and makes any payout needed.
The reason you see the Double Diamond symbol more often than three bars or the cherry is due to the number of times each symbol appears on the virtual reel. It's common for a reel-spinning machine to have half or more of the virtual stops on the last reel map to a blank. That means that you'll see many near misses like symbol-symbol-blank, which is much more exciting than a near miss like blank-symbol-symbol. With symbol-symbol-blank, you're still a possible winner until the last reel stops. With blank-symbol-symbol, the spin is a loser after the first reel stops.
It's also common to have more Double Diamond symbols on the first two virtual reels than on the third. Again, the reason is to generate more near misses like DD-DD-blank. This is also why, when you have a winning combination with a Double Diamond, the Double Diamond is more likely to be on the first or second reel than on the third.
Finally, it's also common to have the blanks above and below the Double Diamond symbol appear more times on the virtual reel than the Double Diamond symbol itself. This imbalance leads to near-the-payline near misses, where the Double Diamond symbol lands above or below the payline.
Most slot regulations are modeled after Nevada's. They state that the outcome of a spin is determined by the numbers from the RNG. The RNG is tested to ensure that it meets certain standards of randomness and has no outside influences whatsoever. The program must display the result determined by the RNG without any alterations whatsoever.
Send your slot and video poker questions to John Robison, Slot Expert™, at firstname.lastname@example.org. Because of the volume of mail I receive, I regret that I can't reply to every question.
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