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Best of John Robison
More on slot cycles and randomness17 July 2006
What is it in this scenario that makes you think it wasn't a random event? Is it because she played only 10 minutes?
There is nothing in this incident to make us question the randomness of the video poker machines.
She won because the combination of cards she held plus the cards she drew was a royal flush. She was not pre-ordained to hit a royal regardless of her actions. That would be impossible. How can you force a royal when someone holds a pair of 2s?
If she hadn't hit a royal, someone else would have eventually.
Best of luck in and out of the casinos,
I hope you will find my answers reasonable. Let's take your points and questions in order.
First, let me say that almost nothing that I write is theory. I write facts. If I'm not sure about exactly how something works, I find out.
There is nothing wrong with using a coin toss to illustrate randomness on a slot machine. The principles and calculations are the same regardless of the number of possible outcomes.
What happens if you play seven lines and a jackpot lands on the 9th line? You lose.
What if you play 50 credits per line rather than one? The number of credits (or lines) played has no effect on the symbols that land on the payline. Now, what could happen is you can sit down at that machine, bet 50 credits, and win $25,000. And every other player can bet only one credit. It will take a long time for the machine's actual payback to get back near its long-term payback. In reality, though, players bet all sorts of different amounts on these machines and the extreme situation in my example just does not happen in the real world.
As for machines that let you double your wins: I have limited experience with these machines, but in the U.S. at least, I think many of them will not let you attempt to double wins over a certain amount. In any case, the double-or-nothing game is usually a fair, 50/50 game. The people who end up losing their win fund the pool for the people who double, quadruple, etc., their win. It seems like the double-or-nothing game should have an effect on a machine's payback, but I think it is correct to say that if you take a game with a house edge and tack on an unrelated fair game, the house edge on the original game is not affected.
The key point is that the add-on game is completely independent of the original game. I point this out to head off any comparison with the odds bet at craps, another fair bet. The odds bet is related to the original game, so it does have an effect on the house edge.
The large jackpot payoffs can have an effect on a machine's actual payback. The size of the effect depends on how much play a machine has received. I can an example in my 6/19/06 column of how a $10,000 payoff changes a machine's actual payback by only 0.3 percentage points.
Here's an analogy. You have a vial of orange dye, a glass of water, and the Atlantic ocean. You put a drop of dye in both the glass of water and the ocean. The water in the glass turns orange. There's no noticeable effect on the ocean.
When a machine has had millions of dollars played through it and has paid out millions of dollars, another jackpot, even one worth tens or hundreds of thousands of dollars, doesn't have much of an effect on a machine's actual payback percentage. And any effect it does have is not likely to move the percentage out of the range expected for the amount of play the machine has received. Try it yourself. Pick a payback percentage, a wager amount, a total amount played through the machine, and a jackpot amount. Keep the numbers realistic, like 90% payback, $3 bet, $5,000,000 in action, and a $25,000 jackpot. Assume that the machine has paid back exactly 90%, then do the math to see what effect hitting the $25,000 jackpot on the next spin has on the machine's actual payback percentage.
Any sort of supervisory code to influence the outcome of a spin is illegal in the United States. The outcome dictated by the RNG is the outcome that must be shown.
A likely reason why you were not allowed to see certain areas of the factory is because the company was working on machines that have not been announced yet. There might have been other trade secrets the company was protecting. You weren't excluded from certain areas because, say, the company didn't want you to discover that Soylent Green is people, if you'll forgive a possibly obscure movie reference.
The frequency of near misses is a direct result of the weightings given to the symbols on the virtual reel. Heavily weighted symbols above or below the jackpot symbols cause frequent near-the-payline near misses. A lightly weighted jackpot symbol on the third reel relative to the weightings on the first two reels will cause on-the-payline near misses.
"Why is a first spin almost in every case a win?" You weaken your position by qualifying it. A first spin is not always a win because spins are not always winners.
Let's simplify the situation by looking only at one machine. You're going to keep track of the result of the first spins of 1,000 players on this machine. You'd find that the percentage of winners would be very close to the machine's hit frequency.
"Why does a machine give you some wins almost every time you put your money in and afterwards it eats your credits ruthless to zero?" You get some wins because not every spin is a loser. The machines tend to eat all your credits because they pay back less than 100%.
"These events happen just way too often to be coincidental." Part of the reason you think these things happen "way too often" is due to selective memory. You remember the times an event confirms your world view and ignore those that don't. Unless you make a conscious effort to keep track of results, you don't have any concrete information about how frequently something really happens. I was once convinced that a Double Diamond-Double Spin machine always re-spun the third reel to the same symbol. The times the same useless symbol re-landed on the third reel were so vivid in my mind that I had completely forgotten about the times a different useless symbol landed on the third reel. When I kept track of the re-spins, I discovered that most of the time the re-spin landed with a different symbol. My selective memory had caused me to come to a completely incorrect conclusion.
You have a theory. Now gather evidence for it by actually keeping track of results. Don't rely on your impressions of what has happened.
The other part of why you think these things happen too often is because you have no idea how frequently they should happen. If I say I have a fair coin and 25% of 1,000 flips are heads, we can say something appears to be wrong. But if I say I have a biased coin and 25% of 1,000 flips are heads, we can't say anything because we have no idea what the bias is.
We don't have access to the PAR sheets for machines, so we can't calculate how frequently these events should be occurring. They just might be — and probably are — occurring with frequencies very close to what the probabilities say they should be.
"...in a take cycle you might get a good bonus and in a give cycle you may 'fall' into a short take cycle..." Again, I think you weaken your position. Cycles exist but you can have sub-cycles within larger cycles and even large hits within take cycles. It seems to me that these events are evidence for randomness more than they're evidence for the existence of cycles.
"Let's try to find out some logical explanations." The logical explanation is quite simple. I have written it many times on this site. Results on a slot machine are determined at random using an RNG function. The results are determined at random with total disregard for what has happened in the past. The principles of Random Sampling with Replacement ensure that a machine's actual payback will approach its long-term payback the more play a machine gets, not a governor function.
"The most important thing is to know when the machine is ending its give cycle." Please tell me how you know this. I would love to know.
Best of luck in and out of the casinos,
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 send a reply to every question. Also be advised that it may take several months for your question to appear in my column.
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