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Ask the Slot Expert: How many spins to get near a slot machine's expected return?20 January 2016
Every Class II machine displays or has the option to display the Bingo card that that is used in determining the result of your spin. The slot technicians will definitely know whether the machines on their slot floors are able to determine the results of their spins on their own or require communications with a central server to determine the results.
There's no one answer to your question. The number of spins depends on the volatility of the payback program -- a term I use to refer to the combination of the paytable and the reel layout. The more volatile the payback program, the more spins it takes to home in on the long-term payback percentage.
To use an extreme example, let's say you get paid 90 cents for every dollar bet on every spin you play on my very boring slot machine. There's no volatility here, so you're at the long-term payback percentage from spin one.
If we make the machine more interesting by introducing some losing spins and some spins that pay more than 90 cents, we raise the volatility and it will take more spins to home in on 90% payback. Add a combination that pays $1000 or more infrequently and more losing spins and some in-between jackpots -- in other words, make our machine like a traditional reel-spinning slot -- and it may take many, many spins to near the long-term payback.
How many spins? We'd need access to the PAR sheet to determine the frequency with which each winning combination hits. With that information, we can calculate confidence intervals, which tell us with the degree of certainty we specified in the calculations, the range our actual payback will fall into after a certain number of spins.
Before you read on, take a guess as to the number of spins it might take to be 90% certain that our results playing a Double Diamond machine will be within three percentage points of the long-term payback? In other words if we're playing a Double Diamond machine with a long-term payback of 97.4%, how many spins do we have to play to be 90% sure that our actual payback will fall in the range 94% to 100%?
[Is it obvious that I have a PAR sheet for just such a Double Diamond machine?]
It can't be 1000 spins. You've probably played that many spins and more in a day at the casino and you've had much better and much worse results than our range.
How about 10,000 spins? Still not enough. You might do this many spins over a multi-day casino visit or in multiple visits.
According to the PAR sheet I have, after 1000 spins we can be 90% sure that the payback we get will fall in the range 63.52% to 131.29%. That's about 30 percentage points away from the long-term payback percentage. At 10,000 spins, the range is 86.69% to 108.12. That's only 11 percentage points away from the long-term, but still not as close as we want.
We actually have to play 100,000 spins on this machine for the range to be 94.02% to 100.79%. That's a lot of spins. For many players, it might take a year or more to play that many spins. At 10,000,000 spins, the range falls to 97.07% to 97.74%.
The center point of the range is the machine's long-term payback and the size of the range depends on the number of spins (the more spins played, the narrower the range) and the volatility of the payback program (the more volatile the payback program, the wider the range). Because it takes so many spins (or hands of video poker) to approach the long-term payback, I say that in reality only the casino experiences long-term payback. Players experience hit frequency.
Double Diamond is a fairly volatile game, but not as volatile of Five Times Pay or Ten Times Pay. Blazing 7s is also a volatile game. Small hits are few and far between in order to make the frequency of mixed 7s and Blazing 7s hits more frequent.
One of the things a casino could check on a PAR sheet is how many spins it takes for the machine's actual payback to fall below 100% -- in other words, to be profitable for the casino. On my Double Diamond machine, it takes a little over 100,000 spins for the casino to be 90% sure that it will have made a profit from the machine.
I recently told the story of how the second casino to test Blazing 7s machines was initially losing money on the machines and was very upset about that fact. If that casino had the confidence intervals for the machines, it would have seen that Blazing 7s is more volatile than the other machines of the time and that it could take more spins than the casino was used to for the machines to be profitable for the casino.
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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