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Confidence Intervals for dummies

**FiveTimesHey**:

While I can't provide technical expertise (yet?), I figured I could contribute with a short explainer on confidence intervals.

PAR sheets are naturally designed for casinos running thousands of machines with hundreds of customers 24/7, and as such they typically offer 2-tailed confidence intervals at a low degree of confidence. For the home-user, confidence intervals can key in telling users to how rare certain hot/cold sessions are, give them a sense on how many credits they could feasibly win during a session, evaluate a machine's volatility, etc.

Every (IGT) PAR sheet comes with a volatility index, but it's important to recognize this number is specific to the confidence interval used. Usually this is 90%, which means 5% of the time the result will be above the interval, and 5% of the time the result will be below it.

To find the raw multiplier, divide the VI by the z-score @ the level of confidence. You can find the z-score here https://measuringu.com/zcalcp/

So for a hypothetical VI of 20 @ 90%:

20/1.65 = 12.12 (i'm an autist and typically use more decimals, this is just an example)

Let's say 90% isn't enough -- we want to see what range the machine will be in 98% of the time:

Lookup the two-tailed z-score for 98% (2.33)

Multiply (2.33) with our base multiplier (12.12) = 28.24. This number is your new Volatility Index.

To find the confidence interval, use the following formula:

Payback % +/- (VI/(square root of(# of spins)))

If our machine has a 95% payback, the confidence interval for 1,000 spins is as follows:

.95 +/- (28.24/sqrt(1,000))

.95 +/- (28.24/31.62)

.95 +/- .8931

Over 1,000 spins, 1% of the time this imaginary machine will return less than 5.69% of what is run through the machine. Over 1,000 spins, 1% of the time the machine will return more than 184.31% of what is run through the machine.

Hope this is helpful for users here, I'm not a math expert but let me know if you have any questions.

**don275**:

those percents are based off 1 million spins paying back 95% , is that correct ,for you to come up with those percents, thx

**don275**:

what i dont like with the payback percent their is no set number of spins ,where it would have to pay back the percent, i was at fort erie they had all the wheel of fortune machine max limit $99,999 , the place closed the stores with those machines never paying the jackpots out,they were like that for years . $99,999 what a scam that is,they should be programmed to pay back percent based on so many spins,or how can you come out with the percent,not on its life time,what is the percent based on, heaven,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

**rickhunter**:

If they had to pay after a certain number of spins, then it wouldn't be "random" would it. To be classified as a class 3 machine and pass jurisdictional approval, all events must be as "random" as technically possible. While a computer cannot really offer a "random" number since it must be calculated, enough variables are introduced into the seed calculation to make it as random as possible. Some games have progressives that "must pay" by a certain amount (usually stated on the screen). It is my understanding that the probability of hitting the progressive on these types of games increases based on the bet amount and the relative closeness to the jackpot limit. I have never seen one of these machines reach the limit and usually the progressive only increases when the machine pays a winning combo.

**rokgpsman**:

There was a story in the news in 2014 how a slot machine in Las Vegas at the MGM Grand finally hit the jackpot after 20 years on the casino floor. Evidently there was some gaming regulation that the machine had to be kept around until it hit, to satisfy the Nevada law, even though MGM had been wanting to get rid of it for a long time. The machine had been installed when the MGM first opened and it was nearly always being played, still took 20 years for it to hit the big one. I guess that's what is meant by "the long run". :garfield:

https://lasvegassun.com/vegasdeluxe/2014/aug/23/after-20-years-lions-share-slot-machine-mgm-grand-/

https://lasvegassun.com/vegasdeluxe/2014/feb/19/cult-2345-million-lion-slot-machine-payoff-mgm-gra/

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