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Author Topic: Confidence Intervals for dummies  (Read 9747 times)

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Offline FiveTimesHey

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Confidence Intervals for dummies
« on: May 23, 2017, 08:21:12 AM »
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.






« Last Edit: May 26, 2017, 08:10:39 AM by FiveTimesHey »

Offline don275

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Re: Confidence Intervals for dummies
« Reply #1 on: January 07, 2018, 11:39:31 AM »
those percents are  based off 1 million spins paying back 95% , is that correct ,for you to come up with those percents, thx

Offline don275

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Re: Confidence Intervals for dummies
« Reply #2 on: January 07, 2018, 11:47:02 AM »
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,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

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Re: Confidence Intervals for dummies
« Reply #3 on: January 07, 2018, 01:48:27 PM »
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.
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Offline rokgpsman

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Re: Confidence Intervals for dummies
« Reply #4 on: January 07, 2018, 04:15:25 PM »
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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Offline don275

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Re: Confidence Intervals for dummies
« Reply #5 on: January 07, 2018, 07:27:18 PM »
makes no sense that they are allowed to never have to pay out,should be a set time or amount that it has to pay out by, to keep it honest, the machines should never be allowed to take in ten times the set jackpot with out paying out ,to me its just common sense,if the math dont add up their is a reason why ,they are stealing 80% to 90% and saying they pay back 90%, that is what i see , like the canadian lottery, they take 50% ,and sports betting proline they want to take 35% of the money bet.that is shown because it has to be on the odds, slots are hidden behind a chip ,that says it pays that percent over its life time,just my way of thinking ,and have played the slots to come up with it,you can go ten times ,you are lucky if you come out winning one of them,just like the banks giving 1,8% interest on your money and homes going up 8% to 10% a year,why put money in the bank ,when you can buy homes rent them out and get 5 or 6 times more on your cash a year, plus rent money,and mortgage payed in 20 years,just my way of thinking,when your ready to retire ,sell your homes and enjoy the rest of your life,let your money work for you, not the bank, i must be going crazy,with my slot machines,hahahahahah........slot fever, 

Offline rokgpsman

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Re: Confidence Intervals for dummies
« Reply #6 on: January 07, 2018, 08:06:02 PM »
They aren't rigged or forbidden from paying out the big jackpot, it's just a smaller chance of it happening than the lower winning spins so can sometimes take a while to happen. When you buy a MegaBucks lottery ticket for a drawing your chance is very small to win the top prize and often there is no winner in the drawing that week, out of millions of tickets sold. But eventually someone does win the big jackpot, its a random event that can be won in the first week or much later. You've seen the ping-pong balls pop out of the machine, that's a random selection.

Some gambling jurisdictions have games based on "pulltabs". Those are what you are referring to. There are a definite number of winners in each cycle and each cycle has a known number of tabs/tickets. That is called Class II gaming and usually is found in Native American casinos but some states also allow pulltab games in bars, convenience stores, truck stops, etc. Vegas-style slot machines are in Class III, they are random and have no set cycle. You can win the top jackpot on a Class III machine, the spin it again and win the top award again. Or you can go months and months without winning it.
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Re: Confidence Intervals for dummies
« Reply #7 on: January 07, 2018, 08:24:04 PM »

A progressive jackpot is actually a marketing tool.
a %% of each coin dropped contributes to the progressive.

So if the machine is programmed to pay out at the 92.5% that means a 7.5% house hold.
They would allocate 0.0125 to the progressive, however the casino gets to write that off as marketing.


Income less expenses = profit, and taxes are paid on profit.
Expenses would be rent, depreciation, marketing, salarys, etc....


If the progressive doesn't pay out it can be moved to another casino or it can be turned over to the state.

If you can't afford to lose you can't afford to win.

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Offline FiveTimesHey

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Re: Confidence Intervals for dummies
« Reply #8 on: April 30, 2018, 12:35:35 PM »
those percents are  based off 1 million spins paying back 95% , is that correct ,for you to come up with those percents, thx


My example was based on 1,000 spins.


You can solve for any number of spins you want:Payback % +/- (VI/(square root of(# of spins)))(VI is determined based on your PAR sheet & the Confidence interval you want to set, see OP)

If our machine has a 95% payback, the 98% confidence interval for 1,000 spins is as follows:.95 +/- (28.24/sqrt(1,000)).95 +/- (28.24/31.62).95 +/- .8931Over 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.  So basically you can get a sense for exactly how representative your sample size is by solving in reverse.

 

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