Checking slot machine performance: Confidence intervals

If I play penny machines and bet say 30 lines at four coins per line, do I win more in the bonus round than betting 30 lines at two coins per line?

Also, on the new Wheel of Fortune, they say in Strictly Slots that the bonus round happens after 60 spins. Is that correct?

Yes, you would win more in the bonus rounds when you bet more. Payouts in bonus rounds are based on either your total bet or your line bet. Both your total bet and your line bet are greater in the four-coin-per-line situation than in the two-coin-per-line, so your potential payouts are bigger when you bet four coins per line.

As for how frequently you hit the bonus round on the new Wheel of Fortune, you won't hit it every 60 spins. You will hit it every 60 spins on the average, but you won't hit it on every 60th spin.

Best of luck in and out of the casinos,
John

Dear John,

I have the joyous task of investigating the group of slot machines with variances from par of 3% or more and more than 100,000 games played. I've tried to tell auditors and regulators that the par sheets give Par, confidence intervals or volatility index, based on 10,000,000 plays. In other words, anything can happen! The NIGC/MICS set this standard of 100,000 games and 3% when it used to be six months and 3%.

Can you dumb down the math for us analyst types? How do I use the confidence interval to arrive at that "range" of expected results?

First, it makes much more sense to have the standard based on games played than calendar days. Time on a slot machine is measured in spins, not ticks of a clock.

Second, it doesn't make any sense to use a 10,000,000 game confidence interval after only 100,000 games have been played. The range is going to be far too narrow, especially on volatile machines. You must have many machines that are not falling into the interval.

You should calculate the intervals for 100,000 spins. You can find the equations in Casino Operations Management by Kilby and Fox if you need them. One thing to keep in mind is that the results are not usually normally distributed with so few spins and the confidence interval equations (which assume a normal distribution) are not entirely correct.

Another thing to keep in mind is the level of confidence. At a 90% level of confidence, there's still a 10% chance that your machine's results will not fall in the interval and still be operating normally.

John

Send your slot and video poker questions to John Robison, Slot Expert, at slotexpert@comcast.net. Because of the volume of mail I receive, I regret that I can't reply to every question.