Payback percentage a complex formula

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Updated: December 21, 2011 10:07PM

I’ve mostly ignored overall slot payback percentages ever since casinos opened in the Chicago area. Knowing which casinos pay more on dollar slots or which offer the highest returns on penny slots is useful information.

The payback percentages on all machines of all coin denominations lumped into one figure? That’s subject to statistical influences that make the final calculation meaningless in terms of searching for a machine.

Nonetheless, a reader who identified himself as Barry e-mailed to say he was trying to make sense of the overall payback percentages on the Illinois Gaming Board report for November. It includes a breakdown by coin denomination of slot returns in October.

“I usually play at Harrah’s [in Joliet], so I looked at their percentages. It said Harrah’s had an AGR percentage of 8.09 percent. That’s the same as a 91.91 percent payback percentage, right? Then I looked at those AGR percentages on the different coin values. It was 12.74 percent on pennies, 6.91 percent on dollars, all these different figures.

“So what I did was take all those numbers of the different coin values, and added them up. Then I divided by the number of different values. There were 10 of them with pennies, 2 cents, 5 cents, up to $100. I thought maybe it would get me somewhere close to the 8.09 percent that was listed for their slots overall, but it didn’t. It gave me 10.9 percent.

“Can you tell me why the difference, and what I was doing wrong?”

The reason you can’t just average the averages and come up with the overall payback percentage for the casino is that there are different numbers of machines at each denomination, and different amounts of money wagered on the games. Harrah’s 218 quarter slots and their 6.18 percent AGR percentage (or 93.82 percent payback) mean more to the overall figure than the 40 nickel slots and their 8.4 percent AGR percentage.

A casino’s overall AGR percentage on slots is calculated by taking all the money held by the casinos and dividing it by the total wagered, then multiplying by 100 to convert to percent. You can’t get there by averaging the percentages on different coin denominations.

John Grochowski is a local free-lance writer. His “Casino Answer Man” tips air at
5:18 p.m. Tuesday-Friday on WLS-AM (890).