Be careful with casino-wide slot paybacks

Most of the time, I ignore casino-wide slot machine payback percentages. That slot machines at one casino return 92.5% of wagers to players while a competitor returns 93.1% doesn't yield much useful information.

That's because there's a hidden statistical influence at work. Does the casino have strong play on high-paying dollar-and-above slot games, or does it grind out its profit on low-paying penny slots? More high-denomination play pushes up overall payback percentages.

Nonetheless, a reader who identified himself as Barry e-mailed to say he was trying to make sense of the overall payback percentages on a report that included a breakdown by coin denomination of slot returns. Some states put such information online, while Strictly Slots magazine publishes statistics for most gambling states each month.

"I looked at the percentages for the casino where I play," he said "The report said the casino had an adjusted gross revenue percentage of 8.09%. That's the same as a 91.91% payback percentage, right? Then I looked at those AGR percentages on the different coin values. It was 12.74% on pennies, 6.91% 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% that was listed for their slots overall, but it didn't. It gave me 10.9%.

"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. The 218 quarter slots at the casino where Barry plays and their 6.18% AGR percentage (or 93.82% payback) mean more to the overall figure than the 40 nickel slots and their 8.4% 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.

For players, it's far more useful to know the payback percentage by individual denominations. If you're a dollar slot player, the number you want is the payback percentage on dollar slots. If you play the penny games, you want the penny data, not the overall percentage.

Lumping them together can be misleading to players. Let's say I have a casino where $1 million is wagered on dollar slots and $1 million is wagered on penny games. My dollar games return 93%, or $930,000, and the penny games return 86%, or $860,000. Overall, I take in $2 million and give back $1.79 million, of 89.5%.

Now let's say your casino takes in $500,000 on dollars and pays back 94%, or $470,000, and $1.5 million on pennies, while paying out 87%, or $1.305 million. Overall, $2 million is wagered, and you pay $1,775 million, or 88.75%.

Your casino pays higher percentages on both dollars and pennies. Both dollar players and penny players get better deals at your casino. But my overall payback percentage is higher. If you're looking at the overall payback percentages, you're not really getting any useful information.

THE VIDEO POKER INFLUENCE: One thing that doesn't get separated out in breakdowns by coin denomination is the video poker factor. Payback percentages, AGR percentages, hold percentages — however each state decides to label the statistics — lump together slot machines, video poker, video keno, video blackjack and any other electronic gaming devices.

Video poker games usually return more to players than slot machines do. In casinos that have a high percentage of video poker games among their electronic gaming devices, the payback percentages by denomination get an extra boost. That's especially true at casinos that offer great video poker with strong pay tables. Slot machines at Las Vegas locals casinos usually pay higher percentages than those on the Las Vegas Strip, but the monthly numbers are skewed a bit because the video poker at the locals joints is MUCH better than that on the Strip.