How can a slot machine pay back 95% when I just lost all my money?

It was a quiet Monday morning, and I was strolling down an aisle of a casino on a barge, dollar slots to my left, video poker to my right. A voice rose over the background hum — not that difficult in this relatively quiet corner, away from the clamor of the penny video slots and their bonus events.

"Ninety-five percent! Hah!"

A middle-aged gentleman with white hair, glasses and a Milwaukee Brewers T-shirt looked right at me and said, "Do you buy that baloney?"

It was nearly lunch time, but I had roast turkey from the buffet carver on my mind. I asked, "What baloney?"

"They say these slot machines pay 95%. Do you believe that?"

Sounds about right for dollar games.

"Well, I just ran a hundred dollars through there and got nothing. Sounds more like zero percent to me."

I shrugged and told him I was sorry to hear that. Anything can happen in a short time, from losing it all to winning a big jackpot and anything in between. The average return will be about 95%.

And I started to walk away. The fellow turned to walk with me.

"You think you know something about these machines, huh?"

Well yeah, a little.

"So tell me how a 95% game can give me absolutely nothing."

Absolutely nothing? Not even a cherry, or three mixed bars?

"Well yeah, I got a few of those. Lot of good it did me."

So the amount you won wasn't zero. It was the value of the mixed bars and the cherries and any other winning combinations you might have hit.

"But in the end it took all my money. I didn't have 95%. I had zero percent."

That's because you chose not to cash out your winnings. You chose to bet them until you lost them instead.

"OK, how do they figure those percentages? Can you explain that to me."

I told him that if he really wanted to talk about this, we should have a seat. This was going to be easier with pen and paper. He suggested the bar, and when we sat down, he ordered a beer, and I had a diet cola.

"So tell me, when I read that the dollar slots here pay 95%, what does that mean?"

It means that of all the money wagered on dollar slots in the last reporting period, 95% was paid back to players, and the casino kept 5%. Some players won money, the majority lost more than 5%. But if in a given month $100 million was wagered on dollar slots and the casino kept $5 million, then $95 million, or 95%, was returned to players.

"Well, they kept 100% of my $100."

That's not quite the way it works. You actually made more than $100 in wagers.

"Go on."

How many mixed bars or cherries or other winners do you suppose you had?

"Let's see … I got a cherry four or five times, but those only paid two coins each. About the same for the mixed bars, and they paid 10. I had three single bars once for 20, and my big win — hah, big win — was three double bars for 40."

OK, so let's estimate your returns. Forty for the double bars, 20 for the single bars. Let's take your low estimate of four mixed bars — that's another 40 — and four cherries for 8 more. Your total winnings are 108 credits, and since this was a dollar machine, that's $108.

"You're not going to tell me I actually won money, are you? Because there's a $100 hole in my wallet that says I didn't."

Of course not. You lost your money, but you didn't get zero return. You just chose to re-wager all those returns. You didn't make $100 worth of wagers, you wagered $208.

For you, we'd calculate your payback percentage by dividing $108 in winnings by $208 in wagers, then multiplying buy 100 to convert to percent. And my scribbled figures show that as 51.9%. Your return wasn't zero percent, it was 51.9%. You just kept playing until that 51.9% was gone.

"They can call it 51.9% or zero percent, but I still lost the $100 I started with."

On a table game, they would look at it as keeping 100% of your original $100. The hold percentage on table games is the percent of BUY-INS kept by the casino, while the hold percentage on slot machines is the percent of WAGERS kept by the house. That's fooled a number of people over the years. A casino marketing exec once tried to argue with me that slots paid much more than tables, but he was just drawing a false conclusion from statistics that don't mean the same thing. Marilyn vos Savant, she of the ultra-high IQ, made the same mistake in her magazine column a number of years ago.

When equipment becomes common to track every table wager, we may well see a change in metrics to track table games the slot way. For one thing, casinos like an accurate track of just how much a customer is wagering for player rewards purposes.

"That's all fine, but let me sure I have all that straight. That 95% doesn't mean everybody's getting back 95% of the cash money they're putting into the games. It means they're getting 95% when you figure in credits they're getting while they play, even if they never cash out those credits."

Right.

"Either way, I'm out a hundred bucks. Guess I'll go try again."