How the casino really makes money

11 October 2018

By John Grochowski

When comparing casino games, the house edge frequently is used as the standard.

But the edge alone can't tell you precisely what you can expect in equivalent times on the games, something I discussed recently with Paul, an old video poker-playing acquaintance.

"I've been playing this game a long time," Paul said recently as he sat down next to me at a bank of multi-game machines. "It's probably 20 years since we met."

That sounded about right. Paul attended a seminar I gave and asked if he could work for me, scouting games and pay tables. He became a lot less enthused when I told him I couldn't pay him, but he's kept in occasional contact via email.

"I've been at this so long I know all the percentages by heart," he said. "You get 99.5% on 9/6 Jacks or Better but only 97.3% on 8/5. You get 100.2% on 10/7/5 Double Bonus but only 99.1 on 9/7/5 or 97.9 on 9/6/5."

Provided you play at expert level, I chimed in. If you don't know the right plays, you'll get less. In any event, there will be times of big wins and times of big losses — those expected returns are averages.

"What I've never actually done, though, is to figure out what that means in dollars and cents," Paul said. "I do know I do better on the higher-paying games. Those payback percentages aren't just numbers."

To calculate the average result per hour, you need three things: the bet size, the house edge and the number of hands per hour.

On a 25-cent, single-hand game in which you bet the maximum five coins per hand, the bet size is $1.25. Assuming expert play, the house edge is the payback percentage subtracted from 100% — 9/6 Jacks or Better, with a 99.5% payback, has a house edge of 0.5%.

The speed of play is variable. For average players, I like to use 500 hands per hour. Beginners play slower, and many experienced players go faster, but 500 is a nice steady pace.

If you’re playing a quarter machine with a five-coin maximum bet, that means you risk $1.25 per hand, or $625 per 500 hands. Multiply that by the house edge, and you get an average loss per hour for an expert-level player.

For calculation purposes, the house edge in 9-6 Jacks or Better can be expressed as 0.005. One percent is the same as saying 1/100, which in decimal form in 0.01. A half percent is half that, or 0.005.

Multiply $625 at risk by 0.005, and you get $3.125. The expected loss per hour for an expert at 9-6 Jacks or Better on a quarter machine is a little over $3.

What if the best you can find is 8/5 Jacks or Better? There, the house edge is 2.7% or 0.027. Multiply $625 by .027, and you get an expected hourly loss of $16.88.

Loss averages increase if you play faster. At 800 hands per hour, quarter players risk $1,000 and average hourly losses are $5 on 9/6 Jacks or Better or $27 on the 8/5 version.

Average outcomes can be calculated for any game and any pay table using the same method.

"Good to know," Paul said. "Last month, I drew a royal flush and won $1,000. Last week, I lost a quick $200. I suppose if I kept track it would lead me to the expected averages, but the variances are sure fun when they're on the win side."

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