Creating the house edge

10 December 2015

By John Grochowski

A few years ago, I answered a question on how slots could be programmed and random at the same time with a comparison to table games.

On double-zero roulette, the game is set up with 38 numbers, any of which could occur on any spin. In that way, it’s random. Winning wagers pay at less than true odds, and over thousands of plays, random results coupled with those payoffs will drive the game toward a 5.26% house edge – or 7.89% on the five-number bet on 0, 00, 1, 2 and 3.

In that way, roulette could be said to be programmed for a 5.26% house edge, but also be random.

It’s the same deal on slot machines. What you see on the screen or reels is a representation of thousands, and sometimes millions, of possibilities. Which combination shows up at any given time is random, but over hundreds of thousands of plays, the random results coupled with the payoffs will lead to a desired payback percentage.

A game whose odds are set up so that it returns 90% could be said to be programmed for that payback percentage, but each result is random.

A friend of a friend brought the subject up at a pizza party in November. Sue is a slot player, and she was having trouble with the roulette-to-slots comparison.

“I can see what’s happening on the roulette wheel,” she said. “But slots have such big jackpots. That has to be directed somehow, doesn’t it?”

I got out a pen and paper, and asked her to imagine five roulette wheels working together. Then I drew five wheels, side by side.

“You can see that all of those wheels have just one double-zero, right?” I asked her. “Would you say that the ball landing on double-zero on any wheel is a random event?”

She agreed that it was.

“And if we released balls on all five of those wheels at the same time, each result is a random event, right?”

Sue nodded agreement.

“OK,” I said. “We have random events on five wheels. Let’s pretend 00 is a jackpot symbol, and we need 00 on all five wheels to hit the jackpot.”

A look of comprehension spread across her face. “That won’t happen very often, will it?”

“It won’t happen often at all,” I told her. “Do you know how many possibilities there are, with results of five wheels and 38 numbers at all. That’s 38 to the fifth power.”

Another friend who had been listening in ran the number on his phone and reported the number was 79,235,168.

“Only one of those possibilities is 00 on every wheel,” I said. “So we’ve just ‘programmed’ a game in which the chances of winning the jackpot are 1 in 79 million-plus, but we’re using random results to get there.”

She said, “I can see that. And that’s how it works on slot machines?”

Basically. Slots are more complex. You have to account for payoffs on other winning combinations, and expected payouts from bonus events are part of the calculation, too. But random results lead to a predictable proportion of winning and losing spins. Then, by making sure you pay at less than the true odds of winners, you use those random results to lead to a predictable payback percentage.

“We could make up a pay table like that right here,” Sue said. “Maybe you could have smaller payoffs on five reds or blacks, or five of the same corner. You could make up a whole game.”

Sure, I told her, but not right then. The pizza had arrived.

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