Monday, May 6, 2013

Time, money and the house edge

If you've been my casinos columns for very long, you've seen the numbers a hundred times: The house has a 5.26 percent edge on American double-zero roulette, a 1.41 percent edge on the pass line at craps, a 2 to 2.5 percent edge against the average blackjack player, but only a half-percent or so edge against a basic strategy player.

Chances are you use those numbers as a rough comparison of games. Which give you the better shot to win? Which are nothing more than "house" games? And that's fine. You do have a much better shot to win if you're betting the pass line at craps than if you're playing roulette.

But those numbers are also statistical averages. They don't mean that every time you bet $100 on the pass line, you're going to lose $1.41, or even that every 100 times you bet $100 on pass, you'll lose $141.

If the losses were that regular, and that certain in the short term, no one would play. Even on the casino games with the highest house edges, results are volatile enough that players will win sometimes.

Given enough trials, though, the house edge will hold up, and the more trials there are, the closer the results will be to giving the casino its expected profit.

One of the more colorful descriptions of how this all works came from the late Peter Griffin, author of the classic The Theory of Blackjack. I'd been invited to spend a week as a student at the Harrah's Institute for Casino Entertainment in Las Vegas, a crash course in casino operations designed to give gaming basics to non-gaming employees Harrah's had marked as up-and-comers. Griffin was a guest instructor.

Imagine a situation, he told us, in which a busload of roulette players have finished for the day and are in the waiting room, waiting to board for the trip home. They decide they have time for one last spin of the wheel if each of the 100 players gives $100 to a casino manager with instructions to place the bets. (This takes place in a jurisdiction with a particularly lenient gaming board, I might add.)

The manager puts all the money --- $10,000 worth --- in a big box, and climbs a staircase to a balcony overlooking the waiting room. He then takes out $526 --- more or less --- and dumps the rest of the money back over the railing to the waiting bus group.

Players scramble for the money. Some get back their $100. Most get back less. Some get more --- a few get considerably more.

There are winners. There are losers. And the house has its 5.26 percent.

Slot machines work the same way. When we say quarter slots at a given casino return an average of 93 percent to players, that's just another way of saying the house edge on those machines is 7 percent. If you play $100 through a quarter slot at that casino, are you likely to wind up with precisely $93? No, most of the time you'll wind up with less. Much of a slot machine's long-term return is tied up in larger jackpots, so sometimes you'll win hundreds, or even thousands of dollars for that $100 in play. You may win big, or more often lose fast, but on balance over hundreds of thousands of plays, the house will get its 7 percent.

If you go to the casino and play a couple of hours on a three-reel quarter slot, you might spin the reels 1,000 times --- 500 plays per hour is a busy, but not hectic, pace. With a three-coin maximum bet, you're risking $750. If the machines in that casino return 93 percent, your expected average loss is $52.50, but you won't land precisely on that figure very often. Most of the time, you'll lose somewhat more than that. Less often, you'll get a big hit or a few medium-sized wins and walk away a winner. In one short trip to the casino, there's no telling what your results will be.

But let's take a page out of Griffin's book and say you're on a bus trip with 100 players all spending a couple of hours on those 93-percent, quarter slots, all betting 75 cents a spin for a total of 1,000 spins each. Now your group is setting the reels spinning a total of 100,000 times, and the casino can almost count on getting something close to its 7 percent take.

There almost certainly will be a winner, or several winners, in your group. There also almost certainly will be those who lose fast and wind up dropping a couple of hundred dollars. The majority will lose some of their money. All told, your group is likely to leave behind a total very close to $5,250 on its $75,000 worth of wagers.

There are winners. There are losers. And the house has its 7 percent.

That's the way it is when you look around any busy casino. A few are winning. Most are paying for their day's entertainment. It's the hope that this time we'll be one of the winners that keeps us going.


  1. Thank you. Please spread the word. As long as people are reading, I'll keep posting.