How does the house edge work?

The house edge remains a mysterious thing to casino players, including the one who asked me recently about roulette.

"Does a 5.26 percent house edge mean the house wins 52.6 percent of all spins?"

That wouldn't be a bad guess if every wager paid even money, and the house edge was made up entirely of the difference between the frequency of house wins and the frequency of player wins. In the red-black wager at roulette, where winners are paid even money, the house wins 52.63 percent of rolls, the player wins 47.37 percent. Subtract 47.37 from 52.63 and you get the 5.26 percent house edge.

It is the difference between win percentage and loss percentage that's important, and you can't just multiply the house edge by 10 and get the percentage of losing wagers. Roulette is a bit of a coincidence that way.

Take craps and the pass line wager, another even-money payoff. The house has a 1.41 percent edge.
Obviously, it wins more than 14.1 percent of the time. Instead, if you want to know the frequency of house wins, divide that 1.41 percent house edge in half, then add the result to 50 percent. The house wins 50.705 percent of wagers, the player wins 49.295 percent. Do the basic subtraction, and you get a difference of 1.41 percent --- the house edge.

Things get more complicated when payoffs get bigger. Let's go back to roulette and single-number bets. A double-zero roulette wheel has 38 numbers, with 1 through 36 as well as 0 and 00. Any time you bet on a single number, you have one way to win, and 37 ways to loses.

Yet the house edge is the same 5.26 percent as it is on red-black, odd-even or first 18-last 18. On those wagers with even-money payoffs, the house wins 52.63 percent of the time, as we have already seen.

Obviously, the house wins far more than 52.63 percent of single-number wagers. It wins 37 of 38, or 97.37 percent of wheel spins.

The reason you're bucking a house edge of 5.26 percent even though you lose 97.37 percent of the time comes in the payoff, of course. Winning single-number bets are paid at 35-1 odds. If it was a truly even bet, you'd be paid 37-1.

The difference between the payoff and the true odds is the key to the house edge. Here's the way it works.

Let's say you bet $10 on 17 on each spin of a perfect sequence in which each number turns up once. You risk a total of $380. On your one win, you get back $360 --- $350 in winnings for the 35-1 payoff, plus the return of your $10 wager on that spin.

That means the house has kept $20 of your $380 in wagers. Divide 20 by 380, and you get .0526. Multiply by that by 100 to get percent, and you see the house has kept 5.26 percent of the money you've wagered.

That's the house edge on single number bets.

It's simple enough to do the same for place bets or proposition wagers in craps, or the player bet in baccarat, or spaces on the Big Six wheel. The house edge is not based on the frequency of winning hands alone, nor is it based solely on the payoffs on winning wagers. Nor is a game with frequent winners necessarily one with a low house edge, nor a game with low payoffs per win a high house-edge proposition.

From a player's perspective, it's not how often you win, nor how much that counts, it's how much how often, working together.