Demystifying the house edge

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

"Does a 5.26% house edge mean the house wins 52.6% 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% of rolls, the player wins 47.37%. Subtract 47.37 from 52.63 and you get the 5.26% 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% edge. Obviously, it wins more than 14.1% of the time. Instead, if you want to know the frequency of house wins, divide that 1.41% house edge in half, then add the result to 50%. The house wins 50.705% of wagers, the player wins 49.295 percent. Do the basic subtraction, and you get a difference of 1.41% — 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% 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% of the time, as we have already seen. Obviously, the house wins far more than 52.63% of single-number wagers. It wins 37 of 38, or 97.37% of wheel spins.

The reason you're bucking a house edge of 5.26% even though you lose 97.37% 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% 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.

HALL OF FAMERS: My e-mail recently brought announcements of Hall of Fame selections in both poker and video poker.

In Las Vegas, the Poker Hall of Fame will induct Duane "Dewey" Tomko and Henry Orenstein as its 36th and 37th members in a ceremony Nov. 9 in conjunction with the World Series of Poker final table even at the Rio All-Suite Hotel and Casino.

Tomko is a three-time World Series of Poker bracelet winner, two-time runner up in the no-limit Hold'em main event and record-holder with 35 consecutive World Series appearances. Orenstein is a Holocaust survivor who won the World Series seven-card stud championship in 1996 and who has cashed twice in the main event.

Meanwhile, the website VPFree has named TomSki to its online Video Poker Hall of Fame. TomSki made a big breakthrough in 1999 with his Video Poker Strategy Master software, helping players to elevate their play, and also has published studies on bankroll requirements for advantage play in various video poker games. You can view the Hall of Fame at http://members.cox.net/vpfree/HOF.htm.