You pays your money and you takes your chances, but the House always has an edge.
Did you ever wonder how big that edge is?
Among the simplest edges to compute is Las Vegas roulette. If your chips are on one of the numbers from 1 to 36, and you win, you get paid 35-1. That means that if you put $1 on each of those 36 numbers, when the ball drops onto one of those numbers, you’ll get your winning bet back plus $35; you’ll break even. Those are fair odds. But the House, as I said, always has an edge. Las Vegas wheels include two other numbers that also pay 35-1: 0 and 00. So to be sure you’ll win, you’d have to place 38 one-dollar bets, thus giving the House a $2 profit on every $38 you bet (a 5.26% margin).
It’s World Series time, typically a big gambling focus. I’m one game late—the Toronto Blue Jays already walloped the Texas Rangers last night in the first game of their American League Division Series—so I’m going to pretend that didn’t happen and use the odds that were in place prior to last night.
As of yesterday, the Vegas odds (Sportsline) were:
Chicago Cubs 9/5
Boston Red Sox 9/2
Texas Rangers 5/1
Los Angeles Dodgers 7/1
Toronto Blue Jays 8/1
Washington Nationals 8/1
Cleveland Indians 12/1
San Francisco Giants 12/1
What do these odds mean? How big is the oddsmaker’s edge? Here’s the math. (Stay with me. No glazed eyes! It’s really easy.)
First, what does the 9/5 for Chicago mean? Simple. For every $5 you bet, you get $9 back…plus your original $5. If you bet $100, and Chicago wins the Series, your $100 comes back with an additional $180. You started with $100; now you have $280. Simple.
Assume you bet on all eight teams to win the World Series. One of them will definitely triumph, so you’re sure of a payout. You bet $35.71 (I’ll explain where that strange number comes from below) on the Cubbies. At 9/5 odds, if Chicago wins, you receive $64.29 plus the return of your bet, totaling $100. On Boston, you bet $18.18. At 9/2, if the Red Sox win, you’ll get $81.82…again totaling $100. And so on down the list until you get to the Giants and the Indians. At 12/1, you you need bet only $7.69 to win $92.31. If you bet all eight teams this way, no matter who wins, you’ll end up with $100.
But what did it cost you?
You made eight bets: $35.71, $18.18, $16.67, $12.50, $11.11, $11.11, $7.69, and $7.69. Your total outlay was $120.67…and even though you win, you get just $100.00. The House keeps $20.67, for a profit margin of 17.1%. It’s a nice business.
I’m a Giants fan. But instead of placing a bet, I’m sending 17.1% of what I would have wagered to charity.
* * * * *
Here’s how the $35.71 bet on the Cubs is computed:
Let B be your bet and L be the line (the odds). If your team wins, you’re going to get your bet returned PLUS your winnings, so B + L*B = $100. The Cubs’ odds are 9/5 or 1.8
B + 1.8*B = $100
2.8*B = $100
B = $100/2.8
B = $35.71
Similarly for the other seven teams.