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).
Coming up this week are the NCAA basketball Final Four games, typically a big gambling focus. Four teams (Connecticut, Michigan State, North Carolina, and Villanova) are vying for the national championship. The odds at the Las Vegas Hilton’s race and sports book (as reported yesterday by the Associated Press) are:
5-1 Michigan State
5-6 North Carolina
What do these odds mean? How big is the Hilton’s edge?
Here’s the math. (Stay with me. No glazed eyes! It’s really easy,)
Assume you bet on all four teams to win the national championship. One of them will definitely triumph, so you’re sure of a payout. You bet $28.57 (I’ll explain where that strange number comes from below) on Connecticut. At 5-2 odds, if UConn wins, you receive $71.43 plus the return of your bet, totaling $100. On Michigan State, you bet $16.67. At 5-1, if the Spartans win, you’ll get $83.33…again totaling $100. On North Carolina, at 5-6, the odds-on favorite, your bet has to be $54.55 to get back $45.45. And on Villanova, the 8-1 long shot, you need bet only $11.11 to win $88.89. No matter who wins, you’ll end up with $100.
But what did it cost you?
You made four bets: $28.57, $16.67, $54.55, and $11.11, totaling $110.90, so for every $110.90 you bet, the House keeps $10.90, for a profit margin of 9.83%. It’s a nice business.
Like President Obama, I’m picking North Carolina. But instead of placing a bet, I’m sending 9.83% of what I would have wagered to charity.
* * * * *
Here’s how the $28.57 bet on UConn 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 UConn odds are 5-2.
B + 5/2 * B = $100
7/2 * B = $100
B = $100 / 3.5
B = $28.57
Similarly for the other three teams.