If you bet on the Final Four (or on almost anything), the bookie’s odds always include a built-in percentage for the house. Last year I calculated the Las Vegas Final Four edge at 9.8%.* *

This year the edge is so big (20.8%) that something must be wrong!

First a repeat of my tutorial on how the house gets its edge:

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 5.3% margin).

Coming up this week are the NCAA basketball Final Four games, on which many bets will be placed. Four teams (Butler, Duke, Michigan State, and West Virginia), are vying for the national championship. As widely reported, the odds quoted by Las Vegas Sports Consultants, a firm that reported provides lines to 90% of the Vegas sports books, are:

7-5 Duke

2-1 West Virginia

5-2 Butler

17-5 Michigan State

What do these odds mean? How did I compute the House’s take at an outrageous 20.8%?

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, and you want a $100 payout. For Duke, the favorite, you need to bet $41.67 (I’ll explain where that strange number comes from below) At 7-5 odds, if the Blue Devils win, you receive $58.33 in winnings (which is 41.67 times 7/5) plus the return of your bet, totaling $100. For West Virginia, the odds are longer, so you need to bet less…only $33.33. At 2-1, if the Mountaineers win, you’ll win $66.67…again totaling $100. On Butler, a slightly longer shot at 5-2, your bet has to be $28.57 to get back $71.43. And on Michigan State, the 17-5 long shot, you need bet only $22.73 to win $77.27. No matter who wins, you’ll end up with $100.

But what did it cost you?

You made four bets: $41.67, $33.33, $28.57, and $22.73. That totals $126.30, but you only got back $100, so the House kept $26.30, for a profit margin of 20.8%. With one-fifth of your money siphoned off, you’d be a fool to bet these Las Vegas odds.

So I tried another site. The odds at belmont.com are better…

6-5 Duke

9-5 West Virginia

3-1 Butler

13-2 Michigan State

…but not by much. Belmont’s take is a fat 16.3%.

So stay away from Vegas and online books. Try to go with one of the blogger’s odds, and make your bets privately. Ken Davis, an NBCsports columnist, touts the match-ups as:

2-1 Duke

4-1 West Virginia

9-1 Michigan State

10-1 Butler

These are ridiculously good odds! To win $100, by laying down bets on all four teams, you risk only $72.42, giving you, not the house, an edge of 38.1%! Clearly, sports expert Ken Davis is no expert on bookmaking.

For sentimental reasons, I’m picking Butler (I like the ancient brick Hinkle Fieldhouse and their home court advantage).

Who’s willing to give me Ken Davis’s 10-1?

## * * * * *

Here’s how the $41.67 bet on Duke 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 Duke odds are 7-5.

B + 7/5 * B = $100

12/5 * B = $100

B = $100 / 2.4

B = $41.67

Similarly for the other three teams.

## * * * * *

UPDATE: 4/3/10

The semi-finals are today, and Vegas has not surprisingly thinned the edge. The new odds are:

6-5 Duke

9-4 West Virginia

7-2 Butler

9-2 Michigan State

Duke has become more of a favorite, while the odds on the other three have lengthened, reducing the house’s edge to 14.3%…still high compared to Vegas table games.

I look at it this way (using the first set of odds):

Bettor D will break even if D wins 42% of the time. Bettor WV, if WV wins 33% of the time. Bettor B, if 29%. And Bettor MS, if 23%. But oops, that adds to 127%. Ain’t gonna happen. And the bookie’s take is the extra 27 of the 127, namely 21%.

I like the odds on UCLA. If you bet the Bruins, you can’t lose. (You can’t win either, but I like the Bruins)

[…] a built-in percentage for the house. In 2009 I calculated the Las Vegas Final Four edge at 9.8%; in 2010, the edge was larger (14.3%). This year the edge, if you can actually get these published odds, is […]