# Steve Cotler

## Final Four Math — 2011

This year’s March Madness has brought us a Final Four with no #1 or #2 seeds, unique in NCAA tournament history. But the absence of high-seed teams has not dulled enthusiasm for the last three games. In fact, some sports pundits are trumpeting the “Cinderella” factor: can a #11 seed, Virginia Commonwealth University, pull off the all-time, unexpected upset?

But no matter who matter who wins the game, the bookies win their money. The bookie’s odds always include 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 unbelievably small…only 2.2%!

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

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).

This weekend’s Final Four games pit Connecticut, Butler, Kentucky, and VCU. The odds quoted by Cantor Gaming, which runs four sports books in Las Vegas, are:

+160 (8-5)   Kentucky
+220 (11-5)  Connecticut
+400 (4-1)   Butler
+700 (7-1)  VCU

What do these odds mean? How did I compute the House’s take at a skimpy 2.2%?

The math is 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 Kentucky, the favorite at 8-5, you need to bet \$38.46 (I’ll explain where that strange number comes from below) If Kentucky wins, you receive \$61.54 in winnings (which is 38.46 times 8/5) plus the return of your bet, totaling \$100. For Connecticut, the odds are longer, so you need to bet less…only \$31.25. At 11-5, if the Huskies win, you’ll win \$68.75…again totaling \$100. On Butler, a longer shot at 4-1, your bet has to be \$20.00 to get back \$80.00. And on VCU, the 7-1 long shot, you need bet only \$12.50 to win \$87.50. No matter who wins, you’ll end up with \$100.

But what did it cost you?

You made four bets: \$38.46, \$31.25, \$20.00, and \$12.50. That totals \$102.21, but you only got back \$100, so the House kept \$2.21, for a profit margin of 2.2%. Something’s wrong, Las Vegas never lets you get in with such thin overhead.

So I tried another site. The odds at vegasinsider.com are what you’d expect…

+150 (3-2)   Kentucky
+200 (2-1)  Connecticut
+300 (3-1)   Butler
+400 (4-1)  VCU

Vegas Insider’s take is a fat 15.5%.

Covers.com is even greedier. They skim 16.9% with their odds set at:

+115 (23-20)   Kentucky
+200 (2-1)        Connecticut
+330 (33-10)   Butler
+480 (24-5)     VCU

Moral of this story: The horses may be the same, but the tracks compute differently.

## *     *     *     *     *

Here’s how the \$38.46 bet on Kentucky 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 kentucky odds are 8-5.

B + 8/5 * B = \$100
13/5 * B = \$100
B = \$100 / 2.6
B = \$38.46

Similarly for the other three teams.

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