Snapshot at the window: Figuring out the house edge

Wednesday, Sept. 1, 2004 | 10:13 a.m.

Jeff Haney

While a great number of people care about which sports books offer the best Super Bowl futures, relatively few care about the underlying mathematics.

For the record, though, courtesy of the Wizard of Odds Web site, here is how to determine the theoretical hold percentage -- or "house edge" -- on a set of futures wagers:

1. Go down the list and convert the betting line on each team into a probability of winning expressed in percentage form. For example, if the odds on the Eagles are 6-1, the probability of winning would be 1/7 or 14.29 percent. Basically, if the odds pay x to y then the probability of winning is y/(x+y).

2. Add all of the probabilities from step 1. You'll get something like 135.4 percent, for example. Call this total "t."

3. The house edge on the future book is 1-(1/t). Sticking with the example from step 2, 1/t would be 1/135.4 percent, or 1/1.354, or .7385. And 1-.7385 is .2615. So the house edge would be 26 percent.

(Source: wizardofodds.com)

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