ask the wizard question

Went over to the wizard of odds site and checked out the ask the wizard #303. This is new or I just hadn't noticed it before but the ask the wizard column is split into subjects as well. Clicking around I found this question in the horse racing section.

Quote:

There is an online sport book that is offering a bet in which you are assigned a random horse (to win) and you receive a guaranteed payout of 15.3 for 1. There are 17 total horses listed. How would you calculate the house advantage on this bet? Does it matter what the odds are on the horses? If so, they are below. Thank you, and I apologize if this is a stupid question.

Anonymous

Assuming you had an equal chance at getting each horse then the probability of winning would be 1 in 17, regardless of how the odds on each horse were distributed. The player’s expected return can be expressed as (1/17)*15.3 + (16/17)*-1 = -0.0412. In other words the house edge is 4.12%. However there is another simple formula you can use. If a = actual odds paid and f = fair odds for bet then the house edge is (f-a)/(f+1). In this case the fair odds are 16 to 1. So the house edge is (16-15.3)/(16+1) = 0.7/17 = 4.12%.

I noticed the FOR 1 odds and the the house edge is calculated on it. It's my understanding the odds should always be calculated on a TO 1 basis. Correct?? The house edge is 10%.

deleted bad post. i made a mistake. it's not my first. won't be my last.

The anonymous respondent was correct on the major points:

Your odds of winning are 1 in 17 and the bet pays off at 15.3 to 1, so the House Edge is 10%.

The pre-race odds on any of the 17 horses in the field are not relevant to understanding this wager.