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comments, especially about your "fair exacta odds"

Posted By: Dunbar
Date: 15 May 02, 9:21 am

First, good work putting in the "fair odds". I continue to think it would be better if you only counted those win bets that satisfied your fair odds criterion. No one would have a legitimate gripe about handling the win bets that way if you used the closing odds as the decision-maker. But if you want to count every pick, that's fine.

I believe you are making an error in calculating fair exacta odds from your estimate of fair win odds. Look at this race:

5th 5f (turf) Alw 57200
#9 Aloha Bold ML: 5-2 fair odds: 5-2
#6 Two Punch Sonny ML: 6-1 fair odds: 4-1
#7 One by the Knows ML: 10-1 fair odds: 6-1
My Wager:
$40 exacta box #9, # 6, & #7 (exacta fair odds: 9/6-6/9= 9-1 or $20 mutuel, 9/7-7/9= 14-1 or $30 mutuel, 6/7-7/6= 23-1 or $48 mutuel)

For one thing, the fair odds for 7/9 exacta should be higher than fair odds for a 9/7 exacta.

To calculate exacta odds from win bets, you need to convert the 2nd horse's win odds into the odds that it will come in 2nd, given that the 1st horse does come in first. In Beat The Racetrack, Ziemba and Hausch used the Harville formula to calculate this. For fair odds of 5 to 2 and 6 to 1, the Harville formula would say that the 6-1 horse has this probability of coming in second, given that the 5-2 horse comes in first:(first, note that 5-2 odds are equivalent to 2/7 probability of winning, and 6-1 odds are equivalent to 1/7 probability of winning.)

(1/7)/(1-2/7) = 0.2.

Therefore, a fair exacta probability would be (2/7) * (0.2) = 5.7%. (That's the probability of the 5-2 horse coming in first times the probability of the 6-1 horse coming in 2nd.) That's 17 to 1, or a $36 mutual (compared to your $30 mutual).

Likewise, the probability of the 5-2 horse coming in second given that the 6-1 horse comes in first would be:

(2/7)/(1-1/7) = 0.33. And a fair exacta would be (1/7) * .33 = 4.8%. That's 21-1, or a $44 mutual (compared to your $30 cutoff).

I'm pretty sure that even these calculations based on the Harville formula are considered too low. I remember seeing an article by Benter that had an improved formula for calculating the odds of a horse coming in second, given that another horse had come in first. But for the purposes of your calculations, I would think that the Harville approach would be adequate.

The general formula is:

odds of horse "x" coming in second, if horse "y" comes in first:

Px/(1-Py), where Px is the win odds of horse "x", and Py is the win odds of horse "y".

I'm not trying to make your workload even greater, but I would like to understand where you are getting your fair exacta odds from. I always appreciate the clear way you present your picks and results.

--Dunbar

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comments, especially about your "fair exacta odds" -- Dunbar -- 15 May 02, 9:21 am

 


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