Quote:
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Originally Posted by SentToStud
I have a proposition bet going with a friend.
I need EITHER Curlin OR Hard Spun NOT to run 1-2-3.
He needs them both to run in the top 3.
What do you think the right price for this is?
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The answer obviously depends on how you see Curlin and Hard Spun's chances relative to the rest of the field. I think even money for your bet is about right, so you got the worst of it IMO.
To get a feel for the answer, I made some simplifying assumptions.
1. Curlin and Hard Spun together have a 62% chance to win the race. (that's what I come up with in my line)
2. They are interchangeable (I know that sounds like a horrible assumption, but as long as you don't think Hard Spun is WAY out of it, I don't think it prevents us from getting a ballpark-type answer.)
3. If Curlin doesn't win, then the chance that he comes in 2nd is the chance that he would have won a race without the horse that came in first. (Harville formula). Same holds for Hard Spun.
If Curlin or Hard Spun finishing in the top 3 is "Y", and finishing off the board is "N", then your friend can win in these 3 ways.
YYN
YNY
NYY
Chance of (YYN) = 62% * 43% = 27% (where "43%" is the chance that Curlin would win a race without HardSpun, and vice versa)
Chance of (YNY) = 62% * (1-43%) * 46% = 16% (where "46%" is the chance that Curlin would win a race without HardSpun and without another horse--I chose a 20-1 longshot for the "other horse", because that gives a more conservative fig.
Chance of (NYY) = (1-62%) * 66% * 46% = 11% (where "66%" is the chance that either Curlin or HardSpun would win a race without the 20-1 shot in there, and the "46%" is same as for YNY.)
Adding those up, I get 54% as a rough estimate of the chance of both Hard Spun and Curlin being on the board. This is very dependent on my first assumption, that the 2 horses have a combined 62% chance to win the race.
If you think there's a huge diff between Curlin's and Hard Spun's chances to win, AND you don't think one or the other even deserve to be favored over the rest of the field, then my 2nd assumption above is a poor one.
My 3rd assumption would be a poor assumption if you think one or both of these horses will either win the race or fall apart completely. I happen to think these 2 will stay on even if they don't win.
--Dunbar