Sorry, you get the reasoning because I'm not doing the work until Saturday morning!
Three lists:
1) Horses that beat the greatest total number of horses
2) Horses that passed the greatest total number of horses (first call --> finish)
3) Horses that faced the greatest total number of horses
There will be some commonality in the three lists. I'm going to take the top remaining horse in each list 1,2,3,1,2,3,1,2,3 until I have 5 unique horses.
Then it's a $1 exacta box - $20.