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Closer to a football-style "squares" game could be an exacta-style grid. I'd set it up like this (to keep it manageable, and give longshot horses a fair shot by bundling them together a bit):
EACH AXIS (first place is across, second place is down):
1
2/4/5
3
6
7/8/9
10
11/13/14
12
15-21
That's 9x9 entries, then you cross off the 5 places where single numbers intersect... so for a $1 play the winner takes home $76, not bad. Or split the final group into two and it's a 10x10 grid with 5 dead spots.
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