The minimal value allotted to a more probable horse is
-- --
| N - 0.5 N K |
| ---------- | q
| n min{q } |
| i |
-- --
where K is the number of probability coordinates less
than 1⁄n, and q is the smallest
probability greater than 1⁄n. We know
that
| 1-1/n |
K < | -------- |
| min{q } |
| i |
-- --
The minimal winning amount when a more probable horse wins, is hence
-- --
| N - 0.5 NK |
| ---------- | nq
| n min{q } |
| i |
-- --
Solve for this quantity greater than or equal to N.