[JaredL]

Firstly, we can normalize the size of the ante to 1 since the only thing that matters is the ratio of bet size to ante size.

The first thing that we need to do is find a cutoff. This cutoff is the highest point where the EV(bet) = EV(fold). At this cutoff, we will get no value from others also betting with a worse hand (think of it like value betting), because it's the smallest hand that anyone will bet.

At this point, which I'll call z, the EV of betting assuming that others will bet if and only if their hand is better than z is:
n*z^(n-1) - y(1-z^(n-1))

The EV of folding is:
1*z^(n-1)

Setting them equal gives:
z = ((y+n-1)/y)^(1/(1-n))
or z = (y/(y+n-1))^(1/(n-1))

Again, my y here is different from your y, since my y is the ratio of bet size to ante size.