The $p$-th guest receives a share of $s_{p,N}=p N^{-p-1} (N-p+1) (N-p+2)_{p-1}$, where $(a)_b$ is the Pochhammer symbol. For large $N$ this approximates to 
$$s_{p,N}=\frac{p}{N}+\frac{p^2-p^3}{2 N^2}+{\cal O}(1/N)^3$$
which equals the fair share $1/N$ for $p=\sqrt{2N}$. So I would estimate the number of fortunate guests as $\sqrt{2N}$ for large $N$.