Choosing a number when the larger pays the smaller

Alice's number $Y$ is uniform on the integers $1,\dots,100$. Bob, not knowing $Y$, chooses an integer $x$ in the same range. If the numbers differ, the holder of the larger one pays the holder of the smaller one an amount equal to the smaller number; equal numbers mean no payment. With Bob choosing optimally, what is his expected gain?

$16.83$. If $Y<x$ Bob pays $Y$, averaging $\tfrac x2$; if $Y>x$ he receives $x$. So his expected gain is $\tfrac{x-1}{100}\big(-\tfrac x2\big)+\tfrac{100-x}{100}x=\tfrac{201x-3x^2}{200}$, a parabola peaking at $x=33.5$. Both $x=33$ and $x=34$ give $\tfrac{3366}{200}=16.83$.