Higher or lower on a d100 paid the second value

A fair die with faces $1$ to $100$ is rolled and you see the result $x$. You then predict whether a second roll $y$ will be at least $x$ ("higher") or strictly below $x$ ("lower"). If your prediction is right you are paid $y$ dollars, otherwise nothing. Playing to maximise expected payout, what is the smallest first roll $x$ for which you should predict "lower"?

$72$. Predicting lower pays $\tfrac{1}{100}\sum_{y<x}y=\tfrac{x(x-1)}{200}$ on average, while predicting higher pays $\tfrac{1}{100}\sum_{y\ge x}y=\tfrac{(100+x)(101-x)}{200}$. Lower wins when $x(x-1)>(100+x)(101-x)$, which first happens at $x=72$ (the crossover is near $71.6$): at $71$, $4970<5130$, while at $72$, $5112>4988$.