Let $f(z)=\sum_{0\leq k\leq n} \epsilon_k z^k$ be a random polynomial, where $\epsilon_k\in \{0,1\}$ independently uniformly at random for $0\leq k\leq n$.
Is it true that the number of real roots of $f(z)$ is, almost surely,
\[\left(\frac{\pi}{2}+o(1)\right)\log n?\]
Erdős and Offord [EO56] showed that the number of real roots of a random degree $n$ polynomial with $\pm 1$ coefficients is $(\frac{2}{\pi}+o(1))\log n$.