  Resolving a conjecture of F\"uredi from 1988, we prove that with high
probability, the random graph $G(n,1/2)$ admits a friendly bisection of its
vertex set, i.e., a partition of its vertex set into two parts whose sizes
differ by at most one in which $n-o(n)$ vertices have at least as many
neighbours in their own part as across. The engine of our proof is a new method
to study stochastic processes driven by degree information in random graphs;
this involves combining enumeration techniques with an abstract second moment
argument.
