Resolving a conjecture of Füredi from 1988, we prove that with high probability, the random graph
G
(
n
,
1
/
2
)
\mathbb {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
)
n-o(n)
vertices have more neighbours in their own part as across. Our proof is constructive, and in the process, we develop 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.