  We provide a relatively simple proof that the expected gap between the
maximum load and the average load in the two choice process is bounded by
$(1+o(1))\log \log n$, irrespective of the number of balls thrown. The theorem
was first proven by Berenbrink et al. Their proof uses heavy machinery from
Markov-Chain theory and some of the calculations are done using computers. In
this manuscript we provide a significantly simpler proof that is not aided by
computers and is self contained. The simplification comes at a cost of weaker
bounds on the low order terms and a weaker tail bound for the probability of
deviating from the expectation.
