In this paper, we consider a class of wireless powered communication devices using hybrid automatic repeat request (HARQ) protocol to ensure reliable communications. In particular, we analyze the trade-off between accumulating mutual information and harvesting RF energy at the receiver of a point-to-point link over a time-varying independent and identically distributed (i.i.d.) channel. The transmitter is assumed to have a constant energy source while the receiver relies, solely, on the RF energy harvested from the received signal. At each time slot, the incoming RF signal is split between information accumulation and energy accumulation with the objective of minimizing the expected number of re-transmissions. A major finding of this work is that the optimal policy minimizing the expected number of re-transmissions utilizes the incoming RF signal to either exclusively harvest energy or to accumulate mutual information. This finding enables achieving an optimal solution in feasible time by converting a two dimensional uncountable state Markov decision process (MDP) with continuous action space into a countable state MDP with binary decision space.