In this paper, we aim to identify the strategies that can maximize and monotonically increase the density of the coding opportunities in instantly decodable network coding (IDNC).Using the well-known graph representation of IDNC, first derive an expression for the exact evolution of the edge set size after the transmission of any arbitrary coded packet. From the derived expressions, we show that sending commonly wanted packets for all the receivers can maximize the number of coding opportunities. Since guaranteeing such property in IDNC is usually impossible, this strategy does not guarantee the achievement of our target. Consequently, we further investigate the problem by deriving the expectation of the edge set size evolution after ignoring the identities of the packets requested by the different receivers and considering only their numbers. We then employ this expected expression to show that serving the maximum number of receivers having the largest numbers of missing packets and erasure probabilities tends to both maximize and monotonically increase the expected density of coding opportunities. Simulation results justify our theoretical findings. Finally, we validate the importance of our work through two case studies showing that our identified strategy outperforms the step-by-step service maximization solution in optimizing both the IDNC completion delay and receiver goodput.