The reliability of broadcasting over vehicular ad hoc networks (VANETs) is one of the most critical factors for driving safety applications. There exists limitations to improve the reliability of broadcast transmissions in saturated VANETs where previous proposals in literature tackle the problem by heuristically adapting the size of the contention window (CW). This paper considers improving the reliability by proposing a new probability model based on the counting methods of permutations and combinations, which counts all the possible cases of broadcast failures in a single-hop broadcast transmission for a given CW. From the model, we calculate the best CW size given the number of contention nodes, which significantly improves the reliability and satisfying the timely dissemination of emergency broadcasting messages. Through extensive VANET simulations with varying densities, we show that our model maintains near 100 percent success rate for single-hop broadcast as well as multi-hop broadcast (e.g. 40 hops) and achieves minimal broadcast delay.