The math in Shadowrun has historically been fairly simple. How many dice do you need to roll to have a 50/50 shot at rolling that 17 you need to jump from roof to roof? Am I better off buying up an attribute or my pistols skill? The fourth edition of Shadowrun introduces hits, which makes that math easier, especially if you decide to just buy hits. The new edge system however provides some interest. The basic question is: should I use edge before or after I roll my dice pool? This question has no mathematical answer, but some related questions do. If I have a dice pool of 10, an edge of 4, and want to get as many hits as possible, should I add edge before or after? (Answer: after) What are my chances of needing to add edge if I'm rolling 15 dice and need 7 hits to dodge that assault cannon? I investigate these and other questions below.

For this quick write-up, I'm going to ignore the case where you add edge before rolling, reroll sixes, and get yet more sixes. This makes the logic easier to follow, and doesn't significantly alter the probabilities since that term is so small relative to the others. Once you make this simplification, you can easily answer the question: if you want as many hits as possible, should you add edge before or after rolling? Clearly the answer will depend on how many dice you're rolling before adding edge (the more dice you roll, the more failures you're likely to get, and therefore the more dice you'll be able to re-roll by adding edge later), as well as what your edge attribute is (higher edge is more useful to add before rolling your skill pool). The basic situation is simply rolling your skill pool. The question then is whether you should add your edge after that, which will let you reroll approximately 2/3 of those dice, or whether you should add your edge before, which will give you your edge attribute in extra dice, plus approximately 1/6 of the total number of dice as rerolled sixes.

For a given edge attribute, if you are rolling a small dice pool you should add edge before rolling; if you are rolling a large dice pool, add edge after. The table below lists, for each edge attribute value, whether edge should be added first or used later to reroll failures, with the goal of maximizing the number of hits. In cases where there is an overlap (eg, 0-7 dice, and 7 or more), there is actually a slight statistical advantage to adding edge first, since an exploding 6 may roll another 6.

Note that, the closer your dice pool size is to the dividing line between the two columns, the smaller the advantage to using the "correct" strategy. At some point, other considerations may weigh in. In particular, if you only need a fixed number of hits (such as for a dodge test), with no advantage to getting more than the required number, it may make sense to elect to add Edge after rolling, hoping for a lucky first roll. Then if you roll well, you can save the Edge point. The slight additional risk may be worth the chance to save that Edge point for later.