Say I have a dice pool of 13 and an edge of 5. I know that I really want to make this next skill roll, and want to do it really well, so I think I'm probably going to use edge on the test in some way.

There are a number of ways to do this, however, so which one do I use?

- Spend Edge before the test, getting 5 extra dice and exploding 6es on all 18 dice.
- Spend edge after the roll for 5 extra dice with exploding 6es.
- Spend Edge to reroll failures.

Now the average number of successes per die using exploding 6es has been worked-out to 2/5 by Ellery here. The probability of success on a normal die is 1/3 (perhaps obvious that one), and the probability of a success on a die which is rerolled if it fails is the probability that it succeeds plus the probability that it succeeds given that the first roll was a failure, or (1/3)+(1/3)*(2/3)=5/9.

So, with an intitial pool of D and an edge of E, the expected number of successes for each of these edge expenditures are:

- 2(D+E)/5
- D/3+2E/5
- 5D/9

- 2(13+5)/5=7.2
- 13/3+10/5=6.3333333333333333333333333333333
- (5*13)/9=7.2222222222222222222222222222222

This assumes that we have made-up our mind about which system to roll already, and it's an important note that if we wait until after the roll then we have a choice of wether to add 5 exploding dice or to reroll failures. If you only failed on 4 dice, wouldn't adding 5 exploding dice ad a higher number of successes to the expected result? More on this tomorrow! Please, feel free to add your own evaluations and observations.