In the other thread the issue of how to model rerolls came up and how they are beneficial for Reapers in particular. I figured I would make a separate thread to analyze it because it's interesting in itself and not just in context of spam reapers. I too thought that Reapers would gain extra benefit from rerolls.
When planning a turn in advance it's useful to know what you should save a command point for. If you should wait for a better opportunity, etc. Let's examine how much benefit you can expect from saving a command point for some reroll algorithms for bands of 1, 3 and 6 Reapers.
We assume you are firing at a T7 target with infinite wounds and 3+ armor, so 1 shot is worth 2/3*2/3*3.5 = 14/9 = approx 1.56 damage.Algorithm 1: "I will re-roll number of shots of X or lower."
Algorithm 2: "I will re-roll damage of X or lower."
Algorithm 3. "I will reroll failed to-wound rolls"
Algorithm 4. "I will reroll failed to-hit and to-wound rolls"
Putting it all together, finally:
1. By saving your reroll for reapers you can expect about 1.5 wounds if you have 1 reaper, about 2 and 1/5 if you have 3 reapers, about 3 if you have 6 reapers, and about 3 1/4 if you have 10 reapers. If you can take more wounds by not saving your reroll for reapers then you should.
2. If you have 1 to 3 reapers you should prepare to reroll failed to wound rolls. If you only have 1 reaper you should also re-roll misses. If you have more than 3 reapers you should save the command point to reroll no. of shots of 2 or less. If you have more than 7 reapers to go you should save it to reroll no. of shots of 1.
The reason why it works this way is because rerolling no. of shots is ultimately better trending towards 3.888... extra damage for rerolling no. of shots if you had infinite extra reapers, but you are less likely to be able to reroll a 1 for shots, so if you save your command point for that with few reapers you will end up with less damage. In real life where you get extra information, of course, if you roll a 1 for shots then you should re-roll after the fact, since this will yield more damage than saving it for re-rolls to wound.
Rerolling damage is the worst strategy of all tested vs T7 targets. But if you were against a T9 opponent reroll 1 for damage would actually be the best if you have many reapers, since you would divide the other strategies damage by 2.