DND_Reborn
The High Aldwin
Because there won't always be 15 in that range; sometimes there will be more and sometimes fewer. If there are more, you're worse off on average than the case you examined, since any rolls after the 5th in that range automatically miss. If there are fewer, you're a bit better off, since the shortfall are more likely to be hits than nat 2s and 1s, but it's not a guarantee. The two cases (>= 15 and <= 15) don't balance out exactly; on average the outcomes that aren't exactly 15 are a bit worse than the outcomes that are exactly 15.
The same is true if you use your dice on 2s, but two things differ. The downside is that on rolls when you use a die, you're hitting a bit less often on average than if you held back on a 2. But the upside is that on the rolls when you don't use a die, you've removed 2 from the set of possibilities that miss, so you are hitting more often then. It turns out that the effect of the latter outweighs the effect of the former, and so you're better off spending a die if you roll a 2.
Sure, that makes sense. When you don't happen to roll 15 misses, say only 10 in the day, the five other dice can't be used for precision attack, and don't factor in at that point. On the other side, if you have more than 21 misses, say 25, then those extra 4 misses also can't benefit because all 15 have already been used. It's interesting that this only changes the outcome by a point or less. Of course, when all 15 dice aren't needed for precision attack, they will contribute to damage through other maneuvers, adding to the overall expected damage.
Anyway, it was fun.
