@FrogReaver — I'll go into more detail on my choice of number of dice to reroll.
Level 1: You have a total of 3 dice, and can reroll 1, 2, or 3 of them. Depending on DM, you
might be able to reroll one at a time, and decide whether to keep rerolling after each one (and this is the more optimal strategy), but I'll assume you have to choose just one amount from the start.
Actually, here's a chart giving the odds of a bounce, assuming a certain number of dice are rerolled from the pool available at given spell levels:
| Spell Lvl | 0 Reroll | 1 Reroll | 2 Reroll | 3 Reroll | 4 Reroll |
|---|
| 1 | 34.38% | 50.78% | 56.04% | 56.93% | 56.93% |
| 2 | 58.98% | 74.37% | 79.81% | 81.97% | 83.18% |
| 3 | 79.49% | 89.75% | 92.99% | 94.32% | 95.07% |
| 4 | 92.31% | 97.12% | 98.32% | 98.77% | 99.00% |
| 5 | 98.08% | 99.52% | 99.76% | 99.84% | 99.88% |
| 6 | 99.76% | 99.97% | 99.99% | 99.99% | 99.99% |
For spell level 1, going from 2 to 3 rerolled dice is barely a difference. I'd say there's no point in rerolling all 3, and just use the last reroll die on the second target to boost any low damage dice.
For spell level 2, again, going above 2 reroll dice will barely matter. If you have 4 reroll dice from Cha, using 2 dice for each of the two bounces will give you better overall averages than trying to maximize the first bounce and only having 1 die for the second.
For spell level 3, we again have diminishing returns after 2 rerolled dice. You also have an 80% chance of a bounce without using reroll dice, so since you have up to 3 bounces and only 4 rerolls at level 5 (assuming 18 Cha), expect that at least one of the rolls will give you a bounce without you needing to reroll any, and save the rerolls for any failures. There's a less than 1 percent chance that all three bounce checks will fail before rerolls.
EDIT: Actually, going 2/1/1 would give you better chances of getting all 3 bounces than 2/2/0 (74.9% vs 68.7%), but obviously succeeding on a bounce without rerolling means you can save dice for later checks. For damage calculations I may change it to assume just 1 reroll per bounce, as that gives 72.3% overall (much closer to the above mixed distribution than the 80.4% than 2/2/2 would give), and doesn't require annoying changes in the spreadsheet.
For spell levels 4-6, a single reroll die puts you in the 97%-100% range for a bounce. There's no point in using more than that, and that gives you room to spread the dice among all your targets. In fact, for spell levels 5+, I wouldn't even expect to need to reroll for bounces at all, and just use them for damage.
That's also why Empowered Spell drops off in utility at higher spell levels. You're vastly more likely to lose a bounce chain due to missing the attack roll than you are to fail to get doubles in the damage.
