#Ask your DM

Simply put, "Maximizing Damage" is not defined in the 5th Edition rules. So what it means depends on what the DM decides it means.

##"Okay, but what's a sensible definition?"

I would argue, based on how I've ruled at my tables, that the sensible definition is to simply rule that all dice rolled are treated as though they rolled their maximum values. This is the easiest way to rule, as I will demonstrate by comparing to other possible intepretations, and constitutes interpretation 1 that I cited.

The reason I like this interpretation is that it doesn't require additional thought about how effects should work. Spells like Chaos Bolt depend on the specific numbers rolled to justify their effects. Any other intepretation means the spell is being treated as though it rolled maximum values on the dice without actually rolling those numbers, and while I won't argue that method is strictly invalid, I do think it over-complicates the process and makes ruling on effects more difficult for the DM.

Now, this interpretation does make spells like Chaos Bolt stronger, as it allows them to automatically chain from target to target so long as the spellcaster can keep succeeding on their Attack Rolls (and they still have additional untargeted targets to hit). But most effects which can cause damage to be maximized are either extremely unreliable (Wild Magic Sorcerer's Wild Magic Surge, constituting a 5% x 2% == 0.1% chance of proccing on any cast spell) or have deep Opportunity Costs (Evocation Wizard's Overchannel, limited to 1 use per day or else suffer increasing Necrotic Damage).

So while there are probably some very powerful ways to exploit this behavior, I'm confident that the uses are limited and unlikely to completely break the game in normal play.

"The effect deals the maximum possible damage"

I don't like this ruling which is essentially Interpretation 2, for different reasons depending on the type of effect.

First: Attack Rolls. The only way for an effect to deal "maximum" damage is that the effect must not only hit the target; but also be a critical hit. So maximizing damage in this manner means any attack-roll-based effect automatically becomes a critical hit.

This is a tremendous increase in power, which not only increases the total damage by doubling the average to the maximum value, but also doubles it again for the critical hit damage. I don't think this is a ludicrous interpretation of the meaning of "Maximize", but the increase in power is more than I'd be comfortable supporting as a DM.

The raw damage is less of an issue for Saving Throw-based effects, given that (except in specific exceptions) these effects nearly always deal half-damage on a successful saving throw, so if we interpret "Maximizing Damage" as meaning "Always fails the saving throw", the increase in damage, while still a theoretical x4 multiplier, is still less dramatic. But if "Maximizing Damage" means always failing a saving throw, then that means the tertiary effects of the spell also always takes effect. This to me is far more objectionable.

So those two factors combined make me think this is probably a wrong interpretation, especially if we also take into consideration things like Vulnerability vs Resistance ("Is the spell really dealing maximum damage if the target is benefiting from Resistance?").

###"The Effect deals damage as though the dice rolled their maximum values; but the dice aren't meant to have rolled their maximum values"

This interpretation is a more tempered version of Interpretation 2. Attack Rolls don't automatically Crit, and Saving Throws don't automatically fail. Spells like Chaos Bolt always deal maximum damage, but it doesn't automatically chain to new targets, because the caster still needs to roll the dice, even if the dice aren't being used to determine the actual damage.

I think this interpretation is probably the easiest to balance around, and if keeping the game balanced is your principal concern, I think this interpretation is probably better. But the reason I don't like it is because it breaks the contracts of how certain effects work, and requires a lot of extra effort by the DM (and the players, for that matter).

For example: Chaos Bolt can never deal 3 Thunder Damage, no matter what the caster rolls. It can also never deal 22 Acid Damage, no matter what the caster rolls. In fact, the only time the spell can deal 22 Damage is if it is dealing Thunder damage; and the only time it can deal 3 Damage is when it is dealing Acid damage. These are constants set by the spell, which uses the 2d8 damage dice to determine damage type.

But if we use this interpretation of what "Maximizing Damage" means, then it suddenly becomes valid for a Chaos Bolt to deal 22 Acid damage, or 22 Fire damage. That's actually kind of cool—but it also means that in maximizing the damage, we've invalidated one of the invariants of the spell, which is that Acid Damage tends to be weakest; Thunder Damage tends to be the strongest. That's a strange outcome of simply "Maximizing Damage", and as a result, I don't think it is a correct way to interpret how "Maximizing Damage" works.

As I said before, the rules for "Maximizing Damage" are not written in the 5e rules, so we need to come up with our own. I've submitted here which interpretation I use at my table, and why I don't use the other interpretations, but I can't say those other interpretations are strictly invalid, and I think other people could probably make a good case for why they might prefer those other interpretations instead.