There's a wonderful moment that happens when you're playing a Paladin in 5th Edition D&D: When you roll a 20 on the die for an attack roll, like anyone else, you get a critical hit.
Paladins have a key class feature (though Warlocks can get an Invocation that gives them the equivalent if they are Pact of the Blade) called Divine Smite. What this does is that when you hit with a melee weapon attack (I don't think it counts on thrown weapons or any ranged weapons,) you can expend a spell slot to make the attack do additional radiant damage. You get, effectively, 1d8 for free, 1d8 if it's undead or a fiend, and then an additional d8 for the spell slot's level (I think it caps at 5d8, or 6d8 for a Fiend or Undead, so you won't get any more out of a 5th level slot than you do for a 4th level.)
Here's what's so great about it:
Unlike the various Smite Spells, which require you to declare it before you make the attack, and if you miss, you risk losing concentration before it goes of, with the class feature Divine Smite, you get to wait to see if you've hit before you choose.
So why does a crit look so amazing when you roll one on a Paladin? Because, since the Smite is considered part of the damage of the attack, it gets doubled as well.
Let's look at a fight that we had tonight during Curse of Strahd: at level 2, while doing the intro-dungeon, Death House, we were fighting some ghouls - pretty tough monsters for a level 2 party, especially when there are multiple (I think we had 3.)
My very first smite on this character was on a crit. A Ghoul is undead, and thus I get the extra d8.
So: I hit this thing, drop a 1st level smite (I only have 1st level slots, and will until we hit level 5) while wielding my Maul.
So that's 2d6 for the weapon and 3d8 for the smite (the free d8, the bonus because it's undead, and the one for the spell slot.) But because it's a crit, I get 4d6 plus 6d8 (and, of course, my Strength bonus, which is 4).
On average, that's 14 bludgeoning damage and 27 radiant damage (I don't recall exactly how much I got, as this was a while ago) for a total of 41 (and a bit more, given that Great Weapon Fighting bumps up that average damage by a bit.) Oh, and make that 45 because of the Strength bonus.
You can smite on a regular hit, and in fact, when we fought a Vampire Spawn tonight, I did to make sure that we could prevent it from recuperating hit points (we also had a cleric doing a bit of Sacred Flame, which helped, and allowed me to conserve spell slots when it worked.) But the fact that you get to choose after the roll whether you want to smite really pours on the power of this ability - by definition, it cannot miss, and while waiting around for a crit isn't very fun if you aren't rolling them, instead you can treat a critical strike like an invitation to pour out massive damage unless you know the thing would die anyway.
Of course, the feature only scales with spell level, which means that in an adventure like Curse of Strahd, you're only going to get it maxed out right at the end. In fact, I think the main "scaling" of the spell is how many spell slots you have to work with. We've just hit level 4 in the adventure, and as such I'm still stuck at just 3 spell slots per day. At level 5, though, I'll have 4 1st level slots and 2 second levels, which means I can afford to be more liberal with smites. Having two attacks per turn also means more opportunities to crit (and also more chances to smite, as the feature requires to additional action - you can smite on any hit, be it an opportunity attack or both in a turn, or even on a bonus action attack if you're dual-wielding or a polearm master).
Paladins get a lot of useful tools (I'm really looking forward to Aura of Protection, which will cushion my -2 to Dex with my +3 to Charisma - I rolled some really good stats and one very terrible one) but Divine Smite is one that is just a delight - getting a real handful of dice to roll feels great.
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