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I am the DM for a level 2 Paladin. Today, he managed to pull off what the table found to be a very powerful, yet simple, combo. The two of us read over the rules and we both think it was by the book, but I'd like to be sure.

The paladin first cast Thunderous Smite as a bonus action on his longsword, then attacked an owlbear as his action. He hit, so he added 2d6 damage to his regular 1d8+STR and incurred a STR save (the results of which are tangential to this question). He then spent his second (and final) spell slot on Divine Smite to add 2d8 radiant damage. The final damage total was 3d8 + 2d6 + STR.

In a later battle, after resting up, he tried this maneuver again and rolled a natural 20 on the attack. Since crits double damage dice, his final total was 6d8 + 4d6 + STR damage.

Is this interpretation of how the Divine Smite class feature interacts with the Smite spells correct? Nobody at my table has a problem with the balance, however it was so comically strong of a single attack that we had doubts of its legitimacy.

Are we missing something here, or is this the correct amount of damage to deal for the presented situations?

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This is correct, but note how much of his available resources this character is using up for each of these attacks. If there's another battle before he gets a long rest, he's not going to be nearly as impressive.

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    \$\begingroup\$ And that, right there, is why Paladins are (potentially) the burstiest class in the game. They can hit really, really hard a few times per day. \$\endgroup\$ – guildsbounty Oct 31 '17 at 21:19
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    \$\begingroup\$ @guildsbounty Superstars in the five minute adventure day ... \$\endgroup\$ – KorvinStarmast Oct 31 '17 at 21:51
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    \$\begingroup\$ Yours is the correct answer, but you might want to link to Jeremy Crawford saying exactly what you just said: twitter.com/JeremyECrawford/status/709532732548734977 \$\endgroup\$ – J. A. Streich Nov 1 '17 at 5:00
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    \$\begingroup\$ In gam parlance, this is often referred to as "nova" or "spike" damage: something you can only keep up for a short time. \$\endgroup\$ – anaximander Nov 1 '17 at 11:31

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