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If a creature has damage resistance, and is dealt an odd amount of damage, do you round the final damage up or down? The Player's Handbook, annoyingly, only gives the example of 20 ÷ 2 = 10. If it had been 21 ÷ 2, would that round to 10 or 11? If the creature is dealt 1, does that round to 0 or 1?

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You always round down unless told otherwise.

In the very beginning of the Player's Handbook it lays down some ground rules for everything that follows. Along with the "how dice are used" and "specific overrides general" stuff, it includes a subsection entitled "Round Down" (p. 7):

There’s one more general rule you need to know at the outset. Whenever you divide a number in the game, round down if you end up with a fraction, even if the fraction is one-half or greater.

So half of 11 damage would be 5, and half of 1 damage would be none.

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    \$\begingroup\$ Note that this is why you're directed on page 197 to apply resistance and then vulnerability to damage in that specific order. The rounding rule means they're not equivalent. \$\endgroup\$ – Bacon Bits Apr 3 '15 at 2:40
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There is some information that deviates away from this. In the Player's Handbook (PHB), it has two examples of rounding both on page 7. The first, under "Game Dice" says:

To simulate the roll of 1d3, roll a d6 and divide the number rolled by 2 (round up).

And later, under "Round Down":

There's one more general rule you need to know at the outset. Whenever you divide a number in game, round down if you end up with a fraction, even if the fraction is one-half or greater.

And sometimes, for whatever it is you are calculating, it may say either.

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    \$\begingroup\$ Welcome to RPG.SE! Take the tour if you haven't already, and check out the help center for more guidance. The first case isn't really a case of "rounding" in the same sense, in that you have to round up in that case for a roll of 1d6 to simulate 1d3; you can't roll a 0 on a die. \$\endgroup\$ – V2Blast Jun 5 at 21:09
  • \$\begingroup\$ Your first quote appears to be specifically about how to roll a d3 when the rules call for one. Round down, on the other hand, is explicitly described as a general rule that applies any time it's not explicitly overridden. \$\endgroup\$ – Oblivious Sage Jun 5 at 22:00

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