My character leveled up and I rolled a D10 to determine the rise in hitpoints. The dice that I used goes from 0 to 9 and I rolled a zero. The DM told me that this means I only add my modifier (0 + 3 = 3).
I didn't agree with this and think it counts as 10. The 0 is probably there for cosmetic reasons.
Who is right in this situation?
This isn't clearly specified in the 5th edition rules, but is clearer in earlier editions of the game, and widely understood among long-time RPG players. However, we can still surmise from the D&D 5th edition rules that d10 is 1-10 like all other dice, from the following:
The reason for the zero is that in many games including D&D, two d10s can be rolled together to generate a two-digit percentile number between 00 and 99. As per PHB p.6, "Two 0s represent 100," another precedent which suggests that zero on the dice doesn't necessarily mean zero.
You are correct. Many old school d10s are marked 0-9 but you count the 0 as 10.
If he doesn’t listen to reason, next level use one of the d10s marked 00-90 instead and demand your 45 or so hit points from that roll.
The Player's Handbook discusses dice on p. 6, in the subsection titled "Game Dice":
In these rules, the different dice are referred to by the letter d followed by the number of sides: d4, d6, d8, d10, d12, and d20. For instance, a d6 is a six-sided die (the typical cube that many games use).
Percentile dice, or d100, work a little differently. You generate a number between 1 and 100 by rolling two different ten-sided dice numbered from 0 to 9. One die (designated before you roll) gives the tens digit, and the other gives the ones digit. If you roll a 7 and a 1, for example, the number rolled is 71. Two 0s represent 100. Some ten-sided dice are numbered in tens (00, 10, 20, and so on), making it easier to distinguish the tens digit from the ones digit. In this case, a roll of 70 and 1 is 71, and 00 and 0 is 100.
It does not actually say that a d10 generates a number between 1 and 10, but that is how it is interpreted. The zero means 10.
The Player's Handbook talks about dice referring to each dX as a die with X sides implying that the number of sides is the maximum roll through context.
There is also some circumstantial evidence in the spell confusion, which states:
An affected target ... must roll a d10 at the start of each of its turns to determine its behavior for that turn.
\begin{array} {|c|l|} \hline 1 & \text{The creature uses all its movement to move in a random direction...} \\ \hline 2-6 & \text{The creature doesn't move or take actions...} \\ \hline 3-7 & \text{The creature uses its action to make a melee attack ... randomly} \\ \hline 9-10 & \text{The creature can act and move normally.} \\ \hline \end{array}
Since there is no 0 in the table but a 10 is included, the most reasonable assumption is that a 0 is a 10.
A d6 goes from 1 to 6. A d12 goes from 1 to 12. A d10 goes from 1 to 10. That zero is the ten.
And in case your GM starts wondering...
While rarer in modern DnD, it's quite a common use of d10 to roll two at the same time to simulate a roll of d100. This is why these dice are often sold in sets with one die having "tens": 00, 10, 20 and so on, and the other having just "ones": 0, 1, 2, 3 and so on. One'd roll two dice and combine the tens and ones to get a result, eg. 80 and 7 yield an 87, with the special case of 00 and 0 typically but not universally meaning 100. Using d10's as d100 is the use where zero means a zero (except in the 00+0 case).
Even when intended for percentage rolls, the "ones" die could of course include a ten instead of a zero, at risk of being suspectible to be confused with the "tens" die (both'd have a 10), being somewhat uglier (at least to my taste) and causing a fair amount of "sixty, uh, tens" which might be jarring to those of us who aren't French. Indeed, d10s with numbers 1-10 do exist, they just don't seem to be as common.
When used as a single die, the aforementioned purpose of the 0 doesn't really exist, so a roll 0 on a d10 is a ten.
