## Likelihood of "hitting" 1 when subtracting random numbers from a positive number?

I play Dungeons and Dragons. In the game, a monster has a given starting number of "hit points" which can be from 1 to almost any number. Damage is done to the monster, and varying numbers of damage dice (1-4, 1-6, 1-8, etc) are rolled and subtracted from the monster's hit points. When the monster's hit points are at 0 or below it is considered out of the fight.

My question is, is there an increased likelihood for monsters to have 1 hit point remaining over other positive numbers prior to crossing the threshold of 0?

My thinking: the goal is to cross that threshold to 0. People don't stop at 10, of course, that'd be silly (the monster is still alive). They don't continue doing damage below 1 in most cases, either (the monster is already dead/disabled). So you have a problem where you start with a number (any number) and then randomly subtract various amounts until you get to 0 or below.

So I'm thinking that since the goal is to cross the threshold of 1 to 0 and below, that it'd be mathematically likely to hit 1 more often than most other numbers (with 2 somewhat likely-because you could still do 1 damage-, 3 slightly less-because you could do 1 or 2 damage-, and then tapering off as the numbers get higher.)

To complicate things further, numbers are added to the dice as well. A die roll could be 1 to 4 plus 1 (2 to 5). I'd hazard that the use of addition in this example case would make 1 and 2 equally likely, but more probable than 3 and 4, which would be more probable than 5 and 6 and so on.

Thank you in advance for any help!