I'm fairly new to D&D and I wanted to run a session with some friends. I've been doing a lot of research but can't seem to find an answer to this question. I understand how the mechanic works, three successes or rolling a 20 being stabilized and the opposite being death. However what I want to know is what would be considered a success? Is this up to the DM or is there a guide? I would assume anything above 10 would be a success and anything below would be a failure but I'd like clarity.
You need to get a 10 or better to succeed on a Death Saving Throw.
From the basic rules and on PHB p. 197 (some emphasis added):
Death Saving Throws
Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving throw, to determine whether you creep closer to death or hang onto life. Unlike other saving throws, this one isn’t tied to any ability score. You are in the hands of fate now, aided only by spells and features that improve your chances of succeeding on a saving throw.
Roll a d20. If the roll is 10 or higher, you succeed. Otherwise, you fail. A success or failure has no effect by itself. On your third success, you become stable (see below). On your third failure, you die. The successes and failures don’t need to be consecutive; keep track of both until you collect three of a kind. The number of both is reset to zero when you regain any hit points or become stable.
Rolling 1 or 20. When you make a death saving throw and roll a 1 on the d20, it counts as two failures. If you roll a 20 on the d20, you regain 1 hit point.
Damage at 0 Hit Points. If you take any damage while you have 0 hit points, you suffer a death saving throw failure. If the damage is from a critical hit, you suffer two failures instead. If the damage equals or exceeds your hit point maximum, you suffer instant death.