The rules
When a character drops to 0 hit points and isn't killed outright, they roll a death saving throw at the start of each of their turns: a plain d20, no modifier.
- 10 or higher is a success. 9 or lower is a failure.
- Three successes and the character is stable: still unconscious, but no longer dying.
- Three failures and the character dies.
- A natural 20 brings them straight back with 1 hit point.
- A natural 1 counts as two failures.
- Taking damage while at 0 hit points counts as a failure, and a critical hit counts as two.
The odds
Left alone, with nobody healing them and nothing hitting them, a dying character:
| Outcome | Chance |
|---|---|
| Rolls a natural 20 and gets back up | 18.1% |
| Stabilizes with three successes | 41.4% |
| Dies | 40.5% |
So about three times in five they live, and about two in five they don't. A healer can change that in one action: any healing brings them back up, and a DC 10 Wisdom (Medicine) check stabilizes them.