Go to Part 3
In the previous parts I suggested two new rules to make 0 hit points a bit more dangerous and dynamic in 5e. For those of you who find they add too much complexity, here's one more suggestion for getting back the urgency of a dying PC. This simple rule should stop the party from coldly calculating (metagaming) how long they can dawdle before they have to heal a fallen foe.
Simply hide the information of how many death save successes and failures a character has from the players! You could do this by having the DM roll death saves behind the screen, and revealing the result when the body is checked/healed. But I think there is another much better way that not only adds more tension, but negates even the possibility of the DM being tempted to fudge the roll: just-in-time compilation. In other words, the rolls are not made until such time that their result becomes relevant. Schrödinger's dead PC, essentially.
Variant rule for 5e: Just-in-time death savesWhenever a character would be called to make a death saving throw, they instead mark a '?' on their character sheet. When the character's body receives magical healing, stabilization is attempted, or the body examined or otherwise interacted with, the player rolls a death saving throw for each '?'. The rolls are made sequentially one at a time, and if they result in the player being stabilized or dying, the rolling is interrupted and all remaining '?' marks erased.
Optional: If you wish to increase the feeling of "discovering what was previously determined", replace the rolls with a standard card deck. Instead of rolling death saves, the player draws a face-down card from a deck. When the body is interacted with, the cards are turned face-up, in order of drawing. A black card is a death save failure, and a red card is a success. With this variant, you can either disregard critical failures/successes, or signify them with black aces/red aces (3.8% chance of each instead of 5%), or the face cards of spades/hearts (5.8% chance of each instead of 5%). Or perhaps you think clubs are more appropriate to signify death than spades, for their crosslike shape - decide for yourself!