Medicine Checks/Stabilization
Rules As Written
Described on p.197 of the Player's Handbook, when a creature is dying a creature can use its action to stabilize the creature by making a DC 10 Medicine check.
Healer's Kit, described on p.151 of the Player's Handbook, indicates that the Healer's kit has ten uses. As an action, you can expend one use to stabilize a creature without making a Medicine check.
House Rule
Healer's kits have infinite uses. Rather than auto-stabilizing, they grant advantage on the DC 10 Medicine check.
Additionally, medicine can be used to tend wounds on short rests. A creature with a healer's kit can make a DC 12 Medicine check to tend to a resting creature. That creature can maximize the first hit die it rolls to recover hit points during the rest. An additional creature can be tended for every 2 points the DC is exceeded (i.e. 2 creatures at 14, 3 at 16, and so on). Without a healer's kit, this is made at a disadvantage.

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