"Running Clock" Death-Saving Throws (5e Variant Rule)
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"Running Clock" Death-Saving Throws
When you roll a death-saving throw, traditionally, a 10 or up means you live while anything under is a strike against you. Get three strikes and your character dies. However, a "Running Clock" Death saving throw provides more chances at the Death Saving Throw with a catch.
When your character is knocked unconscious they must roll a d20, but rather than 10 being the determining value, it starts at 4. This aspect is like a traditional death-saving throw, (if you roll higher than the value three times, you come back to life, miss it three times and you die). However, where it differs is each failure adds to the starting save value for a maximum of 16.
So if this is your character's first death-saving roll and you fail twice, then the next time you are knocked down, your save value becomes 6. Let's now say they go unconscious again and fail once, then the new value is 7.
If a party member tries a medicine roll and passes, then you stabilize (like normal) but your saving value decreases. So if the number you need to get above is 7 and a party member succeeds in a roll, then the next time you go unconscious, it will be a six. On the other hand, a failed medicine roll will is treated like failing a death-saving role.
All in all what it gives players is a sense of frailty and realism in their characters. You can survive indefinitely, but as the save value increases, it will become harder and harder to get back up.