In a fit of OCD, I decided to work out the probabilities of the 3 possible outcomes for death saves resulting from dropping to zero hit points. I used a spreadsheet to work out the numbers after trying unsuccessfully to work it out by hand. Feel free to check my numbers, but the spreadsheet tells me that all the probabilities add up to 1.0, so I think this is accurate. I’m assuming that once the unfortunate PC drops to zero, no additional damage is taken and fate is allowed to take its course.
The outcome will be determined in a maximum of five rolls with the following cumulative probabilities of being resolved:
First roll – 5%,
Second roll – 14%,
Third roll – 42.25%,
Fourth roll – 76%,
Fifth roll – 100%
The (approximate) results are:
3 failures (ie death) – 40.5%
3 successes (ie stabilized) – 41.4%
Rolled a 20 (gain 1 hp) – 18.1%
So, I suppose if you wanted to compress the rolling sequence to save time, and preserve the probabilities of the original rule, you could roll percentile dice against the following table:
That's an interesting way to think of it for situations where the suspense & timing don't matter as much. I think I'll use it for NPC situations.
Side note, I think there is a math error. The difference in resolution between 1 round and 2 seems too high. 1 Round = 5%, 2 Round should be about the same, 95% chance (not resolved in 1st round) there is a 5% chance.
You are neglecting that you can get three or four fails by the end of the second round if a natural one is rolled along with another failure ( nat 1 = 2 fails)
Ok, I ran the numbers for adding bonuses to the death saving throws with the same bonus applied to all rolls. I’ve also kept in the results for natural ones and natural twenties as well (2 saves lost and gain one hp respectively). The approximate results are below:
In a fit of OCD, I decided to work out the probabilities of the 3 possible outcomes for death saves resulting from dropping to zero hit points. I used a spreadsheet to work out the numbers after trying unsuccessfully to work it out by hand. Feel free to check my numbers, but the spreadsheet tells me that all the probabilities add up to 1.0, so I think this is accurate. I’m assuming that once the unfortunate PC drops to zero, no additional damage is taken and fate is allowed to take its course.
The outcome will be determined in a maximum of five rolls with the following cumulative probabilities of being resolved:
First roll – 5%,
Second roll – 14%,
Third roll – 42.25%,
Fourth roll – 76%,
Fifth roll – 100%
The (approximate) results are:
3 failures (ie death) – 40.5%
3 successes (ie stabilized) – 41.4%
Rolled a 20 (gain 1 hp) – 18.1%
So, I suppose if you wanted to compress the rolling sequence to save time, and preserve the probabilities of the original rule, you could roll percentile dice against the following table:
01-41 – death
04-82 – stabilized
83-00 – 1hp
Nice :) But don't be too hasty to go the quick route with percentile dice. Don't forget that Death Saves are actually saving throws.
A Paladin's Aura of Protection helps you with them.
A Monk gets proficiency to them (and can reroll them with a ki point) with Diamond Soul.
Bless helps with them.
etc etc.
...even a Ring of Protection or a Cloak of Protection helps skew the probabilities in your favor.
That's an interesting way to think of it for situations where the suspense & timing don't matter as much. I think I'll use it for NPC situations.
Side note, I think there is a math error. The difference in resolution between 1 round and 2 seems too high. 1 Round = 5%, 2 Round should be about the same, 95% chance (not resolved in 1st round) there is a 5% chance.
Did I mention that it was an OCD attack? Now I have to rework the spreadsheet to account for +1, +2, bonuses to the roll...thanks! ;)
You are neglecting that you can get three or four fails by the end of the second round if a natural one is rolled along with another failure ( nat 1 = 2 fails)
btw, here's the confirmation that you can indeed gain bonuses to the Death Saving throw.
https://twitter.com/jeremyecrawford/status/728656344224432128?lang=en
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Yes! I did totally forget that inconvenience. Thanks
Ok, I ran the numbers for adding bonuses to the death saving throws with the same bonus applied to all rolls. I’ve also kept in the results for natural ones and natural twenties as well (2 saves lost and gain one hp respectively). The approximate results are below:
+1 bonus: 3 failures – 33%, 3 successes – 49% ,1 hp – 18%
+2 bonus: 3 failures – 26%, 3 successes – 56%, 1 hp – 18%
+3 bonus: 3 failures – 20%, 3 successes – 63%, 1 hp – 17%
+4 bonus: 3 failures – 15% , 3 successes – 68%, 1 hp – 17%
+5 bonus: 3 failures – 10%, 3 successes – 73%, 1 hp – 17%
Check here
Yup...agreed. Any differences are due to rounding error.