Wednesday, July 16, 2014

Charting Advantage and Disadvantage in D&D 5th Edition

There are a lot of things that I really like about 5th edition, and one of those things is advantage and disadvantage. In D&D, the primary conflict resolution mechanic is the rolling of a twenty-sided die. Roll the d20, and see if you hit some target number. Modifiers to that roll (and to the target number) reflect how good you are at that task and how difficult that task is. In previous editions, that was more or less all there was - you got a modifier for being behind soft cover, lost some modifiers for being caught unaware, and so on and so forth. 5th edition changes this, by introducing advantage and disadvantage.

  • If you have advantage, roll two d20s and take the higher of the two.
  • If you have disadvantage, roll two d20s and take the lower of the two.
Many of the modifiers have been thrown out in favor of this mechanic, in part so that there's less math involved. But what does this do to the numbers?

The Numbers


First off, it's important to note that advantage is not strictly better than a numerical bonus. If your target number is really high or really low, you're probably better off with the +2 (the default modifier for anything). In almost all other circumstances though, advantage is the bigger bonus. On the other hand, disadvantage also has a much bigger impact, and if you're not doing something that's trivial or impossible, it's the equivalent of a -4 to -5 negative modifier.

I've always lamented the fact that D&D lacks probability curves, which are one of the few things that dice are really good at generating. This helps to make the odds of success and failure more realistic.

Thursday, July 3, 2014

Odds of surviving unconsciousness in D&D 5th Edition

So the new edition of D&D came out today, or at least the Basic Rules, which is more than enough to begin actually playing. When you get hit for enough damage to knock you down to 0 hp, you need to make death saving throws.
  1. If you roll a 20, you are back to 1hp
  2. If you roll a 19-10, you have one success. Three of these and you become stable.
  3. If you roll a 9-2, you have one failure. Three of these and you become dead.
  4. If you roll a 1, it counts as two failures.
There are no modifiers to these rolls at all, so it's just a matter of straightforward probability. There are a total of nine different ways to live:
  1. Roll two successes, then roll a natural 20 or a third success
  2. Roll two successes and a failure in any order, then roll a natural 20 or a third success
  3. Roll a natural 20
  4. Roll two successes and two failures in any order, then roll a natural 20 or a third success
  5. Roll a success, then roll a natural 20
  6. Roll a failure, then roll a natural 20
  7. Roll a success and a failure in any order, then roll a natural 20
  8. Roll two failures, then roll a natural 20
  9. Roll two successes and a natural 1 in any order, then roll a natural 20 or a third success
  10. Roll a success and two failures, then roll a natural 20
  11. Roll a natural 1, then roll a natural 20
  12. Roll a success and a natural 1 in any order, then roll a natural 20
You may be thinking that this order seems a bit strange, but it's actually in roughly the order of probabilities.
  1. One way to do this, 13.75%
  2. Three ways to do this, 5.5% each, for a total of 16.5%
  3. One way to do this, 5%
  4. Six ways to do this, 2.2% each, for a total of 13.2%
  5. One way to do this, 2.5%
  6. One way to do this, 2%
  7. Two ways to do this, 1% each, for a total of 2%
  8. One way to do this, 0.8%
  9. Three ways to do this, 0.69% each, for a total of 2.06%
  10. Three ways to do this, 0.4% each, for a total of 1.2%
  11. One way to do this, 0.25%
  12. Two ways to do this, 0.13% each, for a total of 0.25%
Add all of those probabilities together, and you get the probability that you will survive falling unconscious in 5th edition; 59.51%. (Note: And numbers that seem off above are because everything was rounded to the nearest hundredth of a percent for this post, but the calculations of the numbers were done in Excel.)