What is the crit chance with advantage versus disadvantage? What is the crit chance when you crit on a 19 or 20? How about 18 to 20? 17 to 20?
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D&D 5E Advantage vs Disadvantage : What's the Math?
- Thread starter Ashabel
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clearstream
(He, Him)
I think of advantage as halving my chance of failing.
Disadvantage doubles my chance of failing.
Disadvantage doubles my chance of failing.
CapnZapp
Legend
There is, I think, an easier way to explain advantage.
In the middle, when you need to roll 11 or more to succeed, that's 50% chance.
Since advantage gives you two shots of making the roll, and you only need to roll 11+ once, the total probability is 75%. In layman's terms, the second roll is only relevant if the first one fails, so the second roll's success rate (50%) is halved by the fact that the first roll is only a failure half the time, and 50% + 25% = 75%.
An increase by 25% is what we gamers would express as a +5 bonus on a d20.
Mathematically, of course, you take the probability of each roll failing, multiply them together (since they are independent) to get the chance of not succeeding; to find out the chance of actually succeeding you subtract that number from 1 (100%). In our example this becomes 1-(0,5x0,5)=0,75.
Now let's investigate the extremes. When you need only to roll a 2, that's 95% chance. This time advantage gives you much less of a benefit, because if you roll 2 or better, you've succeeded already, and you gain nothing from advantage. This is the reason advantage can't be pinned down to a single number, and this is the insight you need - no actual math needed.
But let's investigate anyway: while the success rate supplied by advantage is 95%, it only applies 5% of the time (the first roll's failure rate). So we reduce the first number by the second (i.e. we multiply them) to get 0,95x0,05. Before we even whip out our calculators, you should see this will be a number close to 0,05, since we are close to calculating 1x0,05. 0,05 is 5% which is equivalent to a +1 bonus. (The real result is 4,75%)
Mathematically, advantage increases our success rate from 0,95 to 1-(0,05x0,05)=0,9975. The increase is 0,0475 which is the 4,75% number above which we'll round up to 5% because that's +1 on a d20
So already we've concluded that advantage can both mean a +5 bonus and a +1 bonus, depending on whether we're right in the middle of the probability curve, or at either end of it.
If you have a +5 attack bonus, and the monster has AC 16, advantage means a whopping +5.
But if the monster has AC 7 (or indeed AC 25), advantage means only +1.
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Now, while you're "only" getting a +1 on your AC 7 attack, don't forget that you almost don't need it, since after all, you will succeed 19 times out of 20 anyway, even without advantage.
Saying this because it's not just so simple as "advantage is sometimes close to worthless". After all, it's only "worthless" when you either don't need it, or when you're hopelessly behind.
Instead I'd say advantage helps those exposed to pure luck and chance the most. It is when your d20 roll could be reduced to a coin toss advantage carries the most impact.
Advantage is truly a wonderful mechanism
It is far better than statical bonuses, because it levels out the playing field.
Yes, it also leaves the have-nots in the dust, but when has a hero ever had that problem?
The much more common scenario in previous editions was when your hero had a very high chance, and a static +5 would only obliterate any remaining chance at drama or tension, since it would turn a highly likely roll into a statistical certainty.
With a static +5 bonus you can no longer fail at hitting AC 7 (in the example above).
With advantage, you can still roll two ones in a row and thus you can still fail.
Not coincidentally, the chance of that happening is 1 out of 400. Which is, you guessed it, exactly the "missing" 0,25%. The success rate only went up to 0,9975, remember.
This means that advantage is an important part of the entire bounded accuracy concept of 5E.
In the middle, when you need to roll 11 or more to succeed, that's 50% chance.
Since advantage gives you two shots of making the roll, and you only need to roll 11+ once, the total probability is 75%. In layman's terms, the second roll is only relevant if the first one fails, so the second roll's success rate (50%) is halved by the fact that the first roll is only a failure half the time, and 50% + 25% = 75%.
An increase by 25% is what we gamers would express as a +5 bonus on a d20.
Mathematically, of course, you take the probability of each roll failing, multiply them together (since they are independent) to get the chance of not succeeding; to find out the chance of actually succeeding you subtract that number from 1 (100%). In our example this becomes 1-(0,5x0,5)=0,75.
Now let's investigate the extremes. When you need only to roll a 2, that's 95% chance. This time advantage gives you much less of a benefit, because if you roll 2 or better, you've succeeded already, and you gain nothing from advantage. This is the reason advantage can't be pinned down to a single number, and this is the insight you need - no actual math needed.
But let's investigate anyway: while the success rate supplied by advantage is 95%, it only applies 5% of the time (the first roll's failure rate). So we reduce the first number by the second (i.e. we multiply them) to get 0,95x0,05. Before we even whip out our calculators, you should see this will be a number close to 0,05, since we are close to calculating 1x0,05. 0,05 is 5% which is equivalent to a +1 bonus. (The real result is 4,75%)
Mathematically, advantage increases our success rate from 0,95 to 1-(0,05x0,05)=0,9975. The increase is 0,0475 which is the 4,75% number above which we'll round up to 5% because that's +1 on a d20
So already we've concluded that advantage can both mean a +5 bonus and a +1 bonus, depending on whether we're right in the middle of the probability curve, or at either end of it.
If you have a +5 attack bonus, and the monster has AC 16, advantage means a whopping +5.
But if the monster has AC 7 (or indeed AC 25), advantage means only +1.
---
Now, while you're "only" getting a +1 on your AC 7 attack, don't forget that you almost don't need it, since after all, you will succeed 19 times out of 20 anyway, even without advantage.
Saying this because it's not just so simple as "advantage is sometimes close to worthless". After all, it's only "worthless" when you either don't need it, or when you're hopelessly behind.
Instead I'd say advantage helps those exposed to pure luck and chance the most. It is when your d20 roll could be reduced to a coin toss advantage carries the most impact.
Advantage is truly a wonderful mechanism
It is far better than statical bonuses, because it levels out the playing field.
Yes, it also leaves the have-nots in the dust, but when has a hero ever had that problem?
The much more common scenario in previous editions was when your hero had a very high chance, and a static +5 would only obliterate any remaining chance at drama or tension, since it would turn a highly likely roll into a statistical certainty.
With a static +5 bonus you can no longer fail at hitting AC 7 (in the example above).
With advantage, you can still roll two ones in a row and thus you can still fail.
Not coincidentally, the chance of that happening is 1 out of 400. Which is, you guessed it, exactly the "missing" 0,25%. The success rate only went up to 0,9975, remember.
This means that advantage is an important part of the entire bounded accuracy concept of 5E.
clearstream
(He, Him)
One can go into the maths, but I think it helps to have a way of thinking about it that captures the sense. I feel like you can do that by picturing the second roll as contingent on the first. So you get two chances to succeed (or fail).
That captures the curve quite well.
That captures the curve quite well.
Sorcerers Apprentice
Hero
I want to mention that due to bounded accuracy, ACs/DCs tend to cluster around the middle of the 1-20 range, which is where the difference between advantage and disadvantage is the greatest.
clearstream
(He, Him)
Just to have fun with the concept we can also refute that. Rolling a d20 creates 20 possible universes of which at 11+ half (50%) contain failures. Rolling two d20s creates 400 possible universes of which at 11+ one hundred (25%) contain failures. At 2+ rolling a d20 only one of twenty possible universes contains a failure (5%); whereas rolling two d20s only one of 400 possible universes contains a failure (0.25%).
25% goes twice into 50% whereas 0.25% goes twenty times into 5%. So measured in possible universes containing failures out of possible universes the magnitude of the improvement is greatest at high, not medium, chances of success.
Looking at universes containing failures the jump from 1/20 to 1/400 is bigger than that from 10/20 to 100/400.
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Of course at my table the players never remember that they have advantage and so they almost always end up rolling twice in succession rather than two d20s at once. So the second case rarely occurs - I don't bother reminding them that they have advantage if they hit on the first die roll after all.
Sorcerers Apprentice
Hero
You're not seeing the forest for the trees. In both cases you'll be failing almost all the time, so in actual play you won't notice much difference from having advantage or disadvantage if you need to roll a 20 to succeed. The absolute difference in success/failure rates is what matters, not the relative difference.
clearstream
(He, Him)
I'm seeing both the forest and the trees. And as noted, just having some fun with it.
Experientially you would need 400 rolls with advantage before you fail one, if 2+, or 4, if 11+. Compared with 20 rolls at 2+ without, or 2 at 11+. In terms of absolute difference the former will feel like you can't fail while the latter will feel like you fail slightly less often.
Sorcerers Apprentice
Hero
And most actual combats will involve a lot less than 20 rolls per player, so you won't notice any difference. You're still not seeing the forest, but it seems like you're noticing the outline of the underbrush
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