How much of an improvement is double rolling?

[SangoProduction]

You may allow a target to surrender themselves to fate. The target takes a -3 penalty to all saving throws, but rolls each saving throw twice and chooses the better roll. This penalty decreases by 1 for every 10 caster levels.
I believe I heard from someone before that rolling on a d20 with advantage is equivalent to +5. But I'm not sure where or when, nor the math that had them come to that conclusion.

So, is this actually just an effective +2 to saves, with the additional benefit of lowering the chance of crit failure to 1/400, while doubling chance of crit success? Or am I missing something?

[Aotrs Commander]

I believe I heard from someone before that rolling on a d20 with advantage is equivalent to +5. But I'm not sure where or when, nor the math that had them come to that conclusion.

So, is this actually just an effective +2 to saves, with the additional benefit of lowering the chance of crit failure to 1/400, while doubling chance of crit success? Or am I missing something?

Can't cite that maths, either, but I've also heard that said. Have a look around reddit, maybe? I think I recall something there when I was looking around myself for an idea while implementing 3.Aotrs.



One feels the person that wrote that quoted rule ALSO had no idea of the maths, because that is a totally nonsensical mechanic.

[Zancloufer]

Well first if they have no chance of making the save normally without a 20 this works out to a 100% increase to saving throw.

I think there was a chart somewhere but the actual advantage of, advantage, varies but it generally works out equal to a +2~+5 if you are capable of making the saving throw normally.

The quick math overall works to : If you have a greater than 50% chance, or only can save on a 20 this is a buff, but if you land somewhere in-between it can be a nerf. So basically only is good if your never going to make the save normally or the save is really easy yo do.

[SangoProduction]

One feels the person that wrote that quoted rule ALSO had no idea of the maths, because that is a totally nonsensical mechanic.

That may be going a bit too far, as the effect is intended to buff the saves, and I believe the penalty is to just make it not such an absurd buff. (I certainly don't mind getting a better +2 cloak of resistance, myself. Still seems kinda strong for an hour/CL effect.)
I was only asking in case I was mistaken.

[SangoProduction]

Well first if they have no chance of making the save normally without a 20 this works out to a 100% increase to saving throw.

I think there was a chart somewhere but the actual advantage of, advantage, varies but it generally works out equal to a +2~+5 if you are capable of making the saving throw normally.

The quick math overall works to : If you have a greater than 50% chance, or only can save on a 20 this is a buff, but if you land somewhere in-between it can be a nerf. So basically only is good if your never going to make the save normally or the save is really easy yo do.

ooo. Neat.

[Khedrac]

It's a lot more complex than that, and, because rolling twice changes the distribution, the effect on the chance of success highly depends on the target number.

Just rolling a D20 has equal chances of each number coming up, with an average of 10.5
Rolling twice and taking the better gives an average (mean) of 13.825 (so not +5, and if you shove in a "-3" it is barely higher on average) and the following distribution:


Result
Probability
% or higher

1 0.25% 100.00%
2 0.75% 99.75%
3 1.25% 99.00%
4 1.75% 97.75%
5 2.25% 96.00%
6 2.75% 93.75%
7 3.25% 91.00%
8 3.75% 87.75%
9 4.25% 84.00%
10 4.75% 79.75%
11 5.25% 75.00%
12 5.75% 69.75%
13 6.25% 64.00%
14 6.75% 57.75%
15 7.25% 51.00%
16 7.75% 43.75%
17 8.25% 36.00%
18 8.75% 27.75%
19 9.25% 19.00%
20 9.75% 9.75%
(The "% or higher" column is the chance of rolling this or higher.)
Curiously, this means that the single most likely result (the mode average) is actually a "natural" 20.

Does this equate to +5? Well, only if you needed an 11 in the first place.

As for the curse, first up is the question as to whether a natural 20 still auto-makes, if yes, then the chance of that has nearly doubled (5% to 9.75%) so it is probably worth it.

[SangoProduction]

I found this chart
https://lh3.googleusercontent.com/proxy/gIuDZ2mtykFAbC2g9sAyW_-treldCvP_7swWdy7S99hPW1yiWQSzTnRw4LnrykserX2CkMlBD M_r_l7XLDsKKnIOtarKngvTOuwJnzEUXFb_SZOnR1Eg-HeVx_Y1Uz3Vkh1XdKXJoj6PXdrPClvuqO4WOZrD_PbPWBA

So, by adjusting the advantage column's target up 3, the point where it is marginally equivalent to rolling without the effect is when you'd need to roll at least a 14 normally. And it gets worse as the required normal roll increases, except for if you need a natural 20 to succeed period.

It's only the equivalent of +6% chance (roughly +1 to the roll) of success when you'd normally need 12, getting better as the required normal roll gets lower.

So, that actually doesn't seem anywhere near as powerful as I thought it was based on the faulty information I had. Does kinda fit the theme of "just going with the flow of things," being the solution to relatively easy saves.

[Remuko]

I found this chart
https://lh3.googleusercontent.com/proxy/gIuDZ2mtykFAbC2g9sAyW_-treldCvP_7swWdy7S99hPW1yiWQSzTnRw4LnrykserX2CkMlBD M_r_l7XLDsKKnIOtarKngvTOuwJnzEUXFb_SZOnR1Eg-HeVx_Y1Uz3Vkh1XdKXJoj6PXdrPClvuqO4WOZrD_PbPWBA

So, by adjusting the advantage column's target up 3, the point where it is marginally equivalent to rolling without the effect is when you'd need to roll at least a 14 normally. And it gets worse as the required normal roll increases, except for if you need a natural 20 to succeed period.

It's only the equivalent of +6% chance (roughly +1 to the roll) of success when you'd normally need 12, getting better as the required normal roll gets lower.

So, that actually doesn't seem anywhere near as powerful as I thought it was based on the faulty information I had. Does kinda fit the theme of "just going with the flow of things," being the solution to relatively easy saves.

Cant see your image

[SangoProduction]

Cant see your image

Huh. It was just fine for a couple hours. I'll try again here
https://lh3.googleusercontent.com/proxy/_RJmvX6PEZoOkTEdbDDn24__NY6e27G-klJAF1_a9dox98ioU1vM8F0CqRQcLM_sLcEBgujsRx3700B9QI SA5TG-dXx5T6j7v3uSWGeCQyoI8xX0au0SGLJzMCYrwfQ_Xv4ZzsGdLy HB-lmNoSxxrVyFf8xZZBxSbwI

Just in case, Google "d20 advantage chart," images, and it should be the first result.

[Biggus]

Huh. It was just fine for a couple hours. I'll try again here
https://lh3.googleusercontent.com/proxy/_RJmvX6PEZoOkTEdbDDn24__NY6e27G-klJAF1_a9dox98ioU1vM8F0CqRQcLM_sLcEBgujsRx3700B9QI SA5TG-dXx5T6j7v3uSWGeCQyoI8xX0au0SGLJzMCYrwfQ_Xv4ZzsGdLy HB-lmNoSxxrVyFf8xZZBxSbwI

Just in case, Google "d20 advantage chart," images, and it should be the first result.

Looking at the chart, if the great majority of enemies you fight are roughly similar in power to you (requiring between a 4 and 18 to make the save) it averages to being worth roughly a +4 bonus. As Khedrac said, averaging all the numbers gives a +3.325 bonus, but if very strong or very weak opponents are a rarity (as per the table on p.49 of the DMG) its actual value is a bit more than that.

[Kurald Galain]

I believe I heard from someone before that rolling on a d20 with advantage is equivalent to +5. But I'm not sure where or when, nor the math that had them come to that conclusion.

On the chart above, rolling twice is equivalent of a +5 as long as the number needed is in the 9-13 range, and to +4 if it's in the 6-16 range.

Now in a game with "tight math" such as 4E, 5E, or P2, in practice your target number will pretty much always be in this range; that's where the conclusion comes from. This is not necessarily true in 3E / PF, so rolling twice is somewhat less great (but still good) in those games.

[AvatarVecna]

A quick trip over to Anydice is useful.

CL 1/2d20b1-3 (https://anydice.com/program/1bef4): Taking the penalty+advantage has a ~50% chance of helping, a ~45% chance of hurting, and a ~5% chance of changing nothing.

CL 10/2d20b1-2 (https://anydice.com/program/1bef5): Taking the penalty+advantage has a ~55% chance of helping, a ~40% chance of hurting, and a ~5% chance of changing nothing.

CL 20/2d20b1-2 (https://anydice.com/program/1bef6): Taking the penalty+advantage has a ~60% chance of helping, a ~35% chance of hurting, and a ~5% chance of changing nothing.

EDIT: Although an important point is that these conclusions are irrespective of target numbers, they're just literally comparing "what you rolled" vs "what you would've rolled". If you need a 20 to succeed, 2d20b1-1 isn't going to help you even though you're far more likely to roll in that 15-19 range than the flat die roller is.