How much is "advantage" worth?

[SangoProduction]

In 5e, there's "advantage" which lets you roll 1d20, twice, and take the best result. Roughly, on average, what amount of "bonus" is that? I heard it was roughly a +5. Does anyone know why?

[ryu]

In 5e, there's "advantage" which lets you roll 1d20, twice, and take the best result. Roughly, on average, what amount of "bonus" is that? I heard it was roughly a +5. Does anyone know why?

As dice rolls aren't actually affected and you're just taking the best one? All possible results of a dice roll summed and then divided by the total number of result options for the average of the result. Then you've a relatively minor bonus because the probability of massive swings is unlikely. It's more insurance for outlandish results than anything else.

In this case the important number is the expected difference on average between two rolls. The fast way to get this is to subtract smallest roll from biggest than divide by 2.

[ryu]

Actually scratch that. It's late. You'd have to tally all possible differences then average them. I don't think my best this late.

[Elkad]

The average increase only about 3.3 points. But it's nearly a clean double for the chance of that nat20, and your chance of a critical failure (1) is miniscule.

Go here (http://rumkin.com/reference/dnd/diestats.php) and paste 2d20D1 in the box.

[SangoProduction]

The average increase only about 3.3 points. But it's nearly a clean double for the chance of that nat20, and your chance of a critical failure (1) is miniscule.

Go here (http://rumkin.com/reference/dnd/diestats.php) and paste 2d20D1 in the box.

That's a really nice tool.

[AvatarVecna]

Just comparing averages isn't a great way to see how valuable this ability is: 2d20b1 is not the same as 1d20+3.8, even though that's what the average amounts to. To get an idea of how useful this ability is to have, you need to look at the number you need to roll to succeed, and then see what the odds of rolling that number or better are when rolling normally and when rolling with advantage:



# needed
Odds (Normal)
Odds (Advantage)


1
100%
100%


2
95%
99.75%


3
90%
99%


4
85%
97.75%


5
80%
96%


6
75%
93.75%


7
70%
91%


8
65%
87.75%


9
60%
84%


10
55%
79.75%


11
50%
75%


12
45%
69.75%


13
40%
64%


14
35%
57.75%


15
30%
51%


16
25%
43.75%


17
20%
36%


18
15%
27.75%


19
10%
19%


20
5%
9.75%



Advantage makes it where the harder it is to succeed, the more it boosts your odds of succeeding at that task. I't s ridiculously useful, and getting advantage to all d20 rolls is very appropriately a 9th lvl spell in 3.5.

[ryu]

Just comparing averages isn't a great way to see how valuable this ability is: 2d20b1 is not the same as 1d20+3.8, even though that's what the average amounts to. To get an idea of how useful this ability is to have, you need to look at the number you need to roll to succeed, and then see what the odds of rolling that number or better are when rolling normally and when rolling with advantage:



# needed
Odds (Normal)
Odds (Advantage)


1
100%
100%


2
95%
99.75%


3
90%
99%


4
85%
97.75%


5
80%
96%


6
75%
93.75%


7
70%
91%


8
65%
87.75%


9
60%
84%


10
55%
79.75%


11
50%
75%


12
45%
69.75%


13
40%
64%


14
35%
57.75%


15
30%
51%


16
25%
43.75%


17
20%
36%


18
15%
27.75%


19
10%
19%


20
5%
9.75%



Advantage makes it where the harder it is to succeed, the more it boosts your odds of succeeding at that task. I't s ridiculously useful, and getting advantage to all d20 rolls is very appropriately a 9th lvl spell in 3.5.

Actually wouldn't it be a steady bell-curve where the amount of percentage chance of success gained is greater the closer your original chance was to exactly 50%?

[Crake]

Just comparing averages isn't a great way to see how valuable this ability is: 2d20b1 is not the same as 1d20+3.8, even though that's what the average amounts to. To get an idea of how useful this ability is to have, you need to look at the number you need to roll to succeed, and then see what the odds of rolling that number or better are when rolling normally and when rolling with advantage:

~snip~

Advantage makes it where the harder it is to succeed, the more it boosts your odds of succeeding at that task. I't s ridiculously useful, and getting advantage to all d20 rolls is very appropriately a 9th lvl spell in 3.5.

This is incorrect.


Actually wouldn't it be a steady bell-curve where the amount of percentage chance of success gained is greater the closer your original chance was to exactly 50%?

This is the correct answer. The bonus from advantage ranges from +5 (when the chance is exactly 50/50, ie you need to roll an 11 on the dice, advantage jumps that up to 75%, which is the equivilent of +5) to +0 (where a natural 1 is already a pass, or a natural 20 is still a fail). On a roll where a 1 is an auto fail and a 20 is an auto succeess, the chance of an auto success is roughly doubled, while the chance of an auto fail is almost eliminated.

[Nifft]

Actually wouldn't it be a steady bell-curve where the amount of percentage chance of success gained is greater the closer your original chance was to exactly 50%?

No, you only get a bell curve when you add multiple dice.

2d20, or 3d6, would generate a bell curve.

AvatarVecna is correct.

[LordOfCain]

Don't you guys know about AnyDice (http://anydice.com)? The following code should work:

output [highest 1 of 2d20] named "Advantage"

[AvatarVecna]

No, you only get a bell curve when you add multiple dice.

2d20, or 3d6, would generate a bell curve.

AvatarVecna is correct.

They're sort of correct, and sort of not, actually. Their comments are in regards to my comment about the graph formed by the change in odds, and from a certain perspective they're correct: if you're measuring the improved odds additively, the way they're looking at it, you see a bell curve form (2d20b1 when you need 1 increases odds of success by +0%, 2d20b1 when you need 5 increases odds of success by +15%, 2d20b1 when you need 10 increases by +24.75%, 2d20b1 when you need 15 increases by +21%, and 2d20b1 when you need 20 increases by +4.75%). However, the perspective I generally take when considering advantage, and probably should've clarified in my original post, is that where the increase is measured multiplicatively: 2d20b1 when you need 1 succeeds 100% as often as 1d20, 2d20b1 when you need 5 succeeds 120% as often as 1d20, 2d20b1 when you need 10 succeeds 145% as often as 1d20, 2d20b1 when you need 15 succeeds 170% as often as 1d20, and 2d20b1 when you need 20 succeeds 195% as often as 1d20. It is the latter perspective from which I made my statement about the improved odds, but their statements about the increased odds forming a bell curve is also correct.

I am not a statistician by any means, so I'm not actually sure which of these perspectives is the better one to operate under, but in my theorycrafting for 5e (and 3.5 when Choose Destiny is in use), I've generally found the multiplicative view more useful.

[ericgrau]

The average increase only about 3.3 points. But it's nearly a clean double for the chance of that nat20, and your chance of a critical failure (1) is miniscule.

Go here (http://rumkin.com/reference/dnd/diestats.php) and paste 2d20D1 in the box.

Yeah but that is assuming you're equally likely to attempt something extremely hard or extremely easy vs something with normal difficulty. That is unlikely to be the case, not only by player choice but also by bounded accuracy and the CR being too far away. So even for things where you have no choice like saves. You're more likely to do something where your chance of success is about 50-80% (or at least ~30% in the case of a poor save).

So advantage is worth roughly a +4. It's hard to say exactly how much without knowing all the circumstances. But less than +5 and more than +3.3.

[Nifft]

It is the latter perspective from which I made my statement about the improved odds, but their statements about the increased odds forming a bell curve is also correct.
A bell curve is defined as the symmetrical curve exhibited by a normal distribution. Advantage(d20) is none of those things.

If you were to say that, if you blur your eyes & squint at the increase in chance of success curve, it looks a bit bell-ish until you re-focus -- that would pass muster. But Advantage(d20) is not a bell curve, and the increased chance of success curve is also not a bell curve.

[AvatarVecna]

A bell curve is defined as the symmetrical curve exhibited by a normal distribution. Advantage(d20) is none of those things.

If you were to say that, if you blur your eyes & squint at the increase in chance of success curve, it looks a bit bell-ish until you re-focus -- that would pass muster. But Advantage(d20) is not a bell curve, and the increased chance of success curve is also not a bell curve.

*shrug* Perhaps, but considering that the community as a whole refers to 4d6b3 as a bell curve too, despite it also not fitting this technical definition, it looks like it's just them not being super-familiar with the technical definition of the word...and that just means that you're being pedantic enough to publicly out-nerd people based on pointing out the technical definition to avoid having to admit that, while their terminology was a bit off, they did actually have a point. Heck, the 'increase in odds' curve is closer to a bell curve than 4d6b3 is, in that it's symmetrical but goes outside the range of x-values at which we're recording y values.

[Necroticplague]

Anything that's XdYbZ isn't a bell curve in the technical sense (because they aren't symetrical, leaning towards higher values being more likely). However, it's a curve in the sense that most people care about: the distribution isn't flat. d20 has everything at 5%, 3d6 has it much more likely you get a 10 or 11 than any other things, 2d20b1 (what we're talking about in this thread) has a 20 come up 39 times as often as a 1.

Now, a very simple view would be to convert this to average roll, and judge it on that.
1d20:10.5
2d20b1:13.82
So, on average, advantage is worth roughly +3.32.

[JNAProductions]

Except it's worth relatively more the harder the task is. You go from 50% to 75% (a 50% increase) when you need an 11, a 5% to a 9.75% chance when you need a 20 (a 95% increase) and from 95% to 99.75% (a 5% increase) when you need a 2.

[AvatarVecna]

Anything that's XdYbZ isn't a bell curve in the technical sense (because they aren't symetrical, leaning towards higher values being more likely). However, it's a curve in the sense that most people care about: the distribution isn't flat.

@Nifft

This more or less states my point about the argument much more concisely than I did. Responding to somebody who said "it's not really a line, it's more of a bell curve" with "wrong, it's a line", and then when it's pointed out that one way of looking at the change is a curve, responding with "well, it's still not a technical bell curve" is a nitpicky attempt to move to goalpost.

[Nifft]

*shrug* Perhaps, but considering that the community as a whole refers to 4d6b3 as a bell curve too, despite it also not fitting this technical definition, it looks like it's just them not being super-familiar with the technical definition of the word...and that just means that you're being pedantic enough to publicly out-nerd people based on pointing out the technical definition to avoid having to admit that, while their terminology was a bit off, they did actually have a point. Heck, the 'increase in odds' curve is closer to a bell curve than 4d6b3 is, in that it's symmetrical but goes outside the range of x-values at which we're recording y values.

Stats used to be just plain 3d6, and that is a bell curve. Best3(4d6) is a modification of a normal distribution, so it starts out as a bell curve (4d6) and then gets modified (drop 1). So there are two reasons why people might think 4d6b3 is a bell curve:
1/ Simple confusion. "Stats are a bell curve" (they were) => the rolling standards change => people are wrong but close.
2/ 4d6b3 still exhibits many traits of a normal distribution. High results and low results are both less likely than median results.

But Advantage(d20) is based on a uniform distribution (very different from a normal distribution -- please fact-check this, knowing the difference is very useful), and Advantage(d20) was never historically a normal distribution, so neither of those potential excuses apply.

Secondly, the fact that someone elsewhere is wrong about a different type of dice rolling is ... kinda irrelevant to this conversation.

Thirdly, drop the personal "out-nerd" "pedantic" crap. The reason I'm going for technical accuracy here is to help someone understand how this mechanic works, and that is the topic of the thread. Being inaccurate will not help anyone.



@SangoProduction - Advantage(d20) is not really comparable to any static bonus. What it does is modify how well your dice perform. Specifically, it makes every LARGE number much more likely to appear: almost double the chance to roll a natural 20, for example, and slowly decreases. (The disproportionately increased chance to roll a natural 20 is important if you do crit-related stuff.)

It makes every SMALL number much less likely to appear: instead of a 1-in-20 chance to roll a natural 1, with Advantage(d20) you have a 1-in-400 chance. That's 20 times less. (More relevant if you use some kind of fumble house rules.)



Result
plain d20
Adv(d20)


1
1:20
1:400


2
1:20
3:400


3
1:20
5:400


4
1:20
7:400


5
1:20
9:400


6
1:20
11:400


7
1:20
13:400


8
1:20
15:400


9
1:20
17:400


10
1:20
19:400


11
1:20
21:400


12
1:20
23:400


13
1:20
25:400


14
1:20
27:400


15
1:20
29:400


16
1:20
31:400


17
1:20
33:400


18
1:20
35:400


19
1:20
37:400


20
1:20
39:400



Note that on both sides of the median, for 10 and 11, you get almost 1-in-20 chances of each result using Advantage. The difference gets amplified with each step away from the median you go.

At the far end, with Advantage(d20), you have almost a 1-in-10 chance to roll a natural 20.

However, it's not comparable to any bonus, because you will never roll above 20. If you have Advantage, you are confined to the same range of results as you could get without Advantage.

So basically:
- Advantage is great when your roll matters.
- Static bonuses are great to get your roll into the range where it matters, or to get your bonus so high that you don't even need to roll.

[AvatarVecna]

Thirdly, drop the personal "out-nerd" "pedantic" crap. The reason I'm going for technical accuracy here is to help someone understand how this mechanic works, and that is the topic of the thread. Being inaccurate will not help anyone.

I'll say again, to get the point across: saying somebody is wrong for saying it's a bell curve instead of a line, when what they more or less meant was that it's a curve instead of a line, is being overly pedantic when everybody knew what they meant and the context in which they were saying it the first time. It's not like saying "I think you mean 'they're', not 'their' ", it's like saying "I think you mean 'whom', not 'who' ": you might be technically correct, but your technical correction doesn't invalidate the rest of the point being made.

[Buufreak]

Anything that's XdYbZ isn't a bell curve in the technical sense...

Except in any situation where X=Z, because without dropping the low rolls, it will definitely be a bell due to how dice work.

[John Longarrow]

To the OP, advantage is worth a fair amount if your chances otherwise are only about 50/50. If you are either most likely to succeed OR most likely to fail, its rather modest.

Take the case of a fighter with advantage who is +10 to hit.
If the enemy has an AC of 12, the fighter is only going to miss on a 1 so it changes a 1 in 20 chance to a 1 in 400 of failure. If the enemy has an AC of 13 though, the chance of failure is only 1 in 100 so its worth about the same as a +1 weapon in this case.

If same enemy has an AC of 21 you have a 1 in 2 chance of hitting without advantage and a 3 in 4 chance with it. This translates to a +5.

Move the AC to 30 and you have about a 1 in 10 chance to hit with advantage or 1 in 20 without. Once more advantage becomes worth +1.

This doesn't equate to a real bonus to hit though. If we were to assume it was worth +3 the numbers become rather funny.

Your chance to hit AC 30 with a +10 is about 10% from advantage. Hitting AC 30 with a +13 is 20% (roll of 17 or better) so linear bonuses are much better when trying to hit really high OR really low AC. This doesn't include their bonus to damage.

Which is better is situational. Best option would be to get the Shadow Blade Technique (1st level shadowhand maneuver) to get TWO attack rolls along with what ever bonus your weapon has. Best part is if you choose to use the lower roll and it hits, you do extra damage.

[Endarire]

Advantage is worth as much as what you'll most likely and most importantly use it for. This may be crit fishing, DC maximization, or otherwise.

[Crake]

They're sort of correct, and sort of not, actually. Their comments are in regards to my comment about the graph formed by the change in odds, and from a certain perspective they're correct: if you're measuring the improved odds additively, the way they're looking at it, you see a bell curve form (2d20b1 when you need 1 increases odds of success by +0%, 2d20b1 when you need 5 increases odds of success by +15%, 2d20b1 when you need 10 increases by +24.75%, 2d20b1 when you need 15 increases by +21%, and 2d20b1 when you need 20 increases by +4.75%). However, the perspective I generally take when considering advantage, and probably should've clarified in my original post, is that where the increase is measured multiplicatively: 2d20b1 when you need 1 succeeds 100% as often as 1d20, 2d20b1 when you need 5 succeeds 120% as often as 1d20, 2d20b1 when you need 10 succeeds 145% as often as 1d20, 2d20b1 when you need 15 succeeds 170% as often as 1d20, and 2d20b1 when you need 20 succeeds 195% as often as 1d20. It is the latter perspective from which I made my statement about the improved odds, but their statements about the increased odds forming a bell curve is also correct.

I am not a statistician by any means, so I'm not actually sure which of these perspectives is the better one to operate under, but in my theorycrafting for 5e (and 3.5 when Choose Destiny is in use), I've generally found the multiplicative view more useful.

The reason we don't look at it this way, and instead look at the raw increased % chance of success is because that is how you determine the effective "bonus". Looking at it your way, on a check that requires a natural 20, a +1 bonus is a 100% increase, because it went from 5% to 10%, but that sort of relativistic perspective makes it hard to determine what the effective "bonus" is, which was the question posed in the thread's OP.

Looking at it our way, viewing the actual increased %chance of success, and dividing it by 5%, which is what a +1 would normally give you, assuming you weren't at the upper or lower limits of the d20 roll, that is how we determine our answer to that question.

[grarrrg]

On the average +3.325.
Roughly half the results are a 15 or better, roughly half the results are a 14 or lower (204 / 196 chances). This is likely where the "I heard it's +5" comes from, the average is only +3.3, but the median is +4.5.

If Criticals are a factor, have two d20's, designate one the "critical" die, and the other "not". Otherwise it's combat-value goes sky-high.

With regards to "depends on how high/low you need to succeed", that may be helpful from an in-game standpoint, but from a "how much do I cost this bonus?" standpoint it doesn't help that much.
If you were costing this as a bonus, I'd say around +4, depending on exact use as low at +3, as high as +5.

[SangoProduction]

On the average +3.325.
Roughly half the results are a 15 or better, roughly half the results are a 14 or lower (204 / 196 chances). This is likely where the "I heard it's +5" comes from, the average is only +3.3, but the median is +4.5.

If Criticals are a factor, have two d20's, designate one the "critical" die, and the other "not". Otherwise it's combat-value goes sky-high.

With regards to "depends on how high/low you need to succeed", that may be helpful from an in-game standpoint, but from a "how much do I cost this bonus?" standpoint it doesn't help that much.
If you were costing this as a bonus, I'd say around +4, depending on exact use as low at +3, as high as +5.

Ahhh. OK. That's where it's from. That makes sense.

[Crake]

On the average +3.325.
Roughly half the results are a 15 or better, roughly half the results are a 14 or lower (204 / 196 chances). This is likely where the "I heard it's +5" comes from, the average is only +3.3, but the median is +4.5.

If Criticals are a factor, have two d20's, designate one the "critical" die, and the other "not". Otherwise it's combat-value goes sky-high.

With regards to "depends on how high/low you need to succeed", that may be helpful from an in-game standpoint, but from a "how much do I cost this bonus?" standpoint it doesn't help that much.
If you were costing this as a bonus, I'd say around +4, depending on exact use as low at +3, as high as +5.

costing the bonus as a flat number wouldn't be quite right though, because advantage has more than just a flat bonus effect. For rolls where 1s and 20s are auto fails/successes, it almost doubles your change at auto success and almost eliminates your chance at auto failure, which is a big factor for attacks and saves. For skills, where there are no auto successes/failures, the difference between advantage and a flat bonus could quite possibly be the difference between actually enabling a success vs not being able to pass the check to begin with, or completely eliminating failure vs reducing the chance of failure. You honestly can't just price it as a flat +X number, because while it's "on average" +3.3 or whatever, it's actually not at all equivilent in edge cases, which in 3.5, considering it's highly scaled system (as opposed to 5e where bonuses are much smaller, and the dice roll actually makes a big factor in the success/failure), edge cases play a big roll, because all too often it's possible to reduce the chance of failure to either 0, or the chance of rolling a natural 1.

Also the whole "I heard it's worth +5" actually likely comes from 5e itself, where having advantage on a passive check increases it from 10+skill modifier, to 15+skill modifier, or a +5 bonus on the passive check.

[grarrrg]

costing the bonus as a flat number wouldn't be quite right though, because advantage has more than just a flat bonus effect. For rolls where 1s and 20s are auto fails/successes, it almost doubles your change at auto success and almost eliminates your chance at auto failure, which is a big factor for attacks and saves.
Covered that:

If Criticals are a factor, have two d20's, designate one the "critical" die, and the other "not". Otherwise it's combat-value goes sky-high.


For skills, where there are no auto successes/failures, the difference between advantage and a flat bonus could quite possibly be the difference between actually enabling a success vs not being able to pass the check to begin with, or completely eliminating failure vs reducing the chance of failure. You honestly can't just price it as a flat +X number, because while it's "on average" +3.3 or whatever, it's actually not at all equivilent in edge cases, which in 3.5, considering it's highly scaled system (as opposed to 5e where bonuses are much smaller, and the dice roll actually makes a big factor in the success/failure), edge cases play a big roll, because all too often it's possible to reduce the chance of failure to either 0, or the chance of rolling a natural 1.

And? If you make it a 'thing' that can be priced, you have to price it somewhere.
+2 is much too cheap, and +6 is a bit high. +4 is about the happiest middle ground you're going to get.

[Crake]

Covered that:




And? If you make it a 'thing' that can be priced, you have to price it somewhere.
+2 is much too cheap, and +6 is a bit high. +4 is about the happiest middle ground you're going to get.

Or alternatively you could price it as the 9th level spell it is in 3.5: Choose destiny, swift action, verbal only spell, in the destiny domain. 1 round/level, roll two dice and choose which you want to use for all attacks, skill checks, ability checks and saving throws.

[grarrrg]

Or alternatively you could price it as the 9th level spell it is in 3.5: Choose destiny, swift action, verbal only spell, in the destiny domain. 1 round/level, roll two dice and choose which you want to use for all attacks, skill checks, ability checks and saving throws.

That would be assuming it applied to everything all/most the time.
I'm assuming you go and buy a "sword of advantage", or a "chef's hat of advantage" where it only applies to one thing.

[Ualaa]

There's likely a mathematical formula for it.
But I think you'd essentially calculate it as:

Not really sure, exactly, but something similar most likely.

On a natural roll of...
Chance that the second roll is better.
The average improvement of the second roll.

01 (0.95 x ( (02+20) /2) ) = 10.45
02 (0.90 x ( (03+20) /2) ) =
03 (0.85 x ( (04+20) /2) ) =
04
05
06
07
08
09
10
11
12
13
14
15
16
17 (0.15 x ( (18+20) /2) ) =
18 (0.10 x ( (19+20) /2) ) =
19 (0.05 x ( (20+20) /2) ) =
20 (0.00 x .....................) = 00.00

Then add the total improvement, for each of the initial 20 possible rolls, and divide that by 20 since we're looking for the average improvement per single roll.

[Barstro]

Then add the total improvement, for each of the initial 20 possible rolls,

"Improvement" isn't all that important.
If you roll a 1 and then a 4, you have improved. If you needed at least a 14 to succeed, then it didn't matter.

AvatarVecna's chart (along with Nifft's other way of showing it) shows what's important; the gain between one roll and best of two rolls per number needed.

Adding "Advantage" to a weapon (or just attack rolls) almost doubles one's ability to Crit. That bonus alone is worth more than any simple +X to me. That's a lot of extra d6 for your party rogue.

I ran the numbers before when I played a Pathfinder Witch (had a hex that allowed double rolls). The true bonus is quite great and I can understand why Pathfinder only allowed the Witch to use that one per day on a character and that character could use the bonus only once per round.

[Crake]

"Improvement" isn't all that important.
If you roll a 1 and then a 4, you have improved. If you needed at least a 14 to succeed, then it didn't matter.

AvatarVecna's chart (along with Nifft's other way of showing it) shows what's important; the gain between one roll and best of two rolls per number needed.

Adding "Advantage" to a weapon (or just attack rolls) almost doubles one's ability to Crit. That bonus alone is worth more than any simple +X to me. That's a lot of extra d6 for your party rogue.

I ran the numbers before when I played a Pathfinder Witch (had a hex that allowed double rolls). The true bonus is quite great and I can understand why Pathfinder only allowed the Witch to use that one per day on a character and that character could use the bonus only once per round.

I know advantage comes from 5e, but this is still 3.5e where crits don't multiply bonus damage dice.

[Barstro]

I know advantage comes from 5e, but this is still 3.5e where crits don't multiply bonus damage dice.

You are correct.
I was thinking about how much my last character enjoyed his 3x on critical bow shows and somehow tried to bring rogues into the mix.

Striking incorrect points. Thank you.

[P.F.]

"Improvement" isn't all that important.
If you roll a 1 and then a 4, you have improved. If you needed at least a 14 to succeed, then it didn't matter.

AvatarVecna's chart (along with Nifft's other way of showing it) shows what's important; the gain between one roll and best of two rolls per number needed.

Adding "Advantage" to a weapon (or just attack rolls) almost doubles one's ability to Crit. That bonus alone is worth more than any simple +X to me. That's a lot of extra d6 for your party rogue.

I ran the numbers before when I played a Pathfinder Witch (had a hex that allowed double rolls). The true bonus is quite great and I can understand why Pathfinder only allowed the Witch to use that one per day on a character and that character could use the bonus only once per round.

So if "advantage " in general is equivalent to a +4 bonus, and doubles your chance to roll a critical threat, would it be reasonable to price an "advantaged" longsword as a +4 keen longsword?

[ryu]

So if "advantage " in general is equivalent to a +4 bonus, and doubles your chance to roll a critical threat, would it be reasonable to price an "advantaged" longsword as a +4 keen longsword?

Slightly higher unless keen ALSO halves the chances of ones.

[Doctor Despair]

At first I was like "but this makes crit builds so crazy once you start expanding the critical range", but then I thought "eh, mundanes could use the help" :p

[ryu]

At first I was like "but this makes crit builds so crazy once you start expanding the critical range", but then I thought "eh, mundanes could use the help" :p

Precisely. Besides it's not as though a caster has no dice rolls he'd enjoy getting advantage in. Like that fabled story where one of my characters died to rolling three ones in a row, then proceeding to crush that dice in a vice. If I had advantage that would've been SIX chances for everything to not go pear shaped.

[P.F.]

Slightly higher unless keen ALSO halves the chances of ones.

Well, whats more, "advantage" doesn't halve the chance of a one, it twentieths it.

[ryu]

Well, whats more, "advantage" doesn't halve the chance of a one, it twentieths it.

Good point I was still woozy from my epic sleep in.

[Kelb_Panthera]

So if "advantage " in general is equivalent to a +4 bonus, and doubles your chance to roll a critical threat, would it be reasonable to price an "advantaged" longsword as a +4 keen longsword?

That would make it an equivalent +5, minimum value 70k. That doesn't sound terrible for the effect as long as it's restricted to weapon attack rolls.

Let's compare that to the cost of an command version of the spell choose destiny; 9x17x1800=275,400 (an epic item). However, that applies to virtually all d20 rolls. Reducing it by 3/4 to restrict it to attack rolls only seems, to me at least, to be a reasonable ad-hoc adjustment. That gets us in the same neighborhood as the +5 cost.


I'd quite likely allow it at that +5/70k price point in my game afer having seen this thread.

[Godskook]

Just comparing averages isn't a great way to see how valuable this ability is: 2d20b1 is not the same as 1d20+3.8, even though that's what the average amounts to. To get an idea of how useful this ability is to have, you need to look at the number you need to roll to succeed, and then see what the odds of rolling that number or better are when rolling normally and when rolling with advantage:



# needed
Odds (Normal)
Odds (Advantage)


1
100%
100%


2
95%
99.75%


3
90%
99%


4
85%
97.75%


5
80%
96%


6
75%
93.75%


7
70%
91%


8
65%
87.75%


9
60%
84%


10
55%
79.75%


11
50%
75%


12
45%
69.75%


13
40%
64%


14
35%
57.75%


15
30%
51%


16
25%
43.75%


17
20%
36%


18
15%
27.75%


19
10%
19%


20
5%
9.75%



Advantage makes it where the harder it is to succeed, the more it boosts your odds of succeeding at that task. I't s ridiculously useful, and getting advantage to all d20 rolls is very appropriately a 9th lvl spell in 3.5.

Ignoring crits and fumbles, advantage is categorically worse than a +1 modifier at both "fail on a 1" and "fail on a 19". At "fail on a 10", its a +5 modifier, and scales between that and the outliers. You can do the same exact analysis you do for a +1 modifier and get very similar results that it "matters most" on the worst odds.

[Fouredged Sword]

10 or 11 is not the most common single result.

The single most likely outcome of a 2d20b1 roll is a 20. If ether die rolls a 20 that is the roll kept. Out of 400 possible results a 20 will crop up 39 times for odds of 9.75%

19 crops up 37 times
18 crops up 35 times
17 crops up 33 times
..
..
..
3 crops up 5 times
2 crops up 3 times
1 crops up 1 time

Each number is .5% less likely to be rolled than the number higher than it.


I would think of it like both adding +5 to rolls near DC+10 and adding Keen when determining the odds of a critical hit but you still cannot roll more than a 20.

[AvatarVecna]

Ignoring crits and fumbles, advantage is categorically worse than a +1 modifier at both "fail on a 1" and "fail on a 19". At "fail on a 10", its a +5 modifier, and scales between that and the outliers. You can do the same exact analysis you do for a +1 modifier and get very similar results that it "matters most" on the worst odds.

Advantage is successful only .25% less often than a +1 in "fail on 1/19", and is far superior the rest of the time unless you would normally need a 21 on the die. Furthermore, the part I've emphasized in your post is a rather important one: while fumbles aren't commonly present in 3.5 games, criticals definitely are, and when critical threat range increases, the helpfulness of advantage increases as well. In combat, advantage cuts out 95% of auto-misses, doubles the number of auto-hits, and ups the number of critical threats you roll anywhere from 160% to 200% depending on your threat range (with the minimum going lower if you're really pushing your crit-fishing).



Total needed
Odds of Success (1d20)
Odds of Success (2d20b1)
Odds Of Success (1d20+1)


1
100%
100%
100%


2
95%
99.75%
100%


3
90%
99%
95%


4
85%
97.75%
90%


5
80%
96%
85%


6
75%
93.75%
80%


7
70%
91%
75%


8
65%
87.75%
70%


9
60%
84%
65%


10
55%
79.75%
60%


11
50%
75%
55%


12
45%
69.75%
50%


13
40%
64%
45%


14
35%
57.75%
40%


15
30%
51%
35%


16
25%
43.75%
30%


17
20%
36%
25%


18
15%
27.75%
20%


19
10%
19%
15%


20
5%
9.75%
10%


21
0%
0%
5%

[Barstro]

t but you still cannot roll more than a 20.

A very good point.

Assuming that Advantage is about the same as a +4 and taking all armor and other bonuses into account;

If the enemy's AC is so high PC needs a natural 20 to even hit, then Advantage makes hitting almost twice as likely. (5% vs. 9.75%)

If the enemy's AC is to the point that the PC needs to get a 23 between the die and other bonuses;

Advantage will still allow a hit on only a natural 20 (9.75%).
a +4 weapon will allow that hit on rolls of 17-20 and be over twice as likely to hit as the Advantage'd weapon
(20% chance to roll 17-20 vs. 9.75% chance to roll the natural 20 with Advantage. This also has a greater chance of confirming a crit.

[P.F.]

A very good point.

Assuming that Advantage is about the same as a +4 and taking all armor and other bonuses into account;

If the enemy's AC is so high PC needs a natural 20 to even hit, then Advantage makes hitting almost twice as likely. (5% vs. 9.75%)

If the enemy's AC is to the point that the PC needs to get a 23 between the die and other bonuses;

Advantage will still allow a hit on only a natural 20 (9.75%).
a +4 weapon will allow that hit on rolls of 17-20 and be over twice as likely to hit as the Advantage'd weapon
(20% chance to roll 17-20 vs. 9.75% chance to roll the natural 20 with Advantage. This also has a greater chance of confirming a crit.

So here is AvatarVecna's table repopulated to show the relative effects of Advantage versus a +4 bonus on attack rolls.



Total needed
(1d20)
(2d20b1)
(1d20+4)


1
100%
100%
100%


2
95%
99.75%
100%


3
90%
99%
100%


4
85%
97.75%
100%


5
80%
96%
100%


6
75%
93.75%
95%


7
70%
91%
90%


8
65%
87.75%
85%


9
60%
84%
80%


10
55%
79.75%
75%


11
50%
75%
70%


12
45%
69.75%
65%


13
40%
64%
60%


14
35%
57.75%
55%


15
30%
51%
50%


16
25%
43.75%
45%


17
20%
36%
40%


18
15%
27.75%
35%


19
10%
19%
30%


20
5%
9.75%
25%


21
5%
9.75%
20%


22
5%
9.75%
15%


23
5%
9.75%
10%


24+
5%
9.75%
5%



As you can see, the flat bonus wins out on the margins, but through the middle Advantage is better. Also once the AC surpasses the total attack bonus, Advantage is once again more likely to land a lucky hit. Furthermore, if we account for auto-fail, Advantage wins out on the extreme edge there too.



Roll needed
(1d20)
(2d20b1)
(1d20+4)


>1
95%
99.75%
95%

I

[Barstro]

The chart is incorrect at d20+4 at 14 on. You skipped a few numbers.
Fixed

[nettle3305]

For a risk neutral actor, this can be computed from first principles. Note the probability of rolling i on 2d20b1 is 20^{-2}2i-20^{-2}. To compute expectation we find \sum_{i=1}^{20}i(20^{-2}2i^2-20^{-2})=13.825. Hence advantage is worth +3.825 +3.325 (forgot the expected value of 1d20 is 10.5) for a risk neutral actor.

Obviously both risk accepting and risk adverse actors want 2d20b1, since variance is smaller due to the max function "contracting" the induced probability measure, but this calculation assumes that the utility of rolling i is i, that is, a linear increase. If you want to factor in the usefulness or horribleness of natural 20s or 1s, or you want to assign a value to consistency, then that's your own business, since these factors are very contextual. For instance, the utility of a crit with a greatsword is more than the utility of a crit with a quarterstaff. As for the value of consistency, this is determined by whether you are risk accepting or risk adverse. If you like risk, 2d20b1 is worth less than +3.825 +3.325, the exact amount is contextual. Vice versa for the risk adverse.

[P.F.]

The chart is incorrect at d20+4 at 14 on. You skipped a few numbers.

Whoops must've gotten a little overly happy with the ctrl-z there.

Edited to use proper numbers now.

[Fouredged Sword]

There is a level 1 TOB strike that does this (basically). I would price this as a constant use of that, so maybe a +3 modifier.