Favorite Flanking Fixes in Five-E?

[TwoSix]

Maybe I'm doing it wrong; help me check my spreadsheet.
Column 1 picks a number between 1 and 20 (inclusive).
Column 2 picks another number between 1 and 20 (inclusive).
Column 3 chooses the minimum value between the two.
Column 4 chooses the maximum value between the two.
Column 5 determines the difference between min and max.
I copy that across 10,000 rows, and average the results in Column 5. It gives me 6.6.

Because you're subtracting the max from the min, rather that subtracting max from 1st roll, you're in essence doubling your effective bonus. Subtracting (lowest 1 of 2d20) from (highest 1 of 2d20) isn't comparing advantage to a normal roll, it's comparing advantage to disadvantage.

The actual average of (highest 1 of 2d20) is 13.82, from anydice.com, and the average of (lowest 1 of 2d20) is 7.18. Subtracting those gives you 6.64, which matches your Excel sheets.

 

[Dausuul]

Edit: Dang ninjas.

Maybe I'm doing it wrong; help me check my spreadsheet.
Column 1 picks a number between 1 and 20 (inclusive).
Column 2 picks another number between 1 and 20 (inclusive).
Column 3 chooses the minimum value between the two.
Column 4 chooses the maximum value between the two.
Column 5 determines the difference between min and max.
I copy that across 10,000 rows, and average the results in Column 5. It gives me 6.6.

Columns 1 and 2 are "straight d20 roll."
Column 3 is "roll with disadvantage."
Column 4 is "roll with advantage."

You are estimating the difference between advantage and disadvantage, not the difference between advantage and a straight roll. You want to use the difference between column 4 and column 1 (or column 4 and column 2, doesn't matter).

More precise way to do this: Put the following formula in cell A1, then copy it in the range from A1 to T20:

=MAX(ROW(A1),COLUMN(A1))

This will give you a 20x20 grid showing the result of every possible combination of rolls on two d20s. Average all cells from A1 to T20 and you'll have the average result of rolling with advantage. Subtract 10.5 (the average of a straight roll) and you get 3.325.

 

[CleverNickName]

Edit: Dang ninjas.


Columns 1 and 2 are "straight d20 roll."
Column 3 is "roll with disadvantage."
Column 4 is "roll with advantage."

You are estimating the difference between advantage and disadvantage, not the difference between advantage and a straight roll. You want to use the difference between column 4 and column 1 (or column 4 and column 2, doesn't matter).

More precise way to do this: Put the following formula in cell A1, then copy it in the range from A1 to T20:

=MAX(ROW(A1),COLUMN(A1))

This will give you a 20x20 grid showing the result of every possible combination of rolls on two d20s. Average all cells from A1 to T20 and you'll have the average result of rolling with advantage. Subtract 10.5 (the average of a straight roll) and you get 3.325.

Not exactly. I am measuring the difference between two rolls. Then doing it again, and again, and again, ten thousand times. Then I find the average of that difference. Over thousands of iterations, that result approaches 6.6.

It's the same thing as if you sat at a table with two d20s, rolled them, and wrote down the difference between the two dice...ten thousand times...then added up all those results and divided the sum by ten thousand. It doesn't care which die has advantage or which has disadvantage, it's only looking at the raw result.

In my spreadsheet, the min, max stuff is to ensure I don't have negative results. I could have simply used the ABS(COL1-COL2) function now that I think about it. Your 3.3 result is just one half of the absolute distance between the positive and negative integers (which is 6.6).

EDIT: I can sure use a lot of fancy words, can't I? Too bad I'm wrong. [MENTION=58197]Dausuul[/MENTION] and [MENTION=6801328]Elfcrusher[/MENTION] (and others) were precisely right. To measure the net benefit of Advantage, I have to measure from the average d20 result, not from the ends of this range. The result of getting Advantage is +3.325, or +3.3. Whenever you gain Advantage on anything involving a d20, you are statistically getting a +3 bonus. Thanks everyone!

 

[Guest 6801328]

@CleverNickName

First, you don't need 10,000 columns, you need exactly 400: one for each of the 400 possible combinations, which have a perfectly even probability distribution.

Second, the math (or logic) error you made was to assume the benefit is equal to the delta between the two values. 50% of the time the higher value would have been the result even without Advantage, and thus there's no benefit.

Imagine two rolls with Advantage:
The first produces an 8 and a 16
The second produces a 10 and a 4

You might say, "That's an average of 7 (8 + 6 / 2) better!" But if we take the first number to be the result of the "first die", that is, the one you would have rolled if you didn't have Advantage, then it didn't help you on the second roll. So Advantage gave you a bonus of +8 in the first case and 0 in the second case, for an average bonus of 4 not 7.

If you integrate this across all 400 possible combinations, it's the same as just dividing your result in half.

EDIT: Yeah, this is effectively what Dausuul did.

 

[Guest 6801328]

To answer the "why" question, I'm torn:

On the one hand, I do like simple tactical options, for which this qualifies. I do think it adds a measure of interesting complexity to decision-making.

On the other hand, it does collide with some other elements. As mentioned above, it kind of gives Pack Tactics to everybody, which is an implicit nerf on creatures with Pack Tactics.

A variant might be "You cannot have Advantage when you are flanked."

I don't like the idea of using the historical +2 just because it conflicts with a design principal of 5e, which I support, even if they break it themselves on occasion (e.g. rules for Cover). In 5e your attack bonus is supposed to be relatively fixed, and on a round-to-round basis the only variation should be Advantage/Disadvantage. Yeah, it's imperfect, but when playing this particular game I'm going to try to adhere to it.

 

[Staccat0]

Dumb idea I haven’t thought too hard about.

When you are flanking a creature you can give any attack rolls you are making to the other flankers to use in place of their own rolls on their turn. It’s situational but feels thematic. I could see rolling 19 as a Rogue and giving it to the Champion or Paladin standing behind the bad guy.

I’m losing an attack but setting up a bigger hit from an ally.

Or or maybe you can roll with disadvantage and choose to give the higher roll to an ally so you aren’t losing an action completely.

 

[Guest 6801328]

Dumb idea I haven’t thought too hard about.

When you are flanking a creature you can give any attack rolls you are making to the other flankers to use in place of their own rolls on their turn. It’s situational but feels thematic. I could see rolling 19 as a Rogue and giving it to the Champion or Paladin standing behind the bad guy.

I’m losing an attack but setting up a bigger hit from an ally.

Or or maybe you can roll with disadvantage and choose to give the higher roll to an ally so you aren’t losing an action completely.

How about: "The flanker with the lowest roll gets to re-roll."

 

[Staccat0]

How about: "The flanker with the lowest roll gets to re-roll."

That too. It requires you Initative a little funny for flankers if I understand right (as opposed to just handing someone a dice and saying “use this next time if you want”) but it would feel cool as players rolling at once.

 

[smbakeresq]

Well I used it (player request)and it’s overpowering both ways, as monsters get to use it also and in most cases the PC are outnumbered and also outsized (fighting bigger creatures.) When PC get flanked by monsters with multi attack and advantage they can get ripped pretty easy.

However my view is somewhat skewed because I use an old critical hit rule; a crit is max damage on damage dice + you roll again for both PC and monsters. Therefore simple things like a doppelgänger who crits you can hit for 28+4d6 for a CR 3 creature and simple big things like a Frost Giant at CR 8 can hit you for 42+3d12.

I think the fault is my use of both as the critical hit in general favors the PCs a little as they try to generate them a but flanking favors more attackers and more multiattackers.

 

[TwoSix]

Not exactly. I am measuring the difference between two rolls. Then doing it again, and again, and again, ten thousand times. Then I find the average of that difference. Over thousands of iterations, that result approaches 6.6.

It's the same thing as if you sat at a table with two d20s, rolled them, and wrote down the difference between the two dice...ten thousand times...then added up all those results and divided the sum by ten thousand. It doesn't care which die has advantage or which has disadvantage, it's only looking at the raw result.

In my spreadsheet, the min, max stuff is to ensure I don't have negative results. I could have simply used the ABS(COL1-COL2) function now that I think about it. Your 3.3 result is just one half of the absolute distance between the positive and negative integers (which is 6.6).

Obviously, you can do whatever you please with your spreadsheet. The only issue is if you want to assert that advantage gives you the equivalent of a +6.6 bonus to your attack rolls, which is simply not true.