Half (dis)advantage

[Greywander]

I've seen people saying that, while the (dis)advantage system does help cut down on time spent adding up bonuses, they still don't like how binary (dis)advantage is. Now, Elven Accuracy gives us a look at what "double" (dis)advantage might look like, and it's pretty much what you'd expect (just roll more dice and take the highest/lowest one). But what about, say, "half" (dis)advantage? A more minor bonus/penalty than full (dis)advantage.

The best idea I could come up with was to roll 1d20 and 1d12 and take the highest/lowest (1d12 + 8 for half disadvantage). This doesn't seem to affect your odds of rolling 13 or higher, but does make 12 the average result (you expect to get higher than 12 half the time and lower than 12 the other half of the time). Considering that the average was already 10.5, I'm not sure this is a huge benefit, but it definitely does skew the odds toward a middling roll, away from a low roll, and doesn't affect high rolls. (Using 1d12 + 8 for half disadvantage makes it symmetric; low rolls are unaffected, middling rolls more likely, and high rolls unlikely.)

I feel like this would work better with something like a d16 or d14, but I also don't want to ask people to go out and buy a brand new die.

What about stacking? I can see an argument not to make people hunt for every bonus they can find, but if we wanted to allow stacking, what I'd probably do is make three sources of half (dis)advantage combine to full (dis)advantage, and three sources of full (dis)advantage might combine to double (dis)advantage. Maybe with a caveat that half (dis)advantages don't count toward double (dis)advantage no matter how many of them you have. This way, you always stop at three sources.

Edit: Actually, for the purposes of stacking, what I would probably do is say that half (dis)advantage can only be stacked once to create one full (dis)advantage. More than three sources of half (dis)advantage does nothing, but it at least does count as one of the three full (dis)advantages you need to get double (dis)advantage. Hopefully that should be sufficient to add some different levels of bonuses without making it time consuming to total them up.

[Belzique]

Star Wars Saga Edition (and surely some other games) had a system that could possibly be considered half advantage in their "You can reroll once, but you must accept the result of the second roll, even if it worse" features. Such a feature was often considered a +2 bonus when used well. The issue is that this only works well/easily with advantage. Assuming the "correct" use of such a feature is to reroll if you roll lower than the average roll (aka 10 or lower) you could theoretically make a reverse system that says "If you roll an 11 or higher you must reroll, but you must accept the result of the second roll, even if it is better", but that still leaves a system where on one hand (advantage) players have a choice whereas on the other (disadvantage) they don't.

Just something I wanted to throw out there for this discussion.

[Tanarii]

Run it like Lucky with disadvantage in reverse? Roll with advantage first, then roll disadvantage and take the worst of the two rolls?

Where's what the curves look like

https://anydice.com/program/1b586

[MaxWilson]

Star Wars Saga Edition (and surely some other games) had a system that could possibly be considered half advantage in their "You can reroll once, but you must accept the result of the second roll, even if it worse" features. Such a feature was often considered a +2 bonus when used well. The issue is that this only works well/easily with advantage. Assuming the "correct" use of such a feature is to reroll if you roll lower than the average roll (aka 10 or lower) you could theoretically make a reverse system that says "If you roll an 11 or higher you must reroll, but you must accept the result of the second roll, even if it is better", but that still leaves a system where on one hand (advantage) players have a choice whereas on the other (disadvantage) they don't.

Just something I wanted to throw out there for this discussion.

You would reroll whenever the target number was bigger than the rolled number. The target number is not necessarily 11, just your best guess at the minimum needed. With perfect information this is almost exactly equivalent to advantage, and even with imperfect information it's probably significantly better than a +2, more like a +1d8.

My best suggestion for half-disadvantage is to take min(d20, (d20+d8)).

[Tanarii]

My best suggestion for half-disadvantage is to take min(d20, (d20+d8)).
Interesting. Identical odds to 1d20 up to value 8 (5% per result), then changes wildly (higher odds of a 9-14 and lower of 15-20). Here's some breakdowns.
(The normal graph gives the best visual aid IMO, but the at least is also interesting)

https://anydice.com/program/1b594

Did you possibly mean 1d12+8 instead of 1d20+8?

[MaxWilson]

Interesting. Identical odds to 1d20 up to value 8 (5% per result), then changes wildly (higher odds of a 9-14 and lower of 15-20). Here's some breakdowns.
(The normal graph gives the best visual aid IMO, but the at least is also interesting)

https://anydice.com/program/1b594

Did you possibly mean 1d12+8 instead of 1d20+8?

Not d20+8, d20+d8.

[Tanarii]

Not d20+8, d20+d8.
Corrected:
https://anydice.com/program/1b59c

That's surprisingly close to disadvantage of 1d20 and (advantage of 2d20) btw. How did you arrive at it?

[MaxWilson]

Corrected:
https://anydice.com/program/1b59c

That's surprisingly close to disadvantage of 1d20 and (advantage of 2d20) btw. How did you arrive at it?

Well, I was writing an Internet post, and I knew I needed a result which was strictly worse (but not too much worse) than d20 so using d20 as an upper bound seemed natural, but rolling with a random bonus approximately equal to the magnitude of the disadvantage penalty seemed like a good way to offset that penalty, and it fit all the cases I could think of in my head so I finished writing and hit Send on my phone. You did more due diligence with AnyDice than I did checking the exact curves. :P

Basically it just seemed like a good shape which satisfices the requirements and is easy to calculate. Isn't that how we do all our game design? :)

[Tanarii]

Well, I was writing an Internet post, and I knew I needed a result which was strictly worse (but not too much worse) than d20 so using d20 as a upper bound seemed natural, but rolling with a random bonus approximately equal to the magnitude of the disadvantage penalty seemed like a good way to offset that penalty, and it fit all the cases I could think of in my head so I finished writing and hit Send on my phone. You did more due diligence with AnyDice than I did checking the exact curves. :P

Basically it just seemed like a good shape which satisfices the requirements and is easy to calculate. Isn't that how we do all our game design? :)😂😂😂 wasn't expecting that

Pretty much how I arrived at "disadvantage of advantage" but I was an on an ipad so anydice was easish to access compared to a phone and check my work. :smallamused:

[MaxWilson]

😂😂😂 wasn't expecting that

Pretty much how I arrived at "disadvantage of advantage" but I was an on an ipad so anydice was easish to access compared to a phone and check my work. :smallamused:

Yeah, it's not surprising the curves are similar because they're both similar approaches: use d20 as an upper bound, but otherwise use a generous curve. "Advantage with disadvantage" is slightly stingier with the crits but it's subjective whether that's good or bad or neither. Ultimately I think it comes whether your players find doing addition easier than doing a "min(d20, max(d20, d20))" calculation. Personally I feel that "min(d20, max(d20,d20))" is too likely to get confused with "eliminate the highest and the lowest value", which it definitely ISN'T, so I'd opt to just have them roll e.g. a black d20 and a blue d20 + d8 and pick whichever is worse. But maybe I'm underestimating the difficulty of addition.

[Tanarii]

Looking at the normal lines again, what we really need is a way to generate a linear decrease from 7.5% (roughly) of a 1 to 2.5% chance of a 20. Both of our methods resulted in a curve where 1 doesn't have the greatest chance of occurring.

[Warwick]

If you want your linear RNG to stay linear, you're going to need to employ fixed bonuses/penalties.

edit: wait, I misread. You want the probability distribution to be a step function with fixed incremental shifts in probability. I'm not sure you can generate that using a die. At least, not parsimoniously. I guess you could use a d1000 and translate the output through a table.

[MaxWilson]

Looking at the normal lines again, what we really need is a way to generate a linear decrease from 7.5% (roughly) of a 1 to 2.5% chance of a 20. Both of our methods resulted in a curve where 1 doesn't have the greatest chance of occurring.

To me that seems a desirable property for half-disadvantage. You want it moderately weighted towards bad-but-not-the-worst outcomes.

But maybe I'm failing to understand the situations where you'd want to use half-disadvantage. I don't think I'd ever use it myself.

[Tanarii]

If you want your linear RNG to stay linear, you're going to need to employ fixed bonuses/penalties.

edit: wait, I misread. You want the probability distribution to be a step function with fixed incremental shifts in probability. I'm not sure you can generate that using a die. At least, not parsimoniously.
Disadvantage and advantage do it. Each number on the die has an incremental .5% chance more of happening than the previous number, starting at .25% for 1 (advantage) or 20 (disadvantage). That's opposed to the even 5% per individual value in a normal d20.

Trying to think of a way to adjust the slope of the line to be in between the two and still generate using dice.


To me that seems a desirable property for half-disadvantage. You want it moderately weighted towards bad-but-not-the-worst outcomes.

But maybe I'm failing to understand the situations where you'd want to use half-disadvantage. I don't think I'd ever use it myself.
Hmmm. Okay maybe I'm looking at the name too literally then. I'll leave my feedback as is at this point then.

[Warwick]

Disadvantage and advantage do it. Each number on the die has an incremental .5% chance more of happening than the previous number, starting at .25% for 1 (advantage) or 20 (disadvantage). That's opposed to the even 5% per individual value in a normal d20.

Trying to think of a way to adjust the slope of the line to be in between the two and still generate using dice.

Right, I get that. My point (which I phrased poorly) is that it's not something you can fix by adding more dice. More dice is just going to make the curve curvier, and you can't wring anymore granularity out of the d20 (ultimately, you're still dealing with a fixed range of possible outputs). If you want to adjust the slope you can create a table that generates d20 outputs in a weighted manner from a larger die roll, but I'm guessing that's not the elegant solution you're looking for (and it still won't be the same linear increments the whole way).

[Greywander]

So let's see how each of these compare.

The initial method I proposed was for half advantage to be the highest of 1d20 and 1d12. Half disadvantage would then be lowest of 1d20 and 1d12 + 8. Here's the highlights:

High rolls are unaffected, i.e. have the same odds as a straight d20 roll.
Low rolls are less likely, with a 1 being very unlikely.
Rolls between 7 and 12 are more likely, but the probability isn't equal. 12 is the most likely, 7 is only slightly more likely than a straight d20 roll.
Ergo, half advantage doesn't help if you need a high roll, but does help if a middling roll would suffice.
Half disadvantage is a bit awkward due to the 1d12+8.

Tanarii proposed first taking the lowest of 2d20, then rolling another d20 and taking the highest. Half disadvantage would be taking the highest of 2d20, then rolling another d20 and taking the lowest.

Creates a nice, smooth curve.
13 is the most likely roll, so comparable to my method.
Does affect high rolls, making half advantage useful even if you need a high roll.
The two step process makes this awkward, and I could see people getting the rolls for half advantage and half disadvantage mixed up.

For MaxWilson's method, half advantage would be the highest of 1d20 and 1d20-1d8, while half disadvantage would be the lowest of 1d20 and 1d20+1d8.

Not as smoot of a curve as Tanarii's method, but it's not too far off.
Overall very similar to Tanarii's method.
Can be done in a single roll, although you have to have a way of identifying each d20. Or you could roll in two steps.
Comparing two dice is easy. Adding or subtracting two dice, then comparing them to a third die is a bit messier.

Here's the AnyDice comparing half advantage (https://anydice.com/program/1b5af) and half disadvantage (https://anydice.com/program/1b5b0) for each method. The outputs shows are:

A straight d20 roll.
My method (e.g. highest of 1d20 and 1d12).
Tanarii's method (e.g. lowest of 2d20, then roll another d20 and take the highest).
MaxWilson's method (e.g. highest of 1d20 and 1d20-1d8).
Full advantage and disadvantage.

I think it's actually fine for half advantage to skew towards a middling roll, rather than towards a 20. What we don't want is some weird formula where it's actually less likely to roll a high number, but none of these methods do that. All of these methods make a middling roll (and actually a higher than 10 roll) the most likely outcome, but they also make low rolls less likely and high rolls either more likely or just as likely. With any of these methods, rolling with half advantage is never bad (it's always strictly better than a straight d20 roll), which is what we want.

As for which method would work best, I'm not sure. I think Tanarii's has the nicest curve, MaxWilson's simplifies Tanarii's method without changing the curve too much, but mine feels like the easiest to actually do. They all have their own awkward bits, to be sure. Now that I think about it, though, you could do Tanarii's method in one step if you rolled 3d20, but one d20 is a different color. Take the highest/lowest of the two that are the same color, then compare to the remaining d20. This would actually make Tanarii's method perhaps the easiest one to do, as well as having the nicest curve.

[Tanarii]

This would actually make Tanarii's method perhaps the easiest one to do, as well as having the nicest curve.
What we did for Lucky was always have one die that is the Lucky die. Then in a disadvantage situation you knew which is the lucky die that is always compared last. We ignored the Sage/Crawford ruling on Lucky, because unnecessary and frankly doesn't match raw or common sense.

People that only have 2 d20s may need to borrow a dollar and run to the store counter real quick.:smallamused: