# Is this Homebrew Advantage rule broken?

I know about this suggestion. Mine is an even further extension of that, and I'm asking about whether there are any further issues and whether I've fixed Lucky.

I find the way 5e handles multiple forms of Advantage disappointing.

It has prioritised "simplicity" so far that it removes a lot of strategic options from combat—specifically the fact that a second source of advantage grants no benefit, and having lots of advantage is entirely negated by a single disadvantage (and v.v.).

Would this variant rule cause problems?

Variant-Multiple sources of Advantage or Disadvantage.

For each source of Advantage or Disadvantage, roll an additional d20. Then, for each source of Advantage discard the lowest current die, and for each source of Disadvantage discard the next highest die.

Variant-Lucky Feat with multiple sources If a character with the Lucky Feat rolls with any form of disadvantage (and chooses to use their Luck point), then they roll an additional die and discard any single die of their choice.

This reduces down to standard Advantage or Disadvantage, if there's only one source of (Dis)Advantage.

It uses this version of Lucky+(Dis)Advantage from the Sage Advice Compendium:

If a DM wants advantage and disadvantage to play their normal roles even when the Lucky feat is used, here’s a way to do so: roll two d20s for advantage/disadvantage, roll a third d20 for Lucky, eliminate one of the three dice, and then use the higher (for advantage) or lower (for disadvantage) of the two dice that remain.

And it reduces down to this suggestion, for the case of one Advantage and one Disadvantage.

I imagine that the conclusion is likely to be "same as the answers to this suggestion, only more so."

But I want to check there's nothing I've overlooked and that I've fixed the problem with Luck.

Examples:

3 Advantage (Roll 4 dice, take the highest):

4, 6, 7, 18 would become 18.

3 Advantage 3 Disadvantange (Roll 7 dice, take the middle):

3, 5, 6, 10, 14, 20, 20 would become 10.

2 Advantage 4 Disadvantage (Roll 7 dice, take the third lowest / fifth highest):

1, 4, 8, 13, 17, 19, 20 would become 8.

• How would this houserule interact with features that require you to have disadvantage or advantage on a roll in order to work? Would having 3 sources of one and 2 of the other allow both kinds of features to work? Similarly, if a feature lets you forgo advantage on a roll, does this remove only one source, all sources, or something else entirely? Mar 31 at 13:14
• FWIW, here's a quick AnyDice program to model the effects of this rule from a purely probabilistic viewpoint. I haven't explicitly included the luck mechanic, but it's basically equivalent to one extra level of advantage (except situationally slightly more flexible, since they player could choose to discard some die other than the lowest). But I agree that the main effects of this change are likely to be in areas other than the raw probabilities (e.g. game complexity, player incentives, etc.) so this is just provided as an aid for further analysis. Mar 31 at 14:48
• Here's another anydice program where you can adjust the number of adv/dis and get the curve. Mar 31 at 14:51
• Is this a rule that you and your players are interested in amending? Does everyone at the table agree that they'd like something 'more'? Mar 31 at 16:02

## 4 Answers

I tend to agree with the other answers and comments saying that allowing advantage and/or disadvantage to stack risks slowing down the gameplay.

Such mechanics can work in some systems and contexts — there are entire rules-light RPG systems whose core task resolution mechanic boils down to "list every narrative circumstance that could give your character an advantage here, then roll that many dice and take highest" — but the advantage mechanic in D&D 5e is deliberately designed not to allow this kind of circumstantial bonus stacking. Before breaking such a deliberate design decision, I'd recommend discussing it with the entire group you're playing with and making sure that eveybody's OK with it, and I'd also consider playtesting it in a quick one-shot game or two and having another discussion afterwards before adopting it for a longer campaign.

That out of the way, let's look at the mechanical effects of your suggested rules. To help with that, here's a simple AnyDice function to model your mechanic:

function: advantage A disadvantage D { result: (D+1)@(A+D+1)d20 }


All it does is simulate rolling $$\A+D+1\$$ dice, skipping the highest $$\D\$$ and taking the next highest. It doesn't explicitly simulate your luck mechanic, but that's in most cases equivalent to simply adding one source of advantage. (It's slightly more situationally flexible, since a player could in principle choose to discard some die other than the lowest. But if they want to roll high, as they usually do, then they won't.)

Anyway, here's what jumps out at me:

• Yes, your modification to the Lucky feat fixes the problem noted in this answer to the earlier question. In fact, it makes the feat strictly weaker than in vanilla 5e by eliminating the ability to spend a luck point to turn disadvantage into super-advantage. I cannot comment on whether nerfing the feat like that would be a good or a bad thing, except to note that if any of your players currently have the feat, you definitely should discuss it with them.

• As you note, your mechanic matches vanilla 5e behavior in the common cases where there's at most one level of advantage or disadvantage, and not both at the same time. Thus, if players did not actively seek out advantage (or disadvantage for their opponents), your homebrew rule would likely make a difference relatively rarely. But of course they do, and will likely do so even more enthusiastically under your proposed rule.

• In terms of the average result, stacking multiple levels of advantage (or disadvantage) gives diminishing returns. But the effects are far more pronounced at the high (for stacked advantage, or low for disadvantage) end of the d20 range. In particular, for the first 5 or so levels of advantage, the probability of rolling a natural 20 is almost directly proportional to the number of advantage levels you have, and only diminishes slowly with further levels. This makes stacked advantage super valuable for characters aiming for crits.

• When rolling with both advantage and disadvantage, your mechanic results in a distribution that is peaked at the middle (biased up or down depending on which side dominates) with a very low chance of either very low or very high rolls. In the limit with $$\N \to \infty\$$, with $$\N\$$ levels of both advantage and disadvantage, it effectively tends to a "take 10" distribution concentrated at 10 and 11, with a very small chance of rolling much above or below those numbers.

(In particular, as noted in Thomas Markov's answer, both natural 1 and natural 20 are very unlikely results when rolling with both advantage and disadvantage, unless you have a lot more of one than the other.)

Regarding the last point above, traditionally in D&D such low-variance mechanics have been reserved for low-risk, low-pressure situations where characters are allowed to take their time with the task at hand. That seems like the exact opposite of a tense combat or challenge situation with multiple counteracting influences imposing both advantages and disadvantages. It thus seems counterintuitive to me that stacking a combination of advantage and disadvantage should make the outcome of the roll more predictable, as happens under your proposed rule.

If anything, if I wanted to implement stackable (dis)advantage in my game, I'd therefore prefer a rule where simultaneous sources of advantage and disadvantage would cancel out (much like they do also in vanilla 5e), so that e.g. three sources of advantage and one source of disadvantage would equal $$\3-1 = 2\$$ levels of advantage. This would also simplify your house rule slightly (since you'd always take either the highest or the lowest roll) and reduce the average number of dice rolled.

Ps. As a slight tangent that I can't resist including, one could even consider rules where simultaneous advantage and disadvantage would make the roll more swingy, favoring very low or very high rolls over the middle. One way to implement such a mechanic, at the cost of some further complexity, would be as follows:

1. Start with one die. For each level of advantage or disadvantage, add one extra die to the pool.
2. Roll the dice. If there are no levels of disadvantage, take the highest roll. If there are no levels of advantage, take the lowest roll. (These are shortcuts; applying the more complex rule below would give the same result in these cases.)
3. Otherwise skip as many of the highest(!) dice as there are levels of advantage(!) and take the next highest die. (Equivalently, skip as many of the lowest dice as there are levels of disadvantage and take the next lowest die.) Call the value of this die the "anti-roll".
4. Take the die whose value is furthest away from the anti-roll and let it be the result of the roll. (Usually this will be either the highest or the lowest value rolled.) If there are two dice with distinct values equally far away from the anti-roll (one lower and one higher than it), set both aside and take the furthest of the remaining dice, etc. If there are no other dice left, the anti-roll itself will be the result.

Perhaps surprisingly, this complex and strange-sounding mechanic produces very nice distributions of results and achieves its goal of favoring the ends of the d20 range when rolling with simultaneous advantage and disadvantage. Whether it would actually be fun to use in a game would, of course, be another matter entirely.

• To clarify, are skipped values included in the fourth step of your tangent? Apr 4 at 10:28
• @L0neGamer: Yes, the "skipping" in step 3 only applies to that step. (I considered phrasing step 3 e.g. as "choose the $N$-th highest die as the 'anti-roll', where $N$ is the number of advantage levels for this roll plus one", but I felt such phrasing would've been a bit too mathematical.) Apr 4 at 23:12

### Frame Challenge: Complicating the Advantage system is not desirable.

I'll quote from a post I made several years ago on What issues could arise with this Advantage/Disadvantage Variant?

One of the aims of the advantage/disadvantage system is to remove the payoff for "bonus-scrounging". It isn't desirable to have your players constantly trying to find one more reason to get a little plus in their column; that has historically led to a lot of friction, book-diving, and absurd arguments to realism ("I'm standing on the table so I have a high ground bonus against him!"). By making only one advantage 'count', your players are more likely to focus their attention on finding one strong narrative (or mechanical) reason they should have advantage, and then stop looking and roll the dice already.

Your proposed rule partially brings us back to that place -- when there are X disadvantages in play, the players are suddenly strongly incentivized to try to find at least X advantages to balance it back out. Instead of looking for one decent source of advantage, they're hunting for enough to balance things out, and you're back to jumping on tables.

Your suggestion would have an even bigger impact than the one in the linked post, because with your idea, a player is incentivized to hunt down extra sources of advantage on every single roll, not just when there's disadvantage at play -- who wouldn't want to take the highest of three dice if they have the option to do so? Four dice? Five dice?

Restoring the "strategic options" comes at the cost of keeping the game moving. Watching a friend try to justify one more source of advantage generally isn't nearly as much fun as having your own turn come back around faster. The simplicity is a feature, not a bug.

Is your idea mechanically broken? Well, I don't really know, but if it makes the game play worse at the table, that's busted on a deeper level than mere game mechanics.

Like, if the whole table wants to do it, then fine, the Fun Police aren't going to kick down the door and storm the place. But if you're the DM and just thinking to yourself, "Hey, I don't like this!" and you've decided to implement a house-rule that has a strong potential to make the game feel worse to your players, it may be worth really considering why the rule exists in its current form.

### With one source of disadvantage, it takes 6 sources of advantage to have the same chance at a natural 20 as a straight roll.

Using this short anydice program:

ADV: 0
DIS: 0

output {1+DIS}@(1+ADV+DIS)d20


If we set advantage to 6 sources, and disadvantage to 1 source, our probaiblity of rolling a natural 20 is 5.72%:

I can't really say if this phenomenon is "broken", I guess that is up to you to decide, but the important observation for you to consider is that a single source of disadvantage severely neutralizes the effect that multiple sources of advantage has on getting a natural 20. 2 adv/1 dis gives only a 1.4% chance at a natural 20.

• Any idea why it shows 0% on getting 1, 2, or 3? Just such a low % chance that is doesn't display, or something else? Mar 31 at 15:42
• @BaconyRevanant Rounding. The probability there is less than 0.005%, so you can expect a 1 less than 5 times out of 10,000 rolls. Mar 31 at 15:46
• OK, I assumed that was the case, but was unsure. Mar 31 at 15:54
• To be more exact, the probability of rolling at least 7 ones out of 8 rolls is about 0.000000598%, So that's about about one 1 every 160 million rolls. Apr 1 at 2:10
• @ThomasMarkov could you add the rounding clarification to your answer? Apr 2 at 23:49

Thomas Markov’s answer does a good job of showing the probabilities, but doesn’t really explain the ‘why’.

To actually understand this, you have to understand how the normal advantage/disadvantage rules work.

Rolling 1d20 has an equal chance of each value from 1-20 coming up. Rolling 2d20 produces a triangular probability curve with a peak at 21. Rolling 2d20 and then ignoring one die also produces a triangular probability curve, but with the peak at 20 (for advantage) or 1 (for disadvantage).

With your system though, things get a bit strange. Equal amounts of advantage and disadvantage actually produce not a flat uniform distribution like is the case with the standard rules, but instead a bell curve peaking at about average values. This is because in your system, advantage is more likely to eliminate low rolls than high ones, and disadvantage is symmetrically more likely to eliminate high rolls than low ones, so most of the time what you have left will be about average.

Where it gets really complicated though, is when you have unequal numbers. You still get a bell curve, but it’s an asymmetrical one with a different positive and negative standard deviation and the average is not right at the halfway point.

This, in turn, leads to two specific mathematical aspects to your approach that are non-obvious to most people without a background in statistics:

### Both advantage and disadvantage have diminishing returns.

If you have one source of disadvantage, then adding one source of advantage shifts your most likely roll from 1 to 10-11, effectively adding 50% to your chance of success. Adding a second source on top of that only shifts it to 14, which is only effectively about 20% extra. Adding a third then brings you to roughly 15-16, only a 5-10% better chance. The same works in reverse as well, and this feeds into the next point.

### Any source of disadvantage makes is exponentially less likely to roll a 20 overall, and any source of advantage makes it similarly less likely to roll a 1.

If you have six sources of advantage and none of disadvantage, you have a whopping 30.17% chance of rolling a 20. Adding just one source of disadvantage drops that all the way to 5.72%, roughly one fifth of what it would be without that one source of disadvantage. This is huge for combat, because a natural 20 is a guaranteed hit, and a natural 1 is a guaranteed miss.

Overall, whether this is an issue for you or not is up to you. It reduces overall randomness within the game though (you are more likely to see average rolls more frequently), which is generally a factor in making the game shift more towards abstract strategy than realistic tactics, but it does not reduce it that much.

That by itself would not be enough for me to dismiss such a rule outright, but the overall complexity it introduces (touched on in other answers) and the impact it would have on game pacing.