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This is based on the text in Page 5 of Xanathar's Guide to Everything:

Even if more than one factor gives you advantage or disadvantage on a roll, you have it only once, and if you have advantage and disadvantage on the same roll, they cancel each other.

This would imply that an Assassin Rogue, attacking from Stealth, at a target within 5 feet who was Prone and hadn't taken a turn in Combat yet (3 circumstances that grant Advantage, which I will refer to as "instances granting Advantage"), would still only roll normally against a target who happened to be wearing a Cloak of Displacement (one "instance granting Disadvantage"), and thus wouldn't get Sneak Attack damage.

While this probably simplifies "big" encounters where there are a lot of instances granting both Advantage and Disadvantage, it seems to not reward strategic play at all, and vastly increases the power of the Cloak from being a generally-good tool for preventing getting hit for a few turns to entirely countering Sneak Attack on the first turn, meaning that, compared to a Player, an enemy never has to worry about being Assassinated (1st Turn only) or Sneak-Attacked until their later turns, especially since there is no way to Delay a turn in 5e, which means that, if an Assassin Rogue ends-up going first, they can either move and then Ready an Attack (which is a rather clumsy way to work this) or just attack and lose Assassinate.

I know some DMs whom, instead of just ruling that even one instance granting either counters every single instance granting its counterpart, will count each instance granting Advantage, and compare that to each instance granting Disadvantage, and determining which remains after all have been cancelled.

In essence, it can be distilled to the three mathematical expressions, where a is the total of instances granting Advantage, and d is the total of instances granting Disadvantage:

$$ \begin{align} a - d > 0 & → \text{Advantage} \\ a - d = 0 & → \text{Normal} \\ a - d < 0 & → \text{Disadvantage} \end{align} $$

In the case of the above example with the Assassin Rogue, this would mean that, after the single instance of Disadvantage cancels with one of the three instances of Advantage, meaning that the attack ends-up going-through with Advantage because \$3 - 1 = 2 > 0 → \text{Advantage}\$.

How does this houserule change the balance of the game?

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    \$\begingroup\$ Point of note... XGtE in this case is only clarifying what was already put into the PHB in Chapter 7. Also, "Snuck" is an Americanism and it is "proper" to say "sneaked"... \$\endgroup\$ – Slagmoth May 4 '18 at 16:58
  • \$\begingroup\$ @Slagmoth That's fixed, too. Though... "Sneaked-Attacked"... :) \$\endgroup\$ – SeraphsWrath May 4 '18 at 17:15
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    \$\begingroup\$ "Sneak Attacked" is I would say "proper" here, although it would make more sense if the ability was hyphenated, but we work with what he have been given. \$\endgroup\$ – Slagmoth May 4 '18 at 17:23
  • \$\begingroup\$ And some DMs also use double advantage, where you get to make three rolls if the situation permits. \$\endgroup\$ – lynxlynxlynx May 4 '18 at 20:48
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I want to start out mentioning the Cloak of Displacement. It's supposed to mess with sneak attack. Going back several editions, it's done a great job of it. Even thematically, it's very hard to attack a vital point when you effectively have double vision against the target (likely more like multidimensional double vision, but I digress). I don't think you need a way to "fix" that the character couldn't have snuck-attack.

With that said, we're currently utilizing this house rule in a game I'm playing, so....

Generally, it doesn't affect overall game balance

In my opinion, it's less fun, because it's more bean-counting. It very much reminds me of editions from years past where you frantically tried to add various numbers together in order to get to the magic number you needed.

"Okay, I rolled a 7, plus my 6 to hit. That's 13. Wait and I have the plus 2 from charging and another plus 1 because this is my favorite weapon. That's 16. OH OH OH Bardic inspiration! 17!"

Maybe you liked that, but I did not.

In most cases, it's a moot point because you only have one source of advantage and disadvantage anyway. In the rare case that it actually matters and you get to apply [dis]advantage in a case where you couldn't not have otherwise, it's no more or less exciting than any other scenario where you would normally get to apply [dis]advantage.

If this is something you're thinking of instituting at your table, talk it over with the players and come to a consensus. Remember that D&D is, by and large, a bad reality simulator and should not be viewed with too fine a lens, lest you see the frayed threads within.

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    \$\begingroup\$ Notably, a houserule like this also means that class features that grant advantage or disadvantage will have circumstances where one would want to use them, but they'd have no effect - for example trying to use the Protection fighting style for a prone friend against a reckless barbarian. \$\endgroup\$ – Speedkat May 4 '18 at 17:53
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    \$\begingroup\$ @Speedkat yes, but there are an equal number of circumstances where you could get an effect when otherwise you would not. Such as protection fighting style for a friend with a cloak of displacement against a reckless barbarian. (net disadvantage) \$\endgroup\$ – goodguy5 May 4 '18 at 17:59
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    \$\begingroup\$ As the DM for my group I have the same houserule; slows things down marginally but I've noticed a higher degree of tactical thinking from my players. Notably I also embrace optional rules such as flanking to further encourage tactics. Now they have a reason to plan an ambush in which they douse the enemy (non-darkvision) torches, pincer, try to knock them prone and go stab happy instead of just one of those. \$\endgroup\$ – JackChance May 4 '18 at 18:42
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    \$\begingroup\$ @JackChance you should write up your own answer with those details, they will probably get lost in the comments (since they tend to be deleted after a while) \$\endgroup\$ – Erik May 4 '18 at 19:00
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    \$\begingroup\$ Further to the point on bean-counting, it raises questions about what counts as a single instance of dis/advantage, as well as whether redundant instances should stack. For example: The Unconsious condition states that attack rolls against the creature have advantage, but also that they fall Prone and are "unaware of its surroundings". Does that count as one instance or three? The Invisible condition grants advantage on attacks, but attacks against Blinded creatures have advantage, and you also gain advantage for being an unseen attacker. How do these stack? What if you also hide? \$\endgroup\$ – Taxi4Dave Sep 17 at 15:15

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