Quote from Kotath >>

they likely will have already developed it somehow over the course of playing long enough to be that level of player... 

 what do you mean

They are making a joke. A player is the person at the table. A character is the one gaining levels in the game.

The game already gives players something when they hit level 20. If they went single class, they will get a powerful capstone feature. You don't need to give them something additional at 20 any more than any other level.

If the characters continue to play at level 20, you could certainly make an Epic Boon that granted Legendary Resistance if you wished.

monsters tend to have legendary resistance to make up for the terrible action economy.  they have it because a typical group can cast 2-3 high level spells in a turn, and if they fail certain saves. the fight is over.   in addition there are plenty of magic items that give very powerful bonuses akin to legendary resistance.   Giving it to players is cool for the awesome factor, but would unbalance fights that are already past the breaking point.

Quote from gabric >>

monsters tend to have legendary resistance to make up for the terrible action economy.  they have it because a typical group can cast 2-3 high level spells in a turn, and if they fail certain saves. the fight is over.   in addition there are plenty of magic items that give very powerful bonuses akin to legendary resistance.   Giving it to players is cool for the awesome factor, but would unbalance fights that are already past the breaking point.

I've given a player legendary resistance before, but it recharged once every 3 in game days.  So if said player blew it during a dungeon crawl, that was it.  It's not as broken as one would think.  Like all things a player has, it just is all about how tactical they use it, and if they refuse to use it at all until that one life changing event?  Then it still wasn't broken, they horded a precious resource to use.

As a DM, I do caution against any sort of "NOPE, DOESNT WORK" type button.  That being said, at level 20, most of those already exist.  You're the most powerful beings in a realm, most characters never SEE level 20 besides maybe some one shot type situation, so screw it.  Let them be powerful.  Have fun.  Game balance at that level doesn't exist anyway.  You can throw multiple ancient dragons at a level 20 party and their odds of survival are generally pretty good, so why not. 

As a reward for getting to level 20? absolutely not.  As a reward for a quest or something while continuing to play at level 20? possibly.

Please no.

—a DM

It's just not really necessary.

Legendary Resistance is given to boss monsters so that a single bad roll doesn't just bypass the whole fight. It means that it's likely going to take a couple of rounds for the PCs to work through the legendary resistance and start imposing major debuffs. It means they can do all the terrible cool awful awesome stuff that makes them boss monsters before they're dead.

PCs don't have this problem. Their lifespan, in terms of rounds of combat at the table, is way greater. A PC getting paralyzed for one fight is bad, but they'll get to do cool stuff in the next fight. And they'll have friends who can do things like dispel magic, greater/lesser restoration, and hit the bad guy with a big stick until they lose concentration.

I'm tempted to make the Indomitable feature (fighter) into effectively legendary resistance, and maybe similar things for other martial classes that tend to fall behind at high levels, but the basic purpose of legendary resistance is so in a fight against a solo BBEG you don't win by stunlocking the BBEG.

I've actually considered deleting legendary resistance on monsters, and instead giving them special legendary actions that remove status effects.

Legendary Resistance is already a kludge for boss monsters because the game has so many save-or-suck mechanics that they needed to give boss monsters an out or every single fight against a solo boss monster would end in 1-2 rounds. It'd be rather self-defeating to give the kludge meant to level the playing field on behalf of the monsters to the very group (player characters) against whom the kludge is there to level the field in the first place.... and at the stage when the PCs are at their most powerful. That'd be like Bobby Fischer asking for Knight's odds against some rube who plays chess in the local park.

I would definitely give my players that, although not immediately at level 20, and I would do it via Epic Boons so they still have to earn it. My players still have a long way to go though before they get there.

Not giving boss monsters legendary resistance wouldn't make the fights that much shorter, it would just make them boring because the boss wouldn't actually do anything while you were beating it senseless.

Hmm.... just out of curiosity, I glanced through the CR 17+ monsters I had access to.  The overwhelming number of spells and abilities that monsters have access to involve just raw damage, not Save or Suck abilities.  The lich is an obvious exception. Dragons and some large fiends have frightening presence, but that's something I hope level 20 characters would have answers to by now. 

There's abilities here and there that are SoS, and most named monsters have at least one, but overall, I don't think that most monsters really rely on the same kind of abilities PCs do.  So, even if you gave a player access to Legendary Resistance... it might not matter that much, just because of the different tactics employed.

It would make challenging the PCs that much harder. 

Just because monsters have a feature, doesn't mean PCs have to have that feature. It sounds fun but it reduces the threat level by a large margin and would turn the game into whack a mole weapon damage only fights.

The thing about save or suck is that they're most effective when used by the side with more actions, because their value is equal to the value of the actions prevented, and the actions of a CR 20+ monster are generally higher value than the actions of even top level PCs. If you want to hose a level 20 PCs with SoS, I suggest Mind Flayers and relatives, a squad of 5xMind Flayer, 5xIntellect Devourer is a nominally medium difficulty encounter that could mushroom into a TPK depending how the initiative goes.

So I give it as a potion. If you wanted to, you could make a random magic item table for the rarest of items, and see if players get this, or anything else you put on the table. And just like others have pointed out, you would give legendary resistance to players when they are of lower level and dealing with a big threat where they don't have time to get stronger to defeat the foe. Having and using it that way makes it special to the players.

Potion of Legendary Resistance

That would be a horrible magic item. It should have a minimum duration of one hour, if not eight.

Yeah, 3 times in 1 minute is pretty unlikely on the player end of things.

A one minute duration actually makes it more powerful.  Since you know it's not going to last beyond a single fight, there's no reason to ever choose not to use it.  With an eight hour duration, it will force players to think about whether or not they actually *need* to make that saving throw or whether it's an effect that they can afford to simply take.

I'd also put in a limit that drinking more than one potion within a 24 hour period causes 10d10 Force damage to the drinker, which ignores damage resistance and immunity.

Pros and cons; it's easier to use, but more likely to feel wasted if the DM either metas and doesn't throw saves at the player (which technically could count as it "working", but likely won't feel like it) or if there's just not enough saves to throw at the player before combat is over.