Does anybody use any rules regarding rolling two nat 20s when a player rolls with advantage? Or two nat 1s when at disadvantage?

Quote from Stormknight >>

Nope, though I have only seen double nat 20 on advantage happen once while DMing. Seeing double nat 1 on advantage is funnier. :)

 Nat 20 and Nat 1 on disadvantage is even funnier.  Especially when you have a DM who gets creative with fumble rules.  I have had sooooo many swords/axes/staffs thrown at me.

I personally would grant them double critical damage per my house rule (roll a crit, you roll again to confirm and double the already doubled damage, roll 3 in a row and you insta kill whatever it is, yes even the BBEG)

My crit fails rules are already fairly rough so I would probably not double up on it. Depending on a weapon or cast they roll a d6 and a 1 or 2 they hit themselves, a 3-5 and the weapon flies out of their hand 10 feet in a direction and on a 6 they break their weapon. 

With casting depending on the spell they hurt themselves or a party member at half damage. 

I don't know if you *need* to do anything to have a special rule.

I've had my character critted twice in a single combat while taking the Dodge Action.
His first action was "Dodge" to avoid damage, GM rolls two 20s with Disadvantage.

We all stare awstruck.  I say "well this kind of thing happens."

Next turn, I Dodge again because I already took more damage then my low level character really wanted to take....   GM *again* rolls two 20s with Disadvantage.  I turned to him and said "You have the devil's own luck."

In my Tyranny of Dragons came our GM has amazing luck...  we've barely survived battles that were supposed to be easy because he critted every turn for multiple turns.

Quote from csheets416 >>

I personally would grant them double critical damage per my house rule (roll a crit, you roll again to confirm and double the already doubled damage, roll 3 in a row and you insta kill whatever it is, yes even the BBEG)

My crit fails rules are already fairly rough so I would probably not double up on it. Depending on a weapon or cast they roll a d6 and a 1 or 2 they hit themselves, a 3-5 and the weapon flies out of their hand 10 feet in a direction and on a 6 they break their weapon. 

With casting depending on the spell they hurt themselves or a party member at half damage. 

 Our DM has similar crit hit/miss rules, however when we roll the d6 for miss, all players are valid targets, and possibly NPCs if present.  With sword of sharpness I managed to cut my own head off (the rolls went that way - nat one, nat 20 to confirm the crit, d6 roll to see what gets lopped off - oh there goes my head)

I also almost killed/banished our Paladin - nat one on a crossbow bolt that I had just cast banishing smite to use.  Did over 70 damage and he was (luckily) just over the 50 HP limit for the banishing not to work.  He has returned the favour a few times, launching various swords and axes at me, the axe almost got me killed.  I went the rest of that gauntlet/boss fight on 25 HPs or under.  Fighting Zuggtmoy with 19 HPs at the start of the fight was not fun.  Luckily, the only damage I took was from the monk's nat one staff hit.  He rolled low thanks the gods.

My husband had this just last night, and then on his second attack with advantage(barbarian yo) , he got a 16 and a 20. Haha. It was amazing enough with the basic rules, but we also give out star stickers for nat 20s, so that was cool!