I’ve seen and implemented so many house rules in my time that I’ve lost count. I can barely remember any of them, but the rule that keeps coming back is the confirming of critical hits rule in D&D 3.0.
Now, I grumble a lot about D&D and how stupidly power-gamey it can get, so this house rule is a massive example of hypocrisy, but we basically ditched the “confirm crits” rule, which makes the game even more swingy and random than usual.
You see, normally when you roll a critical hit, that guarantees you a hit on the target and you roll again to see if the hit was a critical hit. If that second hit lands, then you’ve critted and all damage is yours for the dealing. For a weapon that only crits on a 20, that’s a 5% chance to even be able to test for a crit, plus whatever the chance is to actually just straight up hit the target at all. This makes chances of crits quite small.
By dumping the need to confirm, suddenly crits happen a lot more often and become far more prone to abuse through stacking abilities like Improved Critical, keened weapons and other things. My character Hextor Francis had a vorpal bastard-sword that after all his crit-focused abilities and magical effects and a 1 in 4 chance of critting and being vorpal, would insta-kill anything with a head that wasn’t undead or a construct. Combining such things with Greater Cleave means that Hex could pretty much defeat and entire army by himself in a single round through constant head-chopping (and he practically did on more than one occasion).
Without the requirement of the second confirm roll, things were a lot more randomly lethal, especially since the rule applied for enemies as well as us players. In a game that was already silly in a number of ways, this house rule decided to drop any pretense of realism and embrace the random for maximum entertainment value.