Pretty much every d20-game uses a d20 roll to determine initiative at the beginning of an encounter. Also, pretty much every d20-game has some instances in which a natural 20 gets a special treatment (e.g. critical hits, auto-success).
Are there notable interesting examples of games featuring a special benefit of a natural 20 for initiative? What is this benefit? Are there common house rules in games without such a feature?
Some thoughts to explain where I am coming from with this question: As far as I am aware, no such rules exist for the games I have played so far (mostly DnD 3.5 and upwards). This question plays with the idea of using the card drawing initiative from Savage Worlds in DnD 5e, and I find the aspect of the joker particularly interesting. If initiative is rolled separately for every round, granting advantage on ability checks, saving throws and attack rolls for that round does sound like a nice little unpredictable factor in an encounter. However, if initiative is fixed for the entire encounter, this would surely be over-powered. I still like the general idea, so I am looking for similar rules and rulings that might inspire a good house rule.