I know there are other threads that deal with this, but i decided to see what the reroll % was for the Bug Luck hat from 2012 because all the other threads have different %

Overall I killed a boss 200 times

Trial 1: Boss: Meathead
9 out of 100= 9%

Trial 2: Boss: Keeper
17 out of 100= 17%

So my overall reroll % was 13%

This was done with BIG LUCK. The one with 2 3 leaf clovers