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57 Leaf Clover basically rolls twice every time you roll for everything. For any item that doesn't gain increased proc chance with more stacks (Ukulele, Missile Launcher, Ranuld's & Kjaro's Bands, etc) it effectively doubles your chance of proccing. The next clover brings you to triple chance, then quadruple, etc, basically multiplying the damage these items do by this amount by increasing the frequency they occur.
It also works on all the other items that stack as well. Sticky Mines, crits, bleeding, stun grenades, etc, doubling their chance to proc as well.
It basically doubles the damage output of ALL of your proc items unless their proc chance is between 60-100%. Proc items make up almost all of your damage output as you progress, so it's a massive damage boost in almost all situations.
It does seem to work wonders on proc chance items though. Stickybombs were destroying everything.
All of that is still amazing, don't get me wrong. Do the maths on Ukulele and you'll find that damage pre-and-post clover are laughably different, especially considering that it seems like Ukelele is capable of proccing MORE Ukuleles.