# pre-flop 3bet concepts

So I'm only 5 months in to my poker journey, and I'm working on my pre-flop 3-bet concepts.
I play online micro sit and goes and the odd micro MTT.

My current understanding is we three bet for a few reasons;
1. put opponents in hard spots,
2. Isolate weaker players,
3. reduce number of players in the pot,
4. try pick up pot pre-flop.
I also understand that some of these situations call for merged ranges and others polarized ranges. And that my bluffs should be at the bottom of my ranges and not hands i want to call with but should still have some pliability post-flop

My question relative to how many bluffs in need to mix into my 3bet range.
My math is if theirs an open raise is of x, and i 3bet 3x.
so the equity equation is something like (3x)/(BB+SB+x+3x), assuming no antes and everyone else gets out the way.
if x is from the range of 2bb to 3bb, the equity is about ~63% to ~67%, so if villain folds that amount or ends up losing the pot its +ev.

Any corrections, advice or points in the right direction would be much appreciated, especially if theirs math to back it up. Thanks :)