Hi guys, i was trying to figure out what 3bet % could i have against shortstacks in BW situation. I kinda suck at game-theory-math so please bear with me :D 

Lets suppose that a shortie is opening a 50% range from the btn and he's 4beting 15%. His 4bet range would be 7,5.  For the purpose of what im trying to calculate im assuming that he doesn't have a flatting range, he's either 4beting or folding.

He opens to 2,5bb  SB folds (0,5bb) i 3bet to 7bb and he shoves to 40b.

He is risking 37,5bb  to win  2.5bb + 0.5bb + 7bb + 37.5

37.5 / 47.5 = 0,79

1-a = 1 - 0.79 = 0.21

So we need to defend "only" 21% of our 3beting range

Now, against a 7,5% 4bet range we could call his shove with something like 88+ AQo+ AQs+ which is a 5,58% range.  If we only need to defend 21% of our 3beting range below im calculating how much we could be our total 3bet % 

5.58/ x =  0.21

5.58/0.21 = x 

x = 26.5

x = total 3bet  = 26.5%

Is this correct or did i do something wrong? how would this scenario change if he's not only 4beting that range but he also has a call 3bet range?  If i wanted to have a cold calling range , not only a 3betting range do i still get to 3bet as much as that or we need to 3bet less? 

Thanks!