Hi

I'm trying to create a somewhat decent CO strategy vs a good reg on the BTN. I want to have some hands I shove, raise/call and raise/fold to a shove. My question is that if we are using nash equilibrium what are the frequencies to my raise/call and raise/fold and how do we find the frequency? If we take this spot as an example 9handed 20bigs 12.5% antes, folded to the CO who raises to 2bb, BTN is a good reg who 3bets to 5bb 13% of the time. No icm considerations. So basically thus far I am shoving most +ev hands but I want to induce raise/call with the of my range 6%~, as my raise/fold range I choose some weaker hands that flops decent that I am going to fold to any 3-bet(these hands are too weak to shove pre anyway or breaking even). I have created a strategy which looks pretty decent but I would like to know how we should adjust in theory, what our raise/call to raise/fold ratio should be so I'm not over or under folding my range. I'm gonna show you my range and the values and hopefully someone can help me with the theoretically optimal ratios.

Thanks

Can't you just put this into HRC/ICMizer/Snapshove/Pio, set the software to "ChipEV calculation" and specify the ranges of each player?
It's really laborious to go through and calculate the EV of each hand in your range. Software will do all the calcs for you almost instantly. I'm pretty clueless about playing 20bb deep, but I think it's probably profitable to 4-bet jam the small pairs and most aces, isn't it?

I'm using HRC to see the shoving ranges etc but I want to induce with some hands as I said in OP. Now if BTN shoves as I mentioned I also know what hands to call. What I wish to know is how many hands I should raise/fold with. For instance, lets say we are raise/calling with 99+,AQo+,ATs+,KQs and raise/folding with 98s(4 combos), obviously we are under folding where leaves room for us to be exploited. Therfore I wish to know how many hands I should raise fold. Sorry if I don't explain my self properly, if you have any questions feel free to ask. Thanks.

There isn't a specific ratio or frequency of raise/folds you should be aiming at, because the pot was still multiway when you first opened. i.e. You opened a bunch of hands that are +EV with 3 people to act, but then the BTN 3-bets with hands that should be +EV when facing a CO open, but he also considers that the blinds are still to act. When the action comes back to you, you have to work out which hands are +EV continues vs BTN's strategy and which are not, given the price you're getting.
Note that you'd have a different strategy if the 3-bet came from the BB, since then you could call in position more often, because equity realization is easier. When you're OOP, you can't do quite as much calling. In short, the ratio or frequencies that you defend depend upon the exact situation, and it's close to impossible to solve it by hand, because the maths is not at all simple. You have to have some hands that can flat call the 3-bet, and some that will should be clear folds, but I wouldn't know where you draw the line, as I'm unfamiliar with playing 20bb deep OOP in a 3-bet pot.
A software solver is your friend for this kind of thing. I think Pio, SPF, and MonkerSolver sell solutions for exactly this kind of thing (20bb deep), but you can presumably compute it with GTO+ or hack together a reasonable continuance range with the other software I mentioned. e.g. Look at the pot odds and estimate how much of their equity your "close decision" combos will realize. If those hands don't "play well" vs BTN's range, just fold them (or in some cases, 4-bet jam as a bluff, if they block or have equity vs villain's calling range). I wouldn't worry too much about "overfolding". With some hands (like A7o), you'll just "know" that it loses money as a call, so you won't call.