Hi, I was looking at this spot and thought it might be somewhere hero could print money due to overfolds.

I gave villain a 13% 3bet range from the sb vs button and wanted to construct a 4bet range given the scenario at hand.

https://gyazo.com/be023b0aeda0bec0d349819f42b5580a

^ this is the range I gave hero and we have 53% raw equity vs a 13% 3bet range.

I left out A,T and other A combos due to hero being dominated most times if called and left hands like low Ace combos for honestly board coverage.

I understand Value should be a key component but wanted to see if the range I gave hero is good or should we have hands like T9s in?.

Any feed back is welcomed

cliff note, I should say I tried justifying some of my 4bets from the BB lol

Should be linear and tight... like 99+, AQ+, KQs, KJs, AJs+

So get rid of a5-a2, KT/K9

Ok, Thank you I guessed value heavy would be the right answer but thought it might be a little wider.

Now for hero button 3bet vs cutoff open - I would guess linear again but hands like k9s A5s become reasonable candidates then again maybe at lower stakes its just about value.

Poker snowies "selection" do seem reasonable but I would assume they are slightly tighter then necessary

for btn vs co and assuming co rfi like 28% you could do something like 11-15%, though if you were playing "optimally" a lot of hands are mixed

Unfortunately you can`t cold 4bet just because you have 50% equity, that`s not how poker works. If you push on 51% equity your opponent is gonna fold every worse hand and continue with better, which means your equity realization is gonna suck.
What you can do is calculate which range your opponent should defend (about 4%).
and assuming he raises, how much equity you need to profitably call his shove(about 40%).
and then you calculate how much he wins if he bluff shoves and thus how much you can bluff 4bet(he loses 32bb if we call and he wins 31.5bb if we fold. Nice numbers, yay.

I did all of that and you can call his shove with 3.1-3.5%(TT is barely in) and you can bluff a 1:1 ratio.
So we have TT+,AK as value and we can get whatever works best as bluff for the remaining 3.5%.
We want good blockers, but also good playability and equity vs our opponent if he decides to call(JJ,TT,AQs and some other suited hands could call). The latter is important wheter opponent decides to call or not, if he only raises we keep 4betting smaller and smaller until he decides he has odds to have a calling range.
We could have AQs,AJs,ATs,KQs,99,AQo(not every combo) and some mix of Axs and SCs until we reach 3.5% bluffs.

And we end up with a 7% range, which is actually similar to the one you posted.
One big limitation with this model is that we are ignoring what happens when villain calls, I used a 2.5 - 9 - 20bb bet sizing, and it`s possible that at those sizes villain simply doesn`have enough hands to profitably make a calling range, but if he does, then TT is surely out of our range, since it doesn`t realize eq well and it`s only making a tiny profit when it calls the shove.
We are also ignoring blocker effects, but whatever. that`s really cumbersome to calculate

Thanks for the math I tend to go with what seems logical in my brain.

I wasnt going by raw equity and get it in obviously, I just thought about the spot and would assume villain is over folding a bunch so thought we could mix in some weaker holdings as a 4bet bluff.
Id assume 99+ is getting it in depending on villains perceived % though.

Would also assume hundreds of top regs have looked at this spot and come to the conclusion that a linear range is best and not to get out of line.

a linear range has nothing to do with not getting out of line here. We are "bluffing". It`s just that since we don`t have a call range we can pick our best folding hands as bluffs and our range ends up being linear. It has nothing to do with not wanting to bluff. If we had a calling we should still bluff almost as much with hands like Axs SCs and some A grabage etc like when we 3bet.
as for not having a call range, it has to do with the pot odds offered being terrible, there`s not many hands that can pay 9bb to see a flop they are not a clear favourite, while not even closing the action
Btw, I did the math back then and, long story short, we can cold 4bet 13,33% of the original raiser`s range for every position, half of it for value(as in, it will call the shove), and half of it as bluff(wont pay the shove)
the numbers are slightly different for every position tough, in particular the "AK/QQ now can value" jump between CO/MP