Question: Developing a 5bet range vs opponents.

I reckon we can start 3betting him very polarized eg. only strong value hands like JJ+,AT+ which dominate his bluffy 4bets and totally weak hands like 78s 68s which are easy to toss when he 4bets.

This way we can 5bet ship pretty much all of the value range, as the fold equity and equity should make it +EV (unless he's calling our 5bets with the QTs, KTs type hands which is even better). I may be wrong though as I am still a fish

But, what I'd ask is why 5bet when we can simply flat his 4bet in position with this entire hypothetical 5bet value range and let him spew postflop when he is dominated?

Well your general plan should be to always 3bet with TT+ and AQ+ for value and pretty much plan to always ship QQ+ and AK and you can extend your value range by shipping AQ and TT and JJ if his 4bet is high enough.

Here it just comes down to some basic math.

Lets say for example your playing nl100 and he opens to 3$ on the CO, you 3bet to 9$ on the BU and he 4bets to 20$. 100BB effective

#1 There is currently 30.5$ of dead money in the pot so our EV when he folds is +30.5$.
#2 We lose 91$ x% of the time. This is how much money we have left in our stack that we risk with our 5bet shove.
#3 We win 30.5+80$ = 110.5$ x% of the time(This is how much money is in the pot + how much money its left in his stack)
#4 Now if he 4bets 9% range and calls off with JJ+AK that's a 3% range meaning he folds 66% of the time and calls 33% of the time.

Now lets say we have AQ which has 29% equity against his calling range. So in the case that he calls we will win 110.5$ 29 % of the time and lose 91$ 71% of the time. So to calculate this

110.5$ * 0.29 - 91$ * 0.71 = 32$ - 64$ = -32$

By this equation we now know that when we are called we lose 32$ on average given our equity whenever he calls.

Now if we are in this spot 3 times then the first 2 times he will fold and he is going to call the 3rd time meaning we win 30.5$ twice and then the third time we will lose 32$ which means that on 3 occasions we will win 61$-32$= 29$.

Now we can see that this is a highly profitable shove given we make 9$ every time we ship against such an unbalanced range.

But what happens in the same scenario if his only 4betting a 6% range? Now we still get called by the same hands but now he only folds 50% of the time. This means that on 2 occasions we win 30.5 the first time and the second time we lose 32$ meaning the EV of the move is -0.75c per hand. Now we see that shoving AQ against a 6% range is slightly -EV.

As a general rule for shoving TT and AQ i would recommend you a 9% 4bet range. This math indeed shoves us it can be profitable even against a lower 4bet range, but it does not consider the rake your going to pay which can be fairly high. It will also be a lot less profitable if he opens to 2.5x and the 3bet and 4bet is smaller, which means there's less dead money in the pot and more left in the stack, basically meaning you risk more to win less. Also him calling your jam with TT and JJ will quickly make your shove -EV as well.

You can run the math and your EV against different range and different preflop sizings off the table to get somewhat of an idea when you can shove certain hands.

You also have to consider your HUD's sample size and the fact that to get an accurate sample size for 4bets by position it will take like 25k hands on your opponent. Those spots really don't come often enough to get those specific stats any sooner. You can always go by feel and game flow and ship it in if you think someones out of line during a particular session.

As for calling 4bets im really not sure its definitely not a part of my gameplan. A part of the problem is he might just check/fold his AKo when he misses which is a total disaster in case you have AA and he will miss most of the time. Calling light is also not my general gameplan unless i 4betted something like 78s and he made the 4bet way to small then i might peel but generally im either shoving or folding.