Hello, I’m a fairly new player who has picked up poker (at least seriously) about a month ago. I’m studying a lot and trying to get a better grasp on how ranges work and interact. This post is my attempt to examine how i would play my range in a hypothetical situation in order to maximize potential profits. It would be very much appreciated if an experienced player pointed out the flaws in my current thinking/understanding of the game and gave explanations and corrections.

Said example is 6max cash game 100bb effective stacks.

Folds to CO, who raises to 3bb
Hero(BTN) – 3-bets to 9bb
Folds back to CO, CO raises to 22bb
Hero calls 13bb

Flop(pot – 45.5bb): 10c 9c 3d
CO raises 20bb

Hero - ?
6 –of 2 + 16 of 1 + 4 of 1
24 combos

My analysis:
Judging by the villains stats and gameplay i put him on a range of AA-QQ(18), AK(16), AQs(4), KQs(4).
My range in said situation is: JJ-77, KQs, QJs.

So the villain has 3*6=18 combinations of overpars(AA-KK), and 16+4+4=24 combinations of high card in said position. 3 combinations of a gutshot draw. 1 combination of a flush draw. 1 combination of gutshot+flush draw.

In hero’s range we have 6 combinations of effective nut hands with which i want to the money in ASAP (TT, 99) in order to make the villain pay for extra cards on his flush + straight draws, and also to make him pay with pocket overpairs.

Now it is my understanding that we have to include some bluffs into our range in order to entice the villain to call. Because if we only raise TT-99 in this spot why would he ever call if he is a competent player.
Judging from the villains fold frequency i want my bluff:value ratio to be about 1.5:1, thus I need 9 bluffing combinations.
They are going to be QJs(4) + KQs(4), because these hands have a chance to improve in case the villain calls. I need one more combination so I will add JhJs (easy to remember red heart+black heart).
Those are all the hands I will be reraising with, and fold the rest of my hands.

Thoughts?

Question:
Is it actually worth including the 1 combination of QcJc in bluffs?
Hero has ~14.2 outs (7 hearts + 4 Jacks + 3.2 Kings) (3.2 kings because 6 of heros combinations have 2 kings and 20 have a single king, so hero’s chance of drawing a king is reduced, so to calculate the average # of kings left in the deck we do this: (2 * 6 + 3 * 20 + 16 * 4)/42 = 3.2, to account for all the villains combos with kings).
Thus in the 18/42 = ~43% of times villain has an overpair we still have an 14.2/(52-5) + 14.2/(52-6) = 61% chance of making the better hand by the river.

These calculations are a little bit rough around the edges(for example when Hero hits straight/flush, not accounting for possible full houses for the villain and so on).

I know there are poker solvers available to figure this kind of stuff out automatically, but i think i learn more from working it out on my own, so i can learn how to do it at the table and fast. Once i get good grasp of ranges on my own i plan on studying solvers to polish it up.

Thank for reading, and all answers will be very much appreciated. And sorry if something is confusing English is not my home language.

Your reasoning seems off

First of all both preflop ranges are flawed, you should have tons of other hands like some AA, some QQ, most AQs, far less 77-99. Vilain also should have tons of TT-JJ and other hands, I won't list the exact ranges because it would be a chore but it seems way off

Postflop CO doesn't raise 20BB, he bets. One can only raise if there is a bet in the present street. The first bet is called a bet.

Then you don't always want to raise nutted hands, here with position and a bloated 4bet pot you absolutely don't want to raise your sets here, you want to call them to protect the rest of your range against the dominating range from the 4better. You do this because you will have no trouble getting the rest of the money in on the turn or river. If Vilain checks turn, you even have the ability to check back and shoves the river easily for about 60BBs in a 85BBs pot

I would advice you to spend less time studying outs and odds and more time refining your ranges and overall strategy and understanding of the game