I'm trying to brush up on my theoretical game and I'm trying to go over a few basic concepts. Could someone please point out there areas where am I incorrect or where I have incorrect thinking?

Game is FR 9 handed NLH 100bb

I open UTG to 3bb with a range of AA-77,AKo-AQo,AKs-ATs,A5s,KQs-KTs,QJs-QTs,JTs-J9s,T9s,98s (128 combos, or 9.65% of hands)

I get 3bet by the CO to 9bb and it folds to me. CO is risking 9bb to win 4.5bb so if I fold > 66.6% of the time, he makes instant profit. So I need to continue with ~42 combos (1/3 of my range) to deny that.

But a lot of the pre-flop range charts I see are advocating changing how many combos you defend based on the position that 3bets you, which logically makes sense (because a BTNs 3bet range is going to be more combos than MPs 3bet range), but I don't understand it from a theory perspective.

Isn't ~42 combos the optimal amount of combos to defend vs that sizing?



Further, if after the 9bb 3bet, I 4bet to 22bb, I am risking 22bb to win 10.5bb so if CO folds > 67.69% of the time I make instant profit, so he has to defend > 32.31% of the time.

So, what ratio of bluff combos vs value combos should I have if I'm risking 22bb to win 10.5bb?

Does this mean that I should have ~67.69% value combos and ~32.31% bluff combos?

Finally, does anyone know a quick trick for figuring out what % of your range you have to defend, given a player is risking x bb to win y bb?

Thanks for reading

If you want to call some 3bet pre you need to call 33% of the times because V will win some % of the time post flop
You need to defend more vs BB then MP because when MP 3bets he needs folds form 8 more players and you to take it down pre but when BB dose that he only need you to fold so the rest of the table defend some % of the time so you dont have to.

When you 4bet you just need enough hands that can call 5bet jam that you dont let V auto profit with any two.So if you 4bet to 22 and V jams.You need to call with at least so ,if Im not wrong, 30 % but you want to be able to call little bit wider because his 5bet bluffs still have lot of equity when you call.So you can 4bet something like 50/50 or 60/40 60% of bluffs

Poker is a multi-street game. Counting pre-flop combos alone won't give you an optimal solution, because the game doesn't always end pre-flop. Some hands obviously do better than others when you don't fold pre, because they literally have more equity. You have to estimate/calculate which range will be profitable against the range that villain is playing, and that requires an understanding of equity realization/post-flop playability, blockers, fold equity and all the other stuff that makes poker so complicated.
To put it another way, the game of poker is not about preventing your opponent from making an 'instant profit'. It's about maximizing your own expectation. Intuitively you know you can profitably continue at a higher frequency if villain's range is wide, but you have to fold at a high frequency if his range is tight/narrow. Working out exactly which hands are profitable against different ranges is the hard part. Combo-counting only gets you part of the way there.

Villain can't make an "instant profit" just because you fold > 2/3 of the time. The earlier he is to act, the more he has to be worried about getting called/cold 4bet by someone other than you. However, every time it folds around and you call, he still has equity in the pot. So ignoring others - even if you call exactly 1/3 of the time, he's profiting from 3betting you. My (possibly very incorrect) judgment then is that if he's 3betting in an earlier position, you'd fold more than 2/3 of your range, and for late positions you'd fold less than 2/3 of your range.

Quick question... Why do you include A5s and not A3s or A4s? Aren't those hands better since it's less likely that somebody has 36 or 46 than 56 when you make the wheel?

I think the answer is you use the MDF formula, which is defending around 33% for 3x raises and around 28% for 4x raises.

Here are some youtube videos that will hopefully address your question (not my videos):

https://www.youtube.com/watch?v=bcehGMu-RkU
https://www.youtube.com/watch?v=i1gePijI_4s&t=1s
https://www.youtube.com/watch?v=GOJxVsxT0Fg

MDF formula is only a hint, even in theory the ranges difer from minimal defence, more in practice. You can easily overfold to 3b pre oop or defend more than MDF ip.

I expect you are playing in the low stakes games and so my advise is to not bother with any of the above calculations. You don't want to shoot for GTO in these games. This villain probably has an amazing hand. All you need to do is continue with; hands that beat his range come showdown, and bluffs in conjunction with how often he will fold.

MDF is useless if you don't take into account equity and postflop play. If you fold 2/3 of the time to a 3bet you will lose money against anyone who plays decently.
Read Applications of NLH, even though he talks about MDF, he points out the obvious thing about sometimes calling correctly and still losing the hand due to future cards.
Therefor, you need to call more often than MDF in most situations to make him unable to bet ATC.

EDIT: And all this "indifference" and "not allowing him to bet ATC" isn't even strict GTO, it's just a simplification that we like to make cuz we don't know wtf we're doing in this game.

I am going to, thank you.