Just played a hand vs a villain who was giving me heck in 3BPots... I ended up shoving this hand and wanted to justify/checkup some math real quick:

Hero ($58.10)
Villain ($93.50)

Dealt to Hero K J

Villain raises to $1.50, Hero raises to $5, Villain calls $3.50

FLOP ($10) 2 7 8

Hero bets $5.50, Villain raises to $13, Hero raises to $53.10 (AI)

After running a tightish calling range we have ~16% equity (range is meh given dynamic).

If anyone can double check this formula I'd appreciate it... Trying to first solve break-even fold% and then for his required raise/fold frequency:

=== break-even fold% ===
X = His fold %

0 = EV(fold)*Fold% + EV(call)*Call%
Call% = 1-Fold%

EV(fold) = $28.50 <-- Current Pot Size
EV(call) = $116.60*16% - $47.50 <-- Final Pot * Our Equity - Our Shove

EV(call) = $-28.84

0 = $28.50(x) - $28.84(1-x)

x = ~50%

=== raise/fold frequency ===
The value/calling combos in the above range are 2% of hands according to pokerstove... This he only needs to be bluffing w/ 2% of (1:1 for the 50% from x above).

Given his If the villain is opening 75% of buttons and folding to 25% of 3bets, then he gets to the flop with 75% * (1-25%) = 56% of all hands possible for UNLIMITED HOLD THEM.

2%/(56%-2%) <-- Bluff Combos / (Flop Range - Value Range)

Thus he only needs to raise/fold as a bluff w/ ~4% of the hands that get to the flop?

=== Why here and not Math forum ===
Assuming he's raise/folding here, I don't mind the shove, but what types of adjustments should we be making to our 3betting range assuming we don't mind variance?
> 3bet wider for value as he's calling more.
> Stack off lighter when we hit?
> I'm lost in GTO land...

As I am lately spending alot of time on EV; this post has drawn my attention.

Imo
call% (and corresponding fold%) is immediately connected to win% and loose % the moment you have defined your hand/range and his hand/range.

I want to say that you first defined his range. And the moment you have done that, you have already defined his call% and such his fold%.

This said; you have developed equations containing win% loss% split% and containing fold% call%.
win% loss% split % = f(hand range opponent)
fold% call% = f(hand range opponent)
I still have to see the first equation that has some parameter X where X is the hand range of opponent that immediately tells us Y with Y being win% loss% split% fold% call% without a program like pokerstove solving this for us

The only possible way to solve these kind of question is by using iterations.
1) define your range
2) define his range
3) stove
4) pop corresponding equity/win-%/loss-%/call-% fold-% in your equations
5) evaluate results

Now, imo decision making in poker is just as strong as the weakest link in it.
With you it are your reads. You said nothing about his 4-betting % and you said nothing about your 3-betting %.
You also said nothing about how frequent you cbet these kind of dry boards and you said nothing about how frequent and how he reacted to your cbet on these kind of boards.
Above this you said nothing about how you would play any other top pair top kicker or better kind of hand on this kind of board.
And another thing is your opponent going to the flop with 56% of all his hands but only calling with the very tight range you described. Meaning you honestly think he would fold any 89o and any better kicker or 910o? Or do you think he stacks here with any 89o or better if you have somekind of PP Ax broadway 3-bet range that cbets tons on these kind of boards and then goes for FE when facing resistance especially when you play your top value range differently then FE range?

To the correctness of your equations I did not looked hard; I have to derive them/ find them somewhere in my notebooks again as I do not know them by head.

craziness itt
math is idiotic

^ I beat nl200 and I don't even know how to calculate pot odds half the time.

shoving with 15% equity then trying to justify it with EV calcs probably isnt the best way to beat 50nl hu

Sounds like you got tilted and spazz shoved with K high to his flop raise. I didn't even look at the math part.

*facepalm*

Truth Bombs ITT. You don't always get what you want... but sometimes you get what you need.

your math is correct. if he's making your life difficult in 3bet pots, then the shove is fine in a vacuum. gameflow wise it could be bad, if he's not just a huge bluffmonkey.

as far as adjustments, obv 3bet for value lighter, 3bet as a bluff less/never. if villain is going to be calling all his 87o type hands and have to play weakish holdings after the flop, just keep 3betting hands that are going to dominate those hands.

as far as all of the "lol math" sentiment, i dont really get it. its cool if you can beat the games without doing any ev calcs, but just completely brushing math aside like its a joke is pretty absurd.