First of All, Hello everyone its my First Post Here

I have some problem, I dont know how to calculate that kind of spots. The question is about how to calculate whether that check/raise AI is profitable or not ?

It's the Hand

BU: 545 (18 bb)
SB: 545 (18 bb)
BB (Hero): 410 (14 bb)

Pre-Flop: (45) Hero is BB with Q♦ T♥
BTN raises to 90, SB calls 75, Hero calls 60

Flop: (270) 6♣ 8♦ 7♥ (3 players)
SB checks, Hero checks, BTN bets 120, SB folds, Hero raises to 320 (all-in), BTN calls 200

Ok, so its my thoughts, I dont know which thought is correct, or both are uncorrect.

1. If I Jam AI I need 45% of Folding Equity ((320+270+120)/710 = 45%)
I assume hypothetically, I have 25% of Equity vs Villain Calling Range and I Have 25% of Folding Equity.
So 25%+25% > 45%, x/r AI is Profitable.

2. If Villain is Calling me I need 35% of Equity vs his range (320/ 910 = 35%)
I assume hypothetically, I have 25% of Equity vs his range and I have 25% of Folding Equity (should i take it into account ? It's a little bit unlogic because i assume Villain Call me)
So 25%+25% > 35%, x/r ai is profitable.

I hope my problem is understandable.
I will be grateful if you help me.

This looks like a spin so no ICM, if there is it becomes more complicated, but you basically work out how often he calls your jam, what the equity of his range is against your hand on that flop, then it's working out if the chip EV you lose when called and seeing if it's more or less than when you're not called.

Of course, you could just play preflop differently and not get in this mess in the first place

For EV analysis you can’t just add equities (card and fold) since the win amounts for each differ.

The applicable EV equation where hero raise is the decision point is

EV = fe*Pot + (1-fe)*(eq*(Pot + V.Call) -( 1-eq)*H.Raise)

where

Pot = 390: V.Call = 200 H.Raise= 320 eq = 0.25


Set EV to 0 and the break-even fold equity (fe) equals 19.2%.

Hero is in a poker hand and he's trying to determine whether shoving is better than folding. That's the wrong formula, and 19.2% isn't close to the correct value for how often folds are needed.

320 is a lot higher that 19.2% * 390 + 80.8% * 25% * 910.

Thank you for answers, things gone brighter. That's Spin&Go I should Mentioned that.
Can I approach to that this simple way ?
First, calculate EV of Action - x/r AI and if EV is higher than zero, it's better to play x/r AI, than Fold, because Folding is always EV0

when your all in is not much more than a min raise you won't have much fold equity

@OP EASY F

@OP Easy Fold pre flop

Yes you can approach it in a simple way - I can't think of a single situation barring a weird button limps in opening level and we check the BB where a check raise is ever a realistic option if we're playing a spin properly, so think about more important things

Of course it is not common situation, but I want to improve my Poker knowledge and that was a good example for me to understand some aspects. Thank you one more time