I’m on the BB with A heart,Q square
The button opens with 3BB. SB folds. I call.

Flop : Q,9,2 Pot 6.5BB
-----------------------------------------------------------------

I've calculated that there are 40 hands (3%) that are ahead at this stage.
AA, KK = 12 hands
QQ, 99, 22 = 7 hands
Q2, Q9, 29 = 21 hands

I'm first to act with a stack of 75BB. Would It be profitable to shove all in?
Villain will only be dealt a hand that beats mine 1/32 times… I’d win 200BB in folds for every overpair/2pair/set villain is dealt at which point I’d likely lose my 75BB, giving me 50BB profit (66%)...

My Questions…
Is my reasoning correct? or would considering villains range increase that 3%?
What is the most profitable play during this scenario?
What would you do?

Am I correct in thinking that in such situations I can calculate that it would be profitable to shove all in if my stack size is less than
((100/Percentage of hands villains hands that are ahead)*Pot) divided by 2
in the above example i’ve worked the maximum stack size to be 108BB?

wtf is a square

but to answer your question, no, because you are making a play where only better hands call unless villain is a drooler. If they have complete trash they fold to a standard bet, but a standard bet has the advantage that worse hands may look you up.

Btn raised and you flat called. You didn't 3 bet with a hand that's ahead of the standard btn raising range. Ok - not great but OK.

Now you flop top pair - a marginal way-ahead/way-behind hand. BTN already was aggressive once.

How do you make the most money but lose the least? That's the concern because your hand is marginal - you may be way ahead, or way behind.

If you donk bet your opponent can fold easily if they had nothing, so you miss some value, but they can raise you as well and then what do you do?

Basically this hand has good showdown equity but can't stand a re-raise, so IMO OTF you look to check/call.

If you improve on the turn (A, Q) then you can check/call or check/raise. Same on the river.

If you check flop/turn and villain slows down, you CAN bet the next street but I wouldn't look to get too tricky here - too easy to get trapped if you ARE beat.

So assuming the villain plays a standard line:
flop - check/call
turn - check/call or check/check
river - (if turn was x/c) check/call or if turn was x/x then bet/fold or check/call

Honestly I'm fine with just checking and calling it down to the river. It only gets risky then if on the river btn decides to get tricky with a shove, then you take a read.

This is a very good hand - not a marginal hand (on this board) - to get a high winrate you can play it very aggressive (or check/call it down and make your 1BB/100.

By the way: never donk shove - worst play possible (but donk/reraise or check/raise)

Without standard reads or history I agree, this hand is much stronger then marginal. Some things that will change the strength of this hand is villains attempt to steal - LP and your Fold to Steal.

After you flop TPTK what is his cbet%, if its high...say above 70%, a check raise would probably be the most profitable action. If it was less then 50% I would probably donk.

Much of this hand is player dependent on how big you want this pot to balloon. Against a spewy fish, I may possibly play for my entire stack...but against regs/nits, I would try to get to the river cheap as possible and possibly Vbet river if villain shows a lot of weakness...I tend to nit up when I play pots oop.

Also, flop suits would help but since you didnt specify I assume it was rainbow.

What are the suits of the board cards?

The 'only' way that I would ever shove here is if I had the 'right' opponent and the board made it look like I was on an obvious draw. Even with that being said there aren't too many players around who would be willing to call 70BB into what was a 6bb pot.

The issue here is if they do call you are behind so much more often than not in my opinion. You are risking that you will win this pot (right now) 11 times before someone calls and beat you .. that's a lot in poker. And if you consistently make plays like this then your opponents will just wait until they can beat you to call.

You have a hand that 'some' people raise with. It's a good hand and you got a good Flop for your hand. Again unless you have the 'right' opponent, you want to give the pre-Flop raiser a chance to bet until he stops betting.

At a minimum you should get 2 bets of value here. One by calling your opponent's c-bet on the Flop and one on the River if your opponent checks the Turn. That doesn't mean your opponent will call your bet on the River, but you will be able to make one.

If your opponent bets the Flop, let him bet the Turn also. If your opponent checks the Flop, then you should lead the Turn for a good sized bet. (probably close to pot) and then go from there.

Poker is all about getting value. Shoving here will give you a good case of 'value owning' yourself since your opponent can 'play perfectly' against you. He is either ahead or behind and will more times than not make the correct decision .. which in either case probably 'cost' you chips in the long run. GL

I've seen this exact same thread before, you got all the answers you needed last time OP.

Circles, triangles and dodecahedrons. I' sure he would have mentioned if he had a backdoor square draw.

I maintain that this is a marginal hand.

Yes, the BTN range is wide but you didn't do anything to narrow it by 3-betting pre. BTN may have opened with Kings or Aces, Nines or Twos. But there are many more hands that still have draws here like TJ, KJ, as well as 9x and 2x.

You don't tell us the board suits - a major problem in your OP, so we don't know if flush draws are out there. If the board has two clubs and he has TJc, you're seriously behind.

Bottom line - top pair is ALWAYS a marginal hand. Overall I agree with answer20's strategy. Don't overplay your top pair.

"But I had top pair" is a terrible bad beat story when you call his all in or shove all in to his set.

"Profitable" compared to what? Definitely compared to folding or just checking it down.

Figuring out whether something is profitable isn't how you decide if it's the right thing to do. You need to figure out the MOST profitable action. Here it's not shoving allin, because you have a hand that will be called by worse if you make smaller bets. By shoving you lose your chance to do that.

You're approaching the game like a computer. You've done all this irrelevant math about the situation but you haven't even considered the basic foundation of what's going on in the hand or attempted to apply any logic or reason to it. Surely villain does not open 100% of hands on the button. So you already need to cut his range by half or more, and consider that it very likely does not have Q2 or 92 in it.

You also failed to consider the multitude of other options you have here, all of which can be used exploitatively against various types of opponents, both pre and post flop. You flopped top pair top kicker on what appears to be a fairly dry board (you also did not mention whether there are flush cards out there, you never know when someone is drawing to the "square" flush after all) so this is an extremely profitable situation just by default. Almost any button you click here other than fold is going to be profitable. You have to find the one that is MOST profitable. And it's not going to be donk jamming for 10x pot.