10nl 6max Th9h - 3bet pot turn implied odds math.

[Dex]

Edit: Reworded things to make more sense, although I can't edit title. I guess this is much more about the EV of calling purely to improve my hand even with so little behind. I'm hoping the math makes sense tho, in terms of understanding whether even a play that looks this bad can be profitable.

Hey all. Despite playing since 2008 this is the first time I've reviewed the EV in a hand and profitability on a call in such a way, so I'd appreciate it if people could look over the hand and my work, and point out any mistakes I've made. I'll give a quick overview of the hand and Villain's range, and then the math. Which BTW, I do not have an advanced degree in. What I do have is a week's worth of codeine, paracetamol and antibiotic intake with almost no food, so there's every chance of a epic math fail.

Villain is 23/17 over 178 hands. Has only 3bet once over 64 opportunities but this was also from the big blind. PTR has Villain tracked as a 3.24BB/100 winner at 10nl over 216k hands. However, over 40k hands at 25nl, he is a 2BB/100 loser. As Villain has played such a large number of hands it is safe to assume he is running a HUD, in which case I look around 24/21 and have been isolating a lot of limps from the fish and two loose passives in front of me. Probably hasn't noticed me get out of line as 1) I likely haven't and 2) He will be multitabling, although I wish I had checked how many.

I very much doubt my preflop call and flop float are ideal, but once I get to the turn I am assuming villain's range for continuing to bet is QQ+, AsQs and I've thrown in AdQd cuz sometimes he'll bet the flop with something that hits the turn so he continues to bet. On the turn I have 28.47% equity vs this range. I appreciate this is a very tight range but once he double barrels that big in a 3bet pot, I can't see his range being much wider than that.

PokerStars No-Limit Hold'em, $0.10 BB (6 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

saw flop

Villain (BB) ($10)
UTG ($18.25)
MP ($19.80)
CO ($8.60)
Hero (Button) ($10)
SB ($13.40)

Preflop: Hero is Button with 10, 9
3 folds, Hero bets $0.30, 1 fold, Villain raises to $1.10, Hero calls $0.80

Flop: ($2.25) 5, 9, 2 (2 players)
Villain bets $1.40, Hero calls $1.40

Turn: ($5.05) Q (2 players)
Villain bets $3.90

Shoving the turn vs the range I have put Villain is a losing play - effectively shoving $7.5 into $12.55 without the odds. As gross as this seems (given it will create a $12.85 pot on the river with $3.60 behind and a villain I expect to shove 100% of the time, giving me $3.60 to call on $16.45), I want to look at if there's any profit in calling to improve only with so little behind.

Assuming I call, am I correct in analysing this by thinking that I am calling $3.90 on the turn to win the $5.05 in the pot and the $7.50 Villain has behind before betting? As long as my intention is to fold any river I do not improve on?

If despite the odds on calling a river shove I will only call if I hit a T, a 9 or a heart*, and acknowledging the times I hit 2pr/trips/a flush and lose to a flush or full house, does the work below make sense?



* Obviously getting a price of $3.60 to win $16.45 calling becomes a smaller mistake, and putting myself in this spot would be gross, as stated I'm using this hand as an example to understand how accurately I have analysed the math of my implied odds and profitability.

Essentially, I found that vs the range I put Villain on, shoving is a losing play and will not be breakeven until Villain folds to the shove 22.8% of the time or more, which clearly will not happen. By contrast, calling purely to improve seems to show a profit. Am I right?