PokerStars - $0.50 NL FAST (2 max) - Holdem - 2 players
Hand converted by PokerTracker 4

SB: 170.1 BB (VPIP: 100.00, PFR: 57.14, 3Bet Preflop: 0.00, Hands: 8)
Hero (BB): 284.76 BB

SB posts SB 0.5 BB, Hero posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has 7 9

SB raises to 2.5 BB, Hero calls 1.5 BB

Flop: (5 BB, 2 players) J 6 T
Hero checks, SB bets 3.62 BB, Hero raises to 9 BB, SB calls 5.38 BB

Turn: (23 BB, 2 players) Q
Hero bets 12 BB, SB calls 12 BB

River: (47 BB, 2 players) 8
Hero checks, SB bets 34.58 BB, Hero calls 34.58 BB

SB shows 9 T (Straight, Queen High)
(Pre 72%, Flop 80%, Turn 91%)
Hero shows 7 9 (Straight, Queen High)
(Pre 28%, Flop 20%, Turn 9%)
SB wins 57.32 BB
Hero wins 57.34 BB

Really botched that one imo

Yeah I agree, I'm still learning, should I have just shoved river?

Flop, checkraising that hand is not going to be hugely profitable unless you have a very specific gameplan on the river. Some players may overfold rivers a ton vs a BB going C/XR/B/B. Other than that, as a default, that's a very marginal hand to xr flop with. It has poor equity and will put you in a lot more marginal spots than clearly good ones. It's never a mistake to save OOP flop semi bluffing for stronger draws.

OTR, we can expect him to have about 45 combos in his range, it's not unreasonable to assume 12 or 13 of those will be AK and K9. It's reasonable to expect he raises half of his 16 AK combos ott, you can take one off for random stupid flats pf and improv 3 bets otf, so estimate that at 7.5 AK combos. Same story with K9, except he starts with 12 combos, since we have a 9. Some people might argue that a few more nutted straights will raise this turn, that may be true but it will only subtract one or two combos from their river range that beats us, so it doesn't matter that much. Just round it down to 12, due to fringe background sht the population does. There are 12 combos out of 45 that beat us. But there are around 25 9x that we push/chop with. (you can even lower the estimate of combos that beat us down to maybe 10 or 11, due to a notable portion of K9s not calling flop, can't say off top of my head how many would actually call there, but it's probably >80%, with maybe 5% three betting.)

If we push vs 25/45 combos, lose to 12 and beat 8, our effective equity vs his calling range is less than 50%, so we don't want to vbet.

On the other hand, the pot is laying 2.38:1 and we are only losing 26% of the time, making it an easy call. (.26*-34)+(.17*81) ≈ +5bb. So wp on the river.

To be clear, checkraising this hand is actually quite bad in terms of EV. XCing is far superior, in large part due to how often people will fold IP going R/B/X/F.

Thank you for such a detailed analysis!

Whoops, believe there needs to be added a +((25/45)*23.5) term in that EV estimate above, because we get half the current pot every time we push. It doesn't change anything though, just makes XCing EV a lot higher.

I'll work the math out tomorrow because I'm in bed on my phone, but if we shove the river are we profiting more BB by pushing him off the chop ever? Or are we just punting off because he never folds and when he has a better hand we stack off.

I guess theoretically, if the bet size equals the pot, getting him to pay off with worse is worth 2 pots. A chop is worth half the pot, while pushing him off a chop is worth one pot. So pushing him off a chop is worth .5 pots more than chopping. That means, for pushing him off chops to be better, in the case where he is calling with worse, we would have to be pushing him off at least 4 times as many chop combos as combos of worse that he would have called with, for it to be considered a bluff. Otherwise it's a value bet, by definition, because most of the value is coming from worse calling, not getting him off of chops.

In practice, that play seems extremely bad because 1) you're not getting him off many chops 2) you will get him to fold a lot of worse if you start seriously raising the bet size (overbetting changes the above numbers, it actually makes it even worse). Bluffing a one card straight there would just be forcing him to play about as perfectly as he would if he could see our cards.

This isn't even touching on what a GTO-like range would look like. Bluffing shoving hands OOP with XC EVs of 13bb is badly deranged, from a GTO perspective.