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Just using this hand as an exercise for my own benefit. Beginner/pedestrian thought process to follow.
Am I an optimist in wanting to put KhQx and AxKh in the villain's range? I mean, surely if KJ (or KJs) is in his range so is all of KQ preflop? Or is that a hand we expect will check on the flop? AxKh is more of a flimsy guess, but if AhKh is in his A range on the flop, I don't see why AhKx and AxKh couldn't be in his C range at least some of the time. Probably more AhKx which means none of them as the Ah comes on the turn.
I'm thinking if these hands are in his range this is a slight nudge towards shoving, while it probably still comes out as a call. Also if KJ (including KJo) is considered in his range, wouldn't he also play ATs? (Renton's small stakes starting hands suggest KJs and ATs being open hands in fifth position and on - thinking about villain having KJ (any flavour) here might be seeing MUBs). ATs I think could be a C hand on the flop if it's in his preflop range (bet/fold).
Anyway, if I were to put a range together I would exclude KJ and AT and it would look like this:
AA(3), QQ(3), 55(3), KhKx(3), KhQx(3), AQ(9)
Against this range you're 63/37 favourite.
If I include KJs(4) I include ATs(1) - 58/42 favourite
If I include KJo(12) I include ATo(2) and QTs(1) - 51/49 favourite
If we shove on the first range and he folds AQ, KhKx and KhQx while calling all sets we'll own 55 and be looking for 1 out against AA or QQ.
We pay $172 9 times (-$1548), win $128 15 times (+$1920) and win 29.5% of $414 9 times (+$1099). So that's -$1551/24 - around $65 positive EV from shoving. We're even +EV here if called only by AA,QQ. So this all hinges on whether not KJ truly is out of the villain's range here.
Same math - adding in KJs (calling) and ATs (folding).
We pay $172 13 times ($-2236), win $128 16 times ($2048) and win 25.7% of $414 13 times ($1383). That's $1195/29 = $41 positive EV from shoving.
Same math - adding in KJo (calling) and ATo (folding) and QTs(folding).
We pay $172 25 times (-$4300), win $128 19 times ($2432) and win 24.3% of $414 25 times ($2515). That's $647/44 = $15 positive EV from shoving.
Of course all our EVs from shoves improve if he calls with any hand that we're ahead of other than 55.
I guess the question then is - is this the best EV we can achieve. We can achieve better EV if we
1) Lose less money to stronger hands
2) Win more more from weaker hands
-while avoiding
3) Losing more to stronger hands (impossible, we're all-in)
4) Winning less from weaker hands (impossible, we already calculate with them folding)
5) Having weaker hands bluff us out of the pot
6) Having weaker hands become stronger hands and extract value from us where they would have folded the turn
River: Pot $166, behind $124
Narrow range - If the river is a:
Heart (not 5) - 9 cards: 6 combos are now flushes so we are beaten by 12 and ahead of 12 combos
Jack - 3 cards: 6 combos are now straights so we are beaten by 12 and ahead of 12
Ace - 3 cards: AA is now only one combo, AQ is 6 combos and a better FH. We are beaten by 10 combos and ahead of 9 combos
Queen - 3 cards: QQ is now only one combo, AQ is 6 combos and a better FH. KhQx is now 2 combos and trips, but we still beat them as we have a FH. We are beaten by 10 combos and ahead of 8 combos
Tc - 1 card: We have the nuts
Any 5 (including 5h) - 3 cards: We have a full house. We are beaten by 7 combos and ahead of 15 combos
Anything else - 24 cards: We are beaten by 6 combos and ahead of 18 combos
On the 24 + 3 + 1 cards where we're clearly ahead we want to extract value from worse. While a T gives us the whole stack of all AA and QQ hands - and probably also 55, the main question here is if AQ and 55 will call a value bet on a blank. KK and KQ will fold almost certainly. Betting here will increase our EV if worse hands call a lot. If checked to a bet in the range of $60 will probably be called by a lot of AQ hands. On this board we have to call any bet.
On the 12 cards where we're about even we don't really want to call off our stacks to KhKx or KhQx hands that improved to a straight or a flush. Calling here will reduce our EV for the whole line, but we may have to do it. The question is how often he'll bet top two or lowest set with a flush or a straight on board. If the answer is never we could conceivably just fold on these boards. He'd have to bet for value 12/12 combos and bluff more than 8/12 combos before it is profitable to call. The only other option here is if he only bets 6/12 that beats us and is willing to fold not only AQ(9) that we are ahead of but maybe also some of the AA/QQ that he doesn't bet. If he's ready to fold AA/QQ every single time, then it's slightly +EV to shove when checked to on this board - if he calls even 1 of the 6 combos then we're better off checking behind.
On the 6 cards where we're slightly behind I just don't like the situation. Would he bet here with KK? Probably not, but that's just 3 combos and the 2 combos of KQ just improved to trips and the 3 combos of 55 just improved to a FH. So if they shove, we beat 5/15 hands in the betting hand range and have to call. If checked to - would any hand that we beat call any bets, even a small one when an A or a Q comes? We're talking KK, KQ, 55 here. Maybe again a $60 or so bet will be called by 55, and probably not too many checks from hands that beat us.
I honestly don't have a firm handle on if playing the river is more or less EV than just shoving the turn, but it seems worth mentioning that there aren't that many blanks in this hand. And shoving is almost certainly most profitable if we can rule KJ out of the villain's range.
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Originally Posted by daven
