Homework hand: KTs on button, turn two pair [long]
(After-the-fact addition: My pardons for the length of the post. It's difficult to trim, but I've tried to format it somewhat for readability.)
Not all hands that I choose to study get posted, since a lot of them I sort of just solve and find the answer and then don't bother posting the result of the calculation. In this particular case, though, I figured I'd solve a hand "live" in a post, so to speak. I don't know beforehand what results I'm going to reach, so the reasoning is how my brain propelled me forward. We'll see how this experiment turns out.
Opponent seems typical/decent. 100BB stacks, $100NL.
On the surface, this is a really trivial pot-sized bet (say $15). I have two pair on a drawy board. But at the table, it struck me that I also have a hand with severe reverse implied odds
, that doesn't really want to play a big pot. So I checked, with the intention of calling a river bet (or raising if a K or T came off). If he checked on the river, I'd bet the river. Either way, I'm not happy about betting three barrels into a non-idiot opponent, so it's essentially a matter of whether to get the money in on the turn or the river.
*** HOLE CARDS ***
Dealt to FPau [Td Kd]
FPau: raises $2 to $3
ova13: calls $2
*** FLOP *** [Jd Kc 5h]
FPau: bets $5
ova13: calls $5
*** TURN *** [Jd Kc 5h] [Th]
He defends with 20% of hands. I've shaved off the hands that I think he's likely to 3-bet with, and then culled it some more based on what hands I think he'd have called a river bet with. That range, incidentally, is pretty wide given that it's a steal situation. Finally, I've looked at THAT range and culled it some more based on "what hands do I think he'll continue with if I bet the turn." Most of the hands in the original range that would fold if I bet the turn are hands that are basically drawing dead, so I'm not too worried about giving a free card. In either case, the cost of giving a free card in a small pot is certainly offset by the gain of having him bluff the river with air.
BETTING THE TURN
His range that he continued with if I bet the turn:
This is 12% of all possible hands. My equity vs. this range is 66%.
A checkraise on the turn is pretty much a committment raise and we're going to play for stacks. The hands I expect to get checkraised by are:
~5% of all total hands. My equity: 36%
The hands he'd call with, then, are*:
~7% of hands, my equity: 82%.
So, I figure that about 60% (7 percentage points out of 12 percentage points) of the time, I'll put in $15 as an 82% favorite. And 40% of the time, I'll put in my entire stack (remaining at this point is $77, but it will be $92 total on the turn) as a 36% favorite.
EV = 0.6 (x) + 0.4 (y), where x is the EV of him calling and y is the EV of him checkraising.
- x = 0.82 ($15 + $15 + $16) + 0.18 ( -$15) = $32.
- y = 0.36 ($112) - 0.64 (-$92) = -$18.50
EV = 0.6 ($32) + 0.4(-$18.50) = $11.80
Clearly, betting the turn is a very +EV move. But is checking the turn and calling/betting the river if checked to better?
CHECKING THE TURN, CALL OR BET THE RIVER.
Range that he will legitimately bet presuming a brick (let's say 2d) on the river with if I check now:
EV of him betting the pot on the river and me calling (pot will be $32 and $16 to call): $11.79.
It may seem spooky-similar, but it sort of isn't. The EV calculation on the river makes two assumptions in my favor:
- The river bricks, and
- He bets as much as the pot.
He will often bet less than the pot, which - since I'm the favorite - drags the EV down. Furthermore, the river may not brick. He might draw out on me, or a scarecard such that he just folds might come along. Finally, there's the risk of him being an ultra-slowplayer with Q9 and checking the river to me. When I bet after he checks the river, he checkraises me all-in and I'm knee-deep in shit. This is a very rare event, though, and can perhaps be traded in for the times that I outdraw him on the river and win a huge pot.
I guesstimate my EV on the river to be somewhere between $6 and $10.
The difference is not huge. It's big, but not to the degree that it's not opponent dependent. If I have a very aggressive opponent (who will bluff the river often) checking behind might be best. If my opponent is passive, betting the turn is very clearly best.
I wonder if I screwed up the calculations somewhere. But it felt like a somewhat close decision and it seems I might have been right, so I've passed at least the most basic sanity test.
Did you actually read all the way down here? Really? Liar. DS.
* I realize there's a disparity between the two bottom ranges and the top one, but I screwed up somewhere and missed a hand and now I can't be bothered to redo it; the difference is small.