# Homework hand: KTs on button, turn two pair [long]

#### F Paulsson

##### euro love
(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.)

Hi guys.

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.

THE HAND

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]
groente99: folds
w4ters: folds
FPau: raises \$2 to \$3
szakall: folds
ova13: calls \$2
*** FLOP *** [Jd Kc 5h]
ova13: checks
FPau: bets \$5
ova13: calls \$5
*** TURN *** [Jd Kc 5h] [Th]
ova13: checks
FPau...

ASSUMPTIONS

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:
• TT,55,ATs,K7s+,Q9s+,J9s+,T9s,AJo-ATo,KTo+,QTo+,JTo
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:
• TT,55,KJs-KTs,Q9s,JTs,KJo-KTo,JTo
~5% of all total hands. My equity: 36%
The hands he'd call with, then, are*:
• ATs,K9s-K7s,QTs+,J9s+,AJo-ATo,QTo+,JTo
~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 , where x is the EV of him calling and y is the EV of him checkraising.
1. x = 0.82 (\$15 + \$15 + \$16) + 0.18 ( -\$15) = \$32.
2. 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:
• TT,55,K7s+,Q9s,JTs,KTo+,JTo
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:
1. The river bricks, and
2. 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.

Conclusion
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.

/FP

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.

#### NineLions

I did actually read to the bottom, FP. Not that I checked your calculations along the way though.

How often do you work through homework like this, even without all the text?

If I ever get back to focusing on one game I'll keep this as inspiration.

#### F Paulsson

##### euro love
How often do you work through homework like this, even without all the text?
Generally speaking, all hands throughout a session that I confuse me enough to warrant looking closer at. This was one of the few that seemed "tricky" enough to make a post about. A lot of them are very obvious as soon as I look at them for more than 10 seconds, and probably wouldn't have been suitable for posting. A hand of this magnitude comes along maybe one per session, which roughly translates to me doing a big work like this once a day. Of course, the work is a lot faster if I don't have to write down and explain and edit my thoughts too much, heh. The calculation part of this homework took maybe five minutes using Excel and PokerStove.

#### c9h13no3

##### Is drawing with AK
I like a turn bet. A lot of the hands that will call you are draws, and scare cards can come on the river that will reduce our ability to valuebet. If we get check raised, we can probably fold pretty safely.

So yeah, bet/fold turn, check behind on river. Mebbe a spot for a thin value bet if you knew this guy was a bit poorer a player.

#### F Paulsson

##### euro love
I like a turn bet. A lot of the hands that will call you are draws, and scare cards can come on the river that will reduce our ability to valuebet. If we get check raised, we can probably fold pretty safely.
You disagree with the range I assumed him capable of checkraising with then. What range do you propose?

#### dj11

##### Legend
Since you have gone this far, could I ask you to detail the reverse implied odds for your audience. Also perhaps how you came to them being considered 'severe'. I must admit ignorance.

#### c9h13no3

##### Is drawing with AK
You disagree with the range I assumed him capable of checkraising with then. What range do you propose?
TT,55,KJs-KTs,Q9s,JTs,KJo-KTo,JTo

Only the only hand there that we beat is JT and other KT's. Also, you wouldn't put AQ in his range? You think Q9 would call a flop bet?

And at least at the limits I play at (can't speak very confidently about 100\$ NL), villains very rarely c/c and then c/r with holdings weaker than ours.

If villain has a hand like JT, KQ, JQ, then we're missing out on a ton of value by not betting the turn. And if say a Q, A, 9, or J rolls off on the river, then its going to kill our ability to value bet, even though we may still have the best hand.

This board is just too wet on the turn to give a free card IMO.

#### F Paulsson

##### euro love
TT,55,KJs-KTs,Q9s,JTs,KJo-KTo,JTo
We're 36%, or 1.78:1 to win vs. that range, though, and even if he checkraises us all-in, we're getting 123:77 to call, or 1.6:1. It's not quite enough to warrant a call, but if we add in any chance at all of him bluffing, or even semibluffing with a heartdraw or an OESD, our odds are good enough to call.

Bet/folding seems out of the question to me.

Regarding Q9 and AQ: I had to cull his range down some, and I took out the likely hands he'd 3-bet with preflop. The fact that Q9s is a bit of a loose call on the flop (honestly, I'm not even sure it's -EV; I probably call with a gutshot and a backdoor flush draw on this flop pretty often vs. a button raiser for the chance of stealing the pot on a later street or hitting a high implied odds hand) kinda makes up for taking AQ out of the equation.

If villain has a hand like JT, KQ, JQ, then we're missing out on a ton of value by not betting the turn.
I'm getting value out of these hands on the river, though. He's either going to bet them or check them to me. Like I said, I'm usually not happy to put in three bets with two-pair vs. a non-idiot, so against the top-pair type hands, it's a matter of whether the pot sized bet happens on the turn or the river.

If a scare card comes on the river, it takes away our ability to value bet, this is true, but it also saves us money the time he has the better hand (which is a not negligible percentage of the time), and it may encourage him to bluff more often; in fact, vs. an aggressive opponent, we might hope for a scare card on the river. You raise a valid point, but I believe you're overestimate the impact a scare card will have on our EV. Some impact, yes, this I will agree with.

Betting the turn is the better play vs. passive opponents. Vs. aggressive opponents it really comes down to whether or not he'll float me on this kind of flop often, because the value that I need to make up if the turn check is going to be worth it has to come from him bluffing.

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