Maximizing Expectation on the River: $50 NL

[Kazlic]

MP 3 is a total calling station. Fold to flop bet is 22%, fold to turn bet is 30%, and fold to river bet is 100%. Basically that means she's calling with hopeless draws and then folding on the river.

Button is a tight player.

$50 NL Texas Hold'em

Seat 4 is the button
Total number of players : 10
Seat 1: MP 2 ( $51.25 )
Seat 2: MP 3 ( $34.22 )
Seat 4: Button ( $54.70 )
Seat 8: UTG ( $46.92 )
Seat 7: Hero ( $56.10 )
Seat 10: MP 1 ( $24.66 )
Seat 3: LP ( $36.72 )
Seat 6: (sitting out) ( $29.65 )
Seat 9: UTG + 1 ( $49.35 )
Seat 5: Small Blind ( $47.70 )
Small Blind posts small blind [$0.25].
Hero posts big blind [$0.50].
** Dealing down cards **
Dealt to Hero [ T [img]/images/graemlins/spade.gif[/img] T [img]/images/graemlins/club.gif[/img] ]
UTG folds.
UTG + 1 folds.
MP 1 folds.
MP 2 folds.
MP 3 calls [$0.50].
LP folds.
Button calls [$0.50].
Small Blind folds.

The calling station and the tight player have both limped to me in the big blind. I likely have the best hand and could raise, but I'm willing to give up a small pre-flop expectation for a potentially large post-flop expectation. Plus I'll be out of position for the rest of the hand, so if I raise and get called, I might have trouble knowing where I stand for the remainder of the hand. For these reasons I decide to lay in the weeds and just check.

Hero checks. Pot is $1.75

** Dealing Flop ** [ 8 [img]/images/graemlins/diamond.gif[/img], 5 [img]/images/graemlins/diamond.gif[/img], 2 [img]/images/graemlins/club.gif[/img] ]

A seemingly safe flop for my hand. I almost certainly have the calling station beat, so I decide to bet right out and let the calling station do her thing.

Hero bets [$2].
MP 3 calls [$2].

Excellent! Plan is going along just great.

Button calls [$2].

Whoa whoa...I didn't want that. The button is tight, so he's not going to call on that flop without something. I have to proceed very cautiously now; I may not have the best hand.

** Dealing Turn ** [ T [img]/images/graemlins/diamond.gif[/img] ]

A rather interesting turn card. I now have top set. Still, with three diamonds now on the board, I have a perplexing decision. If the button called on the flop with a smaller set, I just made a great outdraw and should continue betting. On the other hand, if the button was drawing on the flop and just made a flush, I'll have to fill up to win the hand. (I honestly wasn't exactly sure what to do at this point.)

There is $7.75 in the pot now, so I decide to make a smallish $3 bet. If neither player has a made flush the bet doesn't allow them a free card, and in the case somebody made a flush, if they get cute and decide to slowplay I have just "set the price" be allowing myself to see the river for only $3. I'm open to criticism for this bet - it's possible I should have made the bet larger or simply checked.

Hero bets [$3].
MP 3 folds.
Button raises [$6].

Okay, the calling station has mysteriously folded, and the button has made a minimum raise to $6. Unfortunately for him, (in the words of Ed Miller), the button has just made a big mistake and given himself the worst of both worlds. He has announced the strength of his hand ("I have a flush!") and he has allowed me the odds to continue. I only have to call $3, and with almost $17 in the pot, I'm getting direct pot odds to call with my 10-out draw. What's better, since the button has told me he has a flush, I likely have huge implied odds here. The call was a no-brainer in my mind.

Hero calls [$3].
** Dealing River ** [ 2 [img]/images/graemlins/diamond.gif[/img] ]

A great river card, but also somewhat of a mixed blessing. I have a full house, but with 4 diamonds now the board, the strength of the button’s flush comes into play. If he originally limped in with, say, Q [img]/images/graemlins/diamond.gif[/img] J [img]/images/graemlins/diamond.gif[/img], he might suspect that I just outdrew him and might not pay off a big bet. If he has the nut flush, he's unlikely to fold regardless.

This is where I need help. Taking Skalansky's advice to heart (from "No Limit Hold'em: Theory and Practice"), I seem to think I should worry about the situation that is going to win me the biggest pot, namely, the button having the nut flush. That is to say I COULD bet $5 into the $20 pot and probably get paid off even if the button has Q [img]/images/graemlins/diamond.gif[/img] J [img]/images/graemlins/diamond.gif[/img], but I stand to make more by making a big bet and getting called only if the button has the nut flush. I won't get called as often, but I stand to make more money in the long run; I'm maximizing my expectation.

Still, how big should I bet? The button has $46 left in his stack, but the pot is only $20. If I go all-in I'll be seriously overbetting the pot. Still, the move has to be given consideration, since I didn't see how a player could fold the nut flush in this situation. However, I know the button is tight, and it's possible that he’s weak-tight. Would a weak-tight player be unwilling to call an all-in for fear of a full house (I know weak-tight players often let their fears get the best of them).

How would YOU play the river?

And any all advice is welcome (even on the earlier betting rounds). I'll post the hand results in a couple days so I don't get "Result based" feedback.


Thank you for your time,
Kazlic

[jakerc]

"EV = (pcall)(S) where s = the size of your bet or raise."

so let's say we have two options: we can bet either $15 and hope he stays around, or go ahead and go all-in for your remaining $50.60 (if my math is right). let's say he will call the $15 bet 90% of the time (probably more). so the EV the $15 bet is $13.50 (15x0.90). now if we go all-in, lets go on the conservative side and say he's only calling 40% of the time. in that case our EV is $20.24. drop that number down to 30% and our EV is $15.18. so even if hes only calling our all-in 30% of the time (i think this is very unlikely if hes flushed), in the long run we still make money. so with that being said i would probably push and cross my fingers. (btw my math may be incorrect cause im math impaired, someone correct it if i am).

[Kazlic]

Jakerc,

Thanks for your advice. If you read my post carefully, you'll notice the button only has $46 left in his stack, so that's the effective stack size.

[Kazlic]

Anybody have any thoughts?

Bet pot? Go all in? Bet half pot?

[ReptileHouse]

My gut says to bet his stack size. I'll have to do the math to figure if that's theoretically correct.