River Boat vs Probable Flush.. How to Extract?

[redCashion]

Do you min-raise here? Or bigger raise? Or push and hope he has the nut flush and can't get away from it?

PokerStars No-Limit Hold'em, $0.50 BB (8 handed) internettexasholdem.com (http://www.internettexasholdem.com)

UTG+1 ($52.50)
MP1 ($19.50)
MP2 ($19.45)
CO ($28.60)
Button ($29.25)
SB ($48.05)
Hero ($52.25)
UTG ($125.50)

Preflop: Hero is BB with 6/images/graemlins/heart.gif, 3/images/graemlins/club.gif.
UTG calls $0.50, <font color="#666666">2 folds</font>, MP2 calls $0.50, <font color="#666666">3 folds</font>, Hero checks.

Flop: ($1.75) 7/images/graemlins/club.gif, 3/images/graemlins/diamond.gif, K/images/graemlins/club.gif <font color="#0000FF">(3 players)</font>
Hero checks, UTG checks, MP2 checks.

Turn: ($1.75) 3/images/graemlins/heart.gif <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Hero bets $1</font>, UTG calls $1, MP2 folds.

River: ($3.75) 6/images/graemlins/club.gif <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets $4</font>, <font color="#CC3333">UTG raises to $12</font>, <font color="#CC3333">Hero raises to $50.75</font>, UTG folds.

[Pokey]

The river is fine. Min-raise is a ridiculous waste. Take a look:

For the sake of argument, say that villain will call 100% of the time if you minraise, and say that you win 100% of the time when that happens. In that case, your EV from the minraise is $27.75 (the $3.75 in the pot already, the $4 you already put in the pot, and the $20 villain puts in the pot after calling your reraise).

Now, compare that to pushing. (Again, for convenience we will assume that you win 100% of the time when you are called.) When you push and villain folds, you win $19.75 (the $3.75 in the pot, the $4 you already kicked in, and the $12 villain raised). When you push and villain calls, you win $54.50 ($3.75 in the pot plus $4 from your earlier bet plus $46.75 from villain's call). Therefore, if villain calls "C" fraction of the time (0 &lt; C &lt; 1), then your EV from a push is:

EV = C*($54.50) + (1-C)*(19.75)

This strategy is break-even when that EV equals the $27.75 from the minraise, meaning:

C*($54.50) + (1-C)*(19.75) = $27.75

Solving for C, we find that the two strategies are exactly the same when C = 23%; in other words, if villain calls your push just one-quarter of the time, you get more value out of pushing than out of a minraise.

Obviously, there were several simplifying assumptions in my original setup; for example, there's always a chance that villain four-bets all-in if you minraise, and there's always a chance that villain folds even to the minraise. I'd say these two options roughly cancel each other out.

Also, there's always a chance that villain has a better hand, but it's probably fair to say that with any better hand villain is pushing over your minraise, and you're going to call, so you're getting stacked whether you minraise into a super-monster boat or push into a super-monster boat: again, an irrelevant situation.

I'd say the odds that villain has a hand that can call a river push are significantly greater than 23%, and that makes pushing +EV relative to min-raising or any other form of extraction.

Going for the gold is the correct play, here. You got unlucky -- don't change your behavior in a profit-reducing way because things didn't work out this time.

[redCashion]

Awesome Pokey, thanks a ton for the explanation. I listen to Live at the Bike and they discuss this alot, that river pushes shouldn't be judged on a per case basis but on how they work over time. My feeling was that if a guy could call a minraise, he can probably call my all in, and I don't have to hope he repops me.

Hopefully your post can go in the sticky thread.

[DeuceSeven]

Depends on the read. Is this a dummy who will call a big bet with a weak hand or does he have to have a big hand to call? I think a minraise is rediculous, unless the guy is super tight.

I think a push is probably the right move.

[AZplaya]

what Pokey said