Proposition bet during a hand... what would you do?

[tpir90036]

A bizarre hand that my friend played in the 5/10 NL game at the Borgata last weekend:

6(!) limpers to Hero ($1200) on the button who limps along with A[img]/images/graemlins/heart.gif[/img]T [img]/images/graemlins/heart.gif[/img]. The SB (Donk) makes it 30 to go. BB folds, everyone calls as does the hero.

Flop: 8 players ($250) - A [img]/images/graemlins/diamond.gif[/img]2 [img]/images/graemlins/diamond.gif[/img]A [img]/images/graemlins/club.gif[/img]
SB bets $100, folded to Villain in MP who makes it $500. Villain has the table covered and is the table captain. He does not appear to have a low gear and has been making huge bets and raises at raised pots and taking them all down uncontested. Folded to Hero who decides to go all-in (comments on this play are fine but this is not the point of the post). SB folds. Here is where it gets interesting.

Villain flips over 2 [img]/images/graemlins/spade.gif[/img]2 [img]/images/graemlins/club.gif[/img] and says "if you just give me the $500 and fold we can call it good." The dealer has no problem with this. Your move?

1) Examine the math of the situation. What *should* you do?
2) In the heat of the moment what *would* you actually do?

Later,
tpir

P.S. Yes, this hand actually happened. The details of the flop suits/stacks might not be exact. But it happened.

[gomberg]

Well, I'm getting that with the math, you should take the guy's offer, but it's close. Inuitively, I thought you shouldn't take it because you'll still win the hand 30% of the time and there's enough money in the pot to compensate.

After looking at pokerstove, though, the AT wins only 23% of the time. So comparing to an EV of -500, it would be 1550(.23) - 1170(.77) = -544.5 about, so it's better to take the offer.

In heat of moment, I wouldn't have taken it.

Someone correct me if I messed this up. Thanks...

[NiceCatch]

Ok let's see here... you need one of three tens, the case Ace, or a runner-runner pair. You are essentially risking $670 for roughly $1950, or 3:1 for four outs or runner-runner. Sounds like you take the offer. Would I take the offer and fold? After doing the math, yeah probably. My initial poker intuition told me to take the offer as well.

[nokona13]

Why is this even close? I mean, it's interesting that the guy wasn't willing to take the almost 4:1 odds he'd win the extra $700, but I mean, what if your friend had been OOP and had bet $500, then the guy had pushed and flipped? That's the same math, and it's hugely -EV...

[gomberg]

it's only a difference of $45 EV. Not small, but not huge either...

[U235]

First thought: XXXX you, XXXXer! Let's gambool!

Second thought: I'm drawing to four outs, let's deal.

Math thought: I'd forgotten about the extra outs on the river by pairing the turn card. I'm 23% to win. If I have the deal right, there is $850 in the pot before I go all-in for my remaining $1170, so:

Play and win = $2690
Play and lose = $0
Take the deal = I keep my remaining $670

Playing has an EV of 0.23 * 2690 = $619, so I should take the deal by a fair bit, if I didn't screw up the math.

Edit: bad math, I double counted Villians $500. corrected.

[NiceCatch]

My pot numbers don't agree with you. 7 limpers --> 6 callers of $30 = $10+6*$30 = $180 preflop.
$100 + $500 + $1170 + $670 + $180 = $2620

So it's $670 for $1950

[AdamBragar]

Wow the math turns out to be a lot closer than I thought. When I did the quick math in my head, I felt that the guy must be a communist and hate money and that you should quickly accept the deal. But it is a lot closer than I thought. Still take the deal.

By any chance were you playing against Sklansky? Did he then ask you what the maximum amount you would give him and fold would be and why?

[tpir90036]

[ QUOTE ]
By any chance were you playing against Sklansky? Did he then ask you what the maximum amount you would give him and fold would be and why?

[/ QUOTE ]
Something along those lines was going to be part two of my questioning:

1) Pretend the EV of calling was the same as the EV of taking the offer. Do you go for the tilt value of sucking out or just keep the money now and try to run it back up in the great game you are sitting in? Granted, in the long run it does not matter...but there is no long run. Just this hand right now.

2) If we alter the pot slightly and you realize that calling is a slightly better play than taking the offer... do you still take it or go the high road and try to double it up playing? What if it was your only buy-in?

[NiceCatch]

1) You say "It's probably a good deal. In fact, it definitely is a good deal. BUT I LOVE TO GAMB00L." Then you say "no, thank you," rebuy if you lose, and reap the benefits of your new loose and fast image.

2) You clearly fold if you have only one buy-in. You wait for a situation where you have a much bigger edge. You make back your loss on that one hand, and more.

Regarding the second question... taking rake into account, given that your bankroll is reasonably immune to variance, why would you ever turn down a marginal edge? I.e. if after taking the rake into account, your edge from calling an all-in is 1%, why would you fold? I posted about marginal situations a while back, and I got several answers along the lines of "If you want to gamble, hit the craps table. Play for bigger edges." If you have the long run in mind, why wouldn't you play for any edge?