Interesting No Limit Question

[fnurt]

[ QUOTE ]
From "Tournament Poker for Advanced Players"

"It may seem that giving up a positive EV gamble can never be right. However, even from a purel mathematical standpoint, you sometimes should."

I think this is such a situation, where using a very basic understanding of risk v. reward analysis shows that calling or folding (I lean towards folding), whilst forgoing an immediate positive EV, leads to a greater long term EV. The title of the chapter from which the quote comes perhaps sums it up best, "You're Broke - You're Done".

[/ QUOTE ]

If by "very basic understanding" you meant "overly simplified understanding" I can agree with you. Otherwise you've said nothing, because you can ALWAYS argue for survival over a +EV gamble. But you have to dig deeper than that, and understand exactly how much EV you're giving up, and how large the risk is. Otherwise you're just repeating truisms.

I showed above that raising all-in, which might not even be the best play, is worth 721 more chips of EV than folding, with less than a 2% chance of busting out. I don't think it's a smart decision to give away 7% of your stack to avoid a mere 2% chance of busting.

The broader point is that it is very rarely correct in the early stages of a tournament to forego a +EV move in the name of survival. We could argue all day about a 50.1% edge or something similarly contrived, but this is not such a case. If my math is correct then folding is a large mistake.

[CrisBrown]

Hi fnurt,

I agree, and even with my equity numbers (which are pretty close to yours, although we used slightly different sets of assumptions), pushing all-in has more equity than folding, albeit at much greater risk. That's why I cited the equity:risk ratios. For a call, the equity:risk ratio is about 21:10, a little over 2:1. For a raise that ends up all-in vs. the lead bettor, the equity:risk ratio is about 1:34. That is, you are taking a huge risk relative to the potential gain ... but it's still a positive equity move. Folding is a mistake, IMO.

Cris

[West]

What are your thoughts given that Sklansky has now posted saying that it makes no difference whether or not you assume that the flush draw hand could possibly have the J [img]/images/graemlins/diamond.gif[/img] for a straight?

[fnurt]

[ QUOTE ]
What are your thoughts given that Sklansky has now posted saying that it makes no difference whether or not you assume that the flush draw hand could possibly have the J [img]/images/graemlins/diamond.gif[/img] for a straight?

[/ QUOTE ]

Well, I was just showing that pushing was better than calling or folding. If the flush draw hand could have the Jd, it makes my numbers different, but I doubt it changes the ultimate outcome.

The idea that it "makes no difference" suggests that maybe the best answer is something I didn't address at all, which would be raising some amount less than all-in. I didn't get into this because I thought that after 16 pages, we should at least try and eliminate calling or folding as options before moving on [img]/images/graemlins/smile.gif[/img]

[Vince Lepore]

As the problem is stated you can only do one thing, call. The reason is that the original bettor may have a flush draw with his straight. That fact makes the third players hand mute.

Vince [img]/images/graemlins/smile.gif[/img]

[Photoc]

I dont know if this question was asked....there are 19 pages. Which cards on the board are of which suit and are you as well on a flush draw?

[CrisBrown]

Hi Photoc,

You're not on a flush draw (you have AsJs). You don't know which board cards are of which suits, which might relevant in terms of what order the cards came off, except that David has already specified your reads, that is: the lead bettor has a made straight, and the player behind you has a flush draw. Note that David refuses to specify whether the lead better might also have a flush draw to go with the straight, and whether the player behind you might also have a straight to go with his flush draw. So you have to keep in mind the 20% possibility that you are being free-rolled.

Cris

[Photoc]

Thank you for your reply.

Yes I understand the flush draw that is out there. He said something about the flush draw guy with 2 diamonds in his hand, which is why I was wondering which of the board cards were diamonds and what the suits of the other 2 were as well. The reason I ask this is that if there were 2 spades out there to go with the spades in your hand, you could theoretically be on a royal and a flush draw as well as having the nut straight.

[ClonexxSA]

[ QUOTE ]
You are playing NL.

You are headsup on the flop with an opponent you know well.

Flop: Q [img]/images/graemlins/heart.gif[/img] J [img]/images/graemlins/heart.gif[/img] T [img]/images/graemlins/club.gif[/img]

You have A [img]/images/graemlins/spade.gif[/img] K [img]/images/graemlins/spade.gif[/img]

You bet 20 dollars into a 20 dollar pot and your opponent moves in for 5000 more. You KNOW your opponent will not put all his money in without the nuts.

Do you call here?

I'm just trying to say that folding the nuts in holdem is rare, but POSSIBLE.

While David's example isn't this cut and dried, I still believe folding the nuts is correct, and if it's not it's sure close.

[/ QUOTE ]

Yes, I do call here. The nuts here is any combo of AK. Since you are holding A [img]/images/graemlins/spade.gif[/img] K [img]/images/graemlins/spade.gif[/img] then that discounts him holding them. He could be holding any combination of the other 3 suits of AK, why do you automatically put him on A [img]/images/graemlins/heart.gif[/img] K [img]/images/graemlins/heart.gif[/img] ? That is only one combination out of MANY that he could be holding. Chances are he is NOT holding that. It is more likely he is holding ONE of them and would need runner hearts to make the flush to not split the pot.

You automatically are giving your opponents the best possible hand they could have against you when there could be so many other combos.

[West]

It seems to me if the flush draw could have the made straight, it starts making a bit complicated when you start talking about moving in. Obviously it's bad for you if he has it, since he's freerolling on you. But what are the odds he has it? Given the two diamonds on the board, I think there are 55 possible flush draw combinations he could have, and 10 which would contain the jack. If I butchered that, I'm sure someone will tell me. Course each of the combinations are not equally likely to be held in his hand, and as someone pointed out, which cards on the board are diamonds would affect this likelihood as well. If the ace and the king on the board are diamonds, I would say the odds of the jack being in his hand have to increase - if the queen and the ten are the diamonds on the board, I would have to say they decrease. Anyway...what if we just for fun said there was a 33% chance of the flush draw holding the J [img]/images/graemlins/diamond.gif[/img]? If you moved in, he folds the other two thirds of the time, but calls when he has it. When he calls, I think your EV is:

(9/43 x -10000) + (34/43 x 550) = -1658

I said 9/43, because if you're read on the first guy having the straight is right, then that's another card we know isn't a diamond in this case. Anyway, the other two thirds of the time, we can use the EV you came up with of +721, which was based on when the flush draw folded. If we multiply that by .67, and add it to the EV I came up with x .33, you get a negative EV. Course if you just lower the chance of having J [img]/images/graemlins/diamond.gif[/img] to say, 25%, it's now +EV. At 20%, it's still worse than your calculation of the EV for calling....of course, that calculation didn't include a reduction for those times when the flush draw has the J [img]/images/graemlins/diamond.gif[/img] and puts in a big raise..