Theoretical All-In Call

[TheMainEvent]

[ QUOTE ]
Blinds 5/10

All folds to MP who raises to 40
You call on the button with AhKh, two to the flop

Flop: QdJdTc

MP open pushes for X (you cover him). How big does X have to be for you to fold here?

[/ QUOTE ]

OK everyone is saying not to fold ever because you can't be sure he has AK. What if we changed this to a pure math problem. You are somehow 100% sure that he has AK. All suits are equally likely. You are calling for a split at best. How big does the all-in have to be to fold in this scenario?

[psuasskicker]

There was 90 in the pot (5/10) and someone pushed 3k in there. I had 2k in my stack and folded the nuts, but there was a flush draw on the board.

heh...

This is ridiculous. I think I'm living in bizzaro world.

I played in a local NL $100 game a few years back. Some guy cold calls a PFR to $10 with Q9 after a cold call. Flop comes out JT8 with two clubs. One guy goes all in, the cold caller calls. The guy with Q9 folds cause he's scared of getting outdrawn by the club flush (he also thought flushes are 50/50 to hit by the river).

I will never ... NEVER ... fold the nuts in a cash game against unseen cards, no matter how much the bet. The question was asked "what if you dead knew he was on AK with you?" Ridiculous. The only way you know that with that sort of certainty is if he flips his cards over, at which point it becomes a math problem if he's got one or two diamonds. Cause anything else he has you're a HUGE favorite over, and he's got a very small edge on you if he's got the flush draw with his AK.

What would the bet have to be? Someone would have to be holding a gun to my wife and kid's head and tell me if I lose all my chips on the table they're fire. Other than that, I'm pretty much calling without thinking twice about it.

- Chris

[shtolky]

This is the exact same response I gave to AdamBragar when posed with this question. I have softened my stance somewhat, but those who say this is an "easy fold" must be kidding themselves

In a cash game, the answer for x is lim n->0 F(x)=1/x

Now that half of you are laughing hysterically and half think I'm crazy, I think there are situations where you MIGHT consider folding in a tournament. Against an opponent SO tight you are nearly sure he would only push with AK, that creates many situations where you ae hoping for a split, at best. If he is on a flush draw, he is about 30% to hit. Harrington says in his book when a big bet goes in there is at least a 10% chance an opponent is bluffing. In this situation, early in a tournament, we could assume about 40% of the time he is holding A [img]/images/graemlins/heart.gif[/img]K [img]/images/graemlins/heart.gif[/img]. 50% of the time he is holding AK of other suits, where we do not fear a flush draw. 10% of the time he is on a bluff.

The 40% of the time he holds A [img]/images/graemlins/heart.gif[/img]K [img]/images/graemlins/heart.gif[/img] we can expect to lose our whole stack 30% of the time, and split the rest. We will call it EV -30, with 100 being our whole stack size. 40% * -30 = EV -12. The 50% of the time he holds other AKs we split, or edges are so small they won't much affect our simulation. The 10% of the time he is on a cold bluff, or a weak flush draw, lets even out and say we win 80% of the time (if you disagree with that assessment feel free to do your own simulation, but I think the end point will hold even with slightly different numbers). 80% of the time we will win 100, 20% of the time we lose 100, a total expectation of EV +60. 60*10% = EV +6. Our total EV based on these numbers is -6% of your stack.

So would I fold there? Only if my opponent was SO tight he would only push with the nuts 90% of the time, and even then pushing all-in with the nuts rather than milking is a suspect move. Come to your own conclusions.

[sillyarms]

[ QUOTE ]
OK everyone is saying not to fold ever because you can't be sure he has AK. What if we changed this to a pure math problem. You are somehow 100% sure that he has AK. All suits are equally likely. You are calling for a split at best. How big does the all-in have to be to fold in this scenario?

[/ QUOTE ]

Hand Ev
As Kd 0.477
As Kc .5
As Ks .5
Ad Kd 0.318
Ad Kc 0.477
Ad Ks 0.477
Ac Kd 0.477
Ac Kc 0.5
Ac Ks 0.5

0.469555555 overall ev vs all combos of AK
95 in pot

P = Pot size
x = Stack size
W = odds of winnig

EV = x - W * (P + 2x)
0 = x - 0.469555555 * (95 + 2x)
x = 732.6094749

Public high school math tells me that if we make the assumption he has any combination of AK we should fold if the all in bet is greater than $732.60.

I like the breakdown here. Add the 10% chance of bluffing and we might finally give this man the answer he seeks...other thn the implied "Tell me you aren't seriously folding the nuts." [img]/images/graemlins/grin.gif[/img]

[ezratei]

[ QUOTE ]
Really stupid question.

If you ever consider folding here, leave the table immediately - because you are clearly playing way out of your comfort zone.



[/ QUOTE ]

Wow. I am very suprised by the people who have answered along these lines.

This is clearly an extreme situation but that is why I posted a variable stack size X. Above a certain X, folding is clearly the best option and at extemely large X's folding is the ONLY choice.

In this situation you have the 6th nuts ... I say to you, anyone who is willing to call an all-in with the 6th nuts in a deep-stacked cash game should "leave the table immediately"!

How deep-stacked you need to be to make folding the best option here is the question at hand, but to say "never fold" is simply ridiculous and illogical.

I'll give a simpler real-life example to illustrate my point.

I was recently playing in a 1-2 blind cash game and I called in the SB with 10 [img]/images/graemlins/diamond.gif[/img]7 [img]/images/graemlins/diamond.gif[/img], the BB
checked and the two of us saw
Flop: A [img]/images/graemlins/club.gif[/img]K [img]/images/graemlins/diamond.gif[/img]J [img]/images/graemlins/heart.gif[/img]. Pot=$4
Check, Check
Turn A [img]/images/graemlins/club.gif[/img]K [img]/images/graemlins/diamond.gif[/img]J [img]/images/graemlins/heart.gif[/img](Q [img]/images/graemlins/diamond.gif[/img]) Pot=$4
I checked, he bet $5, I went all-in for $1,000 more (he covered)

Now, what would the same people who said "never fold" to my original question suggest the BB do here? Call? This is an easy fold of the "nuts". (By the way the BB here actually called my $1,000 after thinking for about 3 minutes, then almost had a heart attack when I flipped over my cards. Unfortunately [not that I want anyone to have a heart attack] I missed.

So back to my original question: how big does X have to be to make folding correct. I think that against a very good opponent, you have to start thinking about folding with a stack of as little as 2,000. Once you get to 5,000, I think a fold has to be the primary option barring any specific reads and at 10,000 I think a fold is pretty standard.

Anyway, I'd appeciate any other comments on the stack size. I think this is a pretty good (and fairly complex) problem in order to start thinking about making big moves in deep-stacked cash games.

[rwanger]

[ QUOTE ]

You do not have the actual nuts in the example O.P. mentioned. This is the key to what people are talking about. Think it over.

[/ QUOTE ]

I know. The threading didn't show, but I was responding to the guy who said "yeah I was at the borgata and folded the nuts when this guy went all in".

[rwanger]

[ QUOTE ]

In this situation you have the 6th nuts ... I say to you, anyone who is willing to call an all-in with the 6th nuts in a deep-stacked cash game should "leave the table immediately"!


[/ QUOTE ]

Okay, I'll bite...what are the 5 hands better than yours at this moment?

I suppose if you are saying that AdKd, AdKx, AxKd, AcKc have better equity, then that is correct. Which one am I missing? Do we have to break out AxKd into AcKd and AsKd?

Also, as far as I know, the nuts has nothing to do with equity, it is merely "what hand cannot be beat at this moment". AdKd and AxKx are both the nuts.

Truthfully, I'm trying to be 50% smartass, and 50% "not sure what you mean". [img]/images/graemlins/grin.gif[/img]

[ezratei]

Damn! I forgot about AcKc! The 7th nuts then ... yeah I was talking about each of the AdKx, AxKd combinations as posible better hands.