HU Puzzle

[eastbay]

10k chips, blinds 300/600.

What is the minimum stack for which you should ever consider folding any hand at all when put all-in?

(This is an easy one. Sort of.)

eastbay

[curtains]

I think its 1150 range?

[eastbay]

[ QUOTE ]

I think its 1140 range?

[/ QUOTE ]

Based on what reasoning.

eastbay

[curtains]

Sorry this is wrong, I was thinking of something else. I was thinking smallest # of chips to fold from the SB. I have the K+S chart memorized and I know 32o is like 1.8x BB. Which would mean 1080-1100 remaining after posting.

Anyway this is completely different, I'll make an estimate of 1300-1400 remaining after posting. I didn't do any math so I can't be accused of cheating /images/graemlins/smile.gif

[Elem100]

Well this is my stab at it:

Assume we are dealt 32o, our opponent moves all in
Let x in thousands be our chip count now

We assume we are a 2-1 dog, 33% to win

If we call our expectation of our chip count is 2x/3

If we fold, then next hand assume we are 50% to win when we push all in, our expectation of our chip count then is 1/2(x-1)2 which is just x-1

2x/3 > x - 1 --> x < 3

So my sketch guess is at least 3000.

Edit: If we're sure the opponent has us at 4:1 dog, is 20% to win, then the answer is 1.6k, but this isnt practical cos we cant reasonably assume that.

[Madd]

1596?

[mackthefork]

Intuition tells me its around 2500.

Mack

[ZeeJustin]

Let's say you have a really tight opponent. He only plays aces. You have A2o. You don't need many chips at all before a fold is correct.

Edit: I should clarify that whatever the math shows as a 0 ev decision in this scenario is actually an easy fold. This is because once you rebuild up to enough chips to have any fold equity, you will run over your opponent. In other words, the weaker your opponent plays, the less likely you should be to take a +ev situation for all your chips.

[eastbay]

[ QUOTE ]
Let's say you have a really tight opponent. He only plays aces.

[/ QUOTE ]

That's a pretty uninteresting assumption, IMO.

eastbay

[ZeeJustin]

[ QUOTE ]
That's a pretty uninteresting assumption, IMO.

[/ QUOTE ]

You asked the question, not me. Perhaps you should try rephrasing to make the question somewhat interesting.

[eastbay]

[ QUOTE ]
[ QUOTE ]
That's a pretty uninteresting assumption, IMO.

[/ QUOTE ]

You asked the question, not me. Perhaps you should try rephrasing to make the question somewhat interesting.

[/ QUOTE ]

You are playing an opponent of comparable skill. The usual.

Perhaps I should mention there are 52 cards in the deck?

eastbay

[PrayingMantis]

I think it's time for a 5k HU between you two. That would certainly be interesting.

[The Yugoslavian]

[ QUOTE ]
I think it's time for a 5k HU between you two. That would certainly be interesting.

[/ QUOTE ]

How about a 5 person STT where ZJ get's to play 4 of the seats?? /images/graemlins/wink.gif

I hear he feels pretty comfortable in those.

Yugoslav

[dethgrind]

Eastbay, please enlighten us.

Here's my contribution:

Suppose you have 1100 chips heads-up with 32o in the BB after posting. Assuming your equity is proportional to your stack heads-up (does this assumption work here?), we can say folding has a value of .11 here.

If you call all-in and assume your opponent is pushing any two (not too unreasonable I don't think) you will win about 32.3%. Your stack after winning will be 1200 + 2*1100 = 3400 (remember the blinds).

.323*3400 ~= 1100

Which is about the same as folding. Your opponent might fold some of his worst hands, advancing the case for folding, but I think it's close enough.

[Degen]

lol now now sir...you do have a point but be nice eastbay hehe

[Degen]

so whats the answer?

if i were in the big blind i would never fold if the pot were laying me over 2:1...so i suppose that means anything less than 1800 (including BB) and probably gonna call...unless the guy was folding to every raise of his BB, then i'd prolly fold here, take my 1100 to the next hand and push.


Degen

[Bigwig]

Meh, I think somewhere around 1500. Any two includes 23o, so the whole puzzle is based on that. Including a small chance that the raiser has an overpair, and not knowing the skill of the opponent (will he fold on the next hand to MY push of any 2 when he should call), I say 1500.

Am I right, David?

[Madd]

Assuming villain pushes with any two then 23o wins in 31.2% of all cases according to my table.

x - 600 = 31.2% * x * 2 + 68.8% * 0

=> x = 1595.7