He is pushing any two or?

[derdo]

Here is a question that I had been thinking about for awhile.
I think I know the answer. Let's see what you guys think...

Bubble time. You are in big blind, small blind is a player who is definetely known to be a player that recognizes the situations that requires pushing with any two. And currently he is in a position that clearly states that he should push with any two.

Two folds and no doubt he pushes.
Which is correct?
a) Prob(he has AK) = Prob(he has 97)
a) Prob(he has AK) < Prob(he has 97)
a) Prob(he has AK) > Prob(he has 97)

and why?
Cem

[Freudian]

[ QUOTE ]
Here is a question that I had been thinking about for awhile.
I think I know the answer. Let's see what you guys think...

Bubble time. You are in big blind, small blind is a player who is definetely known to be a player that recognizes the situations that requires pushing with any two. And currently he is in a position that clearly states that he should push with any two.

Two folds and no doubt he pushes.
Which is correct?
a) Prob(he has AK) = Prob(he has 97)
a) Prob(he has AK) < Prob(he has 97)
a) Prob(he has AK) > Prob(he has 97)

and why?
Cem

[/ QUOTE ]

I have to answer a).

[brimstone1]

I'm going to state the obvious, perhaps making me the most ignorant here... but...

169 total unique hands,
AK and AKs are 2 out of the total.

You ask the probability of him having AK, I assume AKs is included. Thus, the probability he his holding AK/AKs is 1.1%, compared to 98.9%, the probability that he is holding any other two cards.

/images/graemlins/confused.gif


Now if you mean a range, of say, AJ+, ATs+, 77+, K8s+, K9o+, QJ, thats something else.

But if you're asking specifically for AK and AKs, your answer is above?


Edit; now I see why the answer is of course A!... meh, did I waste my time or did you make a typo there buddy'o mine?

[derdo]

Clarification:
AK= AKs and AKo
97= 97s and 97o
and only those holdings.

[Freudian]

[ QUOTE ]
Clarification:
AK= AKs and AKo
97= 97s and 97o
and only those holdings.

[/ QUOTE ]

I don't see the point of this question.

If he is pushing truly any two then both are as likely. If he has a narrower pushing range then AK is more likely. Why? Should be fairly obvious.

Definitely a)

[deathpotato]

I think he's asking if the player is more likely to do something other than push with AK even though he is supposed to be pushing with any two. If the player is good enough to know to push any two then he is almost certainly good enough to know to push AK, as giving away a cheap flop would be terrible and at any rate our pushes need to have some mystery about them.

If the hand in question were KK rather than AK I think you will see a push slightly less often than when he holds a random crap hand, as even a good player will try to be overly tricky from time to time, and doing so with KK would be a lot better than doing so with AK.

[derdo]

My answer is (c).

I always used to think the answer should be (a) but after some thinking I changed my mind.
The prob of having AK or 97 should be equal if he is pushing with two hands with 100% in this situation.
But the knowledge that we have that he is a good player and he should see this situation and should be pushing with any two is a little strict. There is no way that you can be sure that he is pushing with any two.
There could be many reasons for a good player not to push with a weak hand although it is +EV to push with any two. He could think that, the opponents are fed up and he is gonna get called, he might be just a little careless and misread the situation, he might think that you are a loose player and would call with many hands, he might be trying to make a table image etc. etc. There could be a lot of reasons.
So assuming that an opponent is pushing with any two is the extreme assumption that you can make.
So even though we might read a player to be in a position of pushing with any two,
Prob(he has AK)> Prob (he has 97) in my opinion.

Practical value to this discussion is if ICM says that calling is +EV just marginally with the assumption that your opponent is pushing with any two, it is most probably -EV to call since pushing with any two range is the extreme assumption.

That's my take on this...

[se2schul]

[ QUOTE ]
Here is a question that I had been thinking about for awhile.
I think I know the answer. Let's see what you guys think...

Bubble time. You are in big blind, small blind is a player who is definetely known to be a player that recognizes the situations that requires pushing with any two. And currently he is in a position that clearly states that he should push with any two.

Two folds and no doubt he pushes.
Which is correct?
a) Prob(he has AK) = Prob(he has 97)
a) Prob(he has AK) < Prob(he has 97)
a) Prob(he has AK) > Prob(he has 97)

and why?
Cem

[/ QUOTE ]

Well, this probability actually depends somewhat on what your cards are...
Are you holding an A,K,9 or 7??
Let's pretend for a minute that your cards don't matter.

What's the probability that he gets dealt AKo or AKs?

Well, there's 4 ways to pick a K and 4 ways to pick an A, so that's 16 possible ways to pick AK out of 52C2 ways to choose any 2 cards.
That's 16/1326.

Now, what's the probability of getting deals 97o or 97s? Well, let's see... there's 4 ways to pick a 9 and... I'll just skip to the answer. It's also 16/1326.

That's also the probability that someone gets dealt 23o or 23s.

So, the answer is a).

I don't really see how this relates to STTs. Perhaps it should be in the Probability forum. I don't really think that the probabilities do you much good.

You'd probably be better off asking someone what you should be calling with when you know the SB is pushing any 2 into you.

[deathpotato]

If the player should be pushing any two he will not fold 97. He might fold 32, but this is all beside the point. If a situation is so marginally +EV that the removal of a few hands from the pusher's range is going to tip it over the scale to negative, you shouldn't call anyway because a) if you outchip him there is more value in the chips you lose than in the chips you win and b) if he outchips you the risk of busting (and therefore being able to make no more +EV moves in the tournament) outweighs a marginally +EV situation.

[derdo]

I posted this here because I think this is relevant to the basic assumption we make about hand ranges while using ICM in bubble time.
For example we assume that a pusher's range is 99+,AQ+. This means we assume that pushing probability for these hands is 1 and 0 for all the other holdings.
However, since our assumption is never perfect, the prob of seeing AA is higher than 99. And the probability of this guy pushing with 66 is not 0.
You might think one offsets the other but with extreme hand assumptions like pushing with any two (or pushing with 80%) it doesn't.
We use a discrete proabbaility function. If he has a hand in this range he is pushing 100% of the time, if not he is folding 100%.
But in reality the probability function is a continous decreasing one.
I am not sure if this has a practical value for ICM calculations but I feel like it might, particularly with extreme range assumptions about your opponents...

I think (c). Since he is in the small blind he has the option of waiting two more hands to try to get something better than a random middle-middle. Odds are that one of the next two hands will be better (higher).

[ QUOTE ]
My answer is (c).

I always used to think the answer should be (a) but after some thinking I changed my mind.
The prob of having AK or 97 should be equal if he is pushing with two hands with 100% in this situation.
But the knowledge that we have that he is a good player and he should see this situation and should be pushing with any two is a little strict. There is no way that you can be sure that he is pushing with any two.
There could be many reasons for a good player not to push with a weak hand although it is +EV to push with any two. He could think that, the opponents are fed up and he is gonna get called, he might be just a little careless and misread the situation, he might think that you are a loose player and would call with many hands, he might be trying to make a table image etc. etc. There could be a lot of reasons.
So assuming that an opponent is pushing with any two is the extreme assumption that you can make.
So even though we might read a player to be in a position of pushing with any two,
Prob(he has AK)> Prob (he has 97) in my opinion.

Practical value to this discussion is if ICM says that calling is +EV just marginally with the assumption that your opponent is pushing with any two, it is most probably -EV to call since pushing with any two range is the extreme assumption.

That's my take on this...

[/ QUOTE ]

I think your wrong, in your first post you told us:
A.villain knows when it's correct to push any two.
B.the situation at hand warrants an any two push.
C.villain pushes.

Your implying that he should be pushing any two in this spot, you dont mention any other variables, AK=97.

a) is the correct answer.

[derdo]

hey man I am not trying to scam anybody here (big lewboski quote:))
I didn't try to trick anybody...

[ QUOTE ]

A.villain knows when it's correct to push any two.
B.the situation at hand warrants an any two push.
C.villain pushes.


[/ QUOTE ]
Yes this is exactly what I have described.
I think P(AK)> P(97) for the reasons I stated in the above two posts...

[Freudian]

[ QUOTE ]
hey man I am not trying to scam anybody here (big lewboski quote:))
I didn't try to trick anybody...

[ QUOTE ]

A.villain knows when it's correct to push any two.
B.the situation at hand warrants an any two push.
C.villain pushes.


[/ QUOTE ]
Yes this is exactly what I have described.
I think P(AK)> P(97) for the reasons I stated in the above two posts...

[/ QUOTE ]

That is an impossibility with the assumptions you make. You have to change your assumptions to be able to come to that conclusion.

[pergesu]

The probability of being dealt AKo is the same as the probability of being dealt 97o, unless you hold an A/K/9/7. If he's truly pushing 100% of hands, the chances of it being AKo are exactly the same as it being 97o.

Any deviation from that is because the initial assumption, that he will push with 100% of hands, is incorrect.

[derdo]

[ QUOTE ]

Any deviation from that is because the initial assumption, that he will push with 100% of hands, is incorrect.


[/ QUOTE ]
I didn't state that he is pushing with any two 100%, I just gave a strong read about the villian. Can you ever be sure that villian is pushing with any two?

Theoratically, if he is pushing 100% of his hands than the probability is equal. But in a real SNG, can you ever be sure of this?
Even the villian is good, even when pushing with any two is +EV for him, you still should not assume that his range is any two cards.
What I believe is, when you assume that your opponent is pushing with any two (even with good reasons, based on very solid reads), probability of seeing AK is higher than seeing 97. Because there could be a lot of different reasons that he is not pushing with bad cards.
"he is pushing with any two here" is the most extreme assumption that you can make about his hand range. if you are calling a push only based on this assumption then you are more likely to be making a mistake than making a correct call.

well anyway maybe I am just talking nonsense:)
thanks for all the responses...
Cem

[se2schul]

[ QUOTE ]

[ QUOTE ]

A.villain knows when it's correct to push any two.
B.the situation at hand warrants an any two push.
C.villain pushes.


[/ QUOTE ]
Yes this is exactly what I have described.
I think P(AK)> P(97) for the reasons I stated in the above two posts...

[/ QUOTE ]

Well, if that's the case, then either villain is NOT pushing any 2, or your deck contains more As and Ks than 9s and 7s.

He's either pushing ANY 2 or not. If he really is pushing any 2, then him having 23 is just as likely as 97 is just as likely as AK is just as likely as any non-pocket pair hand.

[Nicholasp27]

the initial assumption wasn't that he would push 100% of hands

the initial assumption was that it is correct to push 100% and that villian KNOWS it's correct

we all do things that we know aren't correct at times, and villian is more likely to do an incorrect fold with 97 than with ak

[eastbay]

I think this is a silly question not worth much debate, but the nit in me wants to point out that most critics of the OP in this thread are wrong when they say the question was stated such that villian pushes 100%. What he said is:

"
A.villain knows when it's correct to push any two.
B.the situation at hand warrants an any two push.
C.villain pushes.
"

There is a difference between knowing what's correct and doing what's correct. The OP only assumed the former. But that was just a waste of 15 seconds of my life to point that out.

eastbay

[se2schul]

[ QUOTE ]
the initial assumption wasn't that he would push 100% of hands

the initial assumption was that it is correct to push 100% and that villian KNOWS it's correct

we all do things that we know aren't correct at times, and villian is more likely to do an incorrect fold with 97 than with ak

[/ QUOTE ]

Well, of course if someone is going to play less than 100% of hands, they'd be rock stupid to play the worse hands and fold the better ones.

He's either playing any 2 or he's not. If he IS playing any 2, then AK is just as likely as 97 or 23. If he's NOT playing any 2, then out of any 2 hands that aren't pocket pairs, the better one is more likely.

Can the OP please clarify the assumptions???

[Nicholasp27]

yes, if he is playing any 2, then it's obviously a) unless hero has an a/k/9/7 in his hand (although one could make an argument that if 3 people folded before him, their likelyhood of holding a 9 or a 7 is greater than their likelyhood of holding an a or k, and therefore he is more likely to hold ak than 97 if he truly pushes any 2, even if it's a very small change in %)

however, the OP's assumptions are clear and he uses them in his argument of why it's not a)

the assumption is only that it is a +ev situation and that villian knows it's a +ev situation...the assumption is not that villian will take every +ev situation