He is pushing any two or?

derdo · #1 09-15-2005, 10:11 PM

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 · #2 09-15-2005, 10:23 PM

[ 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 · #3 09-15-2005, 10:30 PM

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.

[img]/images/graemlins/confused.gif[/img]

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 · #4 09-15-2005, 10:35 PM

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

Freudian · #5 09-15-2005, 10:36 PM

[ 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.

#6 09-15-2005, 10:39 PM

Definitely a)

deathpotato · #7 09-15-2005, 10:43 PM

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 · #8 09-15-2005, 10:50 PM

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 · #9 09-15-2005, 10:52 PM

[ 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 · #10 09-15-2005, 10:55 PM

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.