Little Teaser

Hyzepher

Just a quick teaser for all you poker brains out there - its really an exercise to help focus on probability etc.

- lets say you are in a heads up situation with an opponent you know very well. You hold QQ and bet. He raises. Now you know him very well and know for certain that he will only raise if he has AA, KK or AK.

a) Should you call?
b) If you do call - what is the likely % that you will be ahead preflop.

Hyzepher

Hippo

I do know you're a big dog against AA or KK, and I think about a 52% favourite against AK, though maybe not AK suited. If it's a limit game, don't call the first two. If it's no limit, it depends on the size of the raise and how desperate you are!

Hippo

Er, about 25/1 to hit your miracle Queen against the overpairs?

Hyzepher

Thanks for the input Hippo - but try and view the question based on - If you do call what is the chance you will be ahead pre-flop. Remember your opponent has one of 3 possible hands, but you do not know which one.

Hyzepher

Davey Devil

I think the question is flawed, I don't care how well you know him, if it's heads-up his definition of a raising hand will change. Therefore in my opinion his hand could be as bad as A,10. If I were in that position, head's up, and someone made a raise and I had queens, I'd be getting all my chips in as fast as I could.

Ok let's just say you did by some miricle know he was holding one the these three hands, I would say you have about a 30% chance of winning the hand.

Hyzepher

OK - dont get too head up about 'what-if' - take it that he only raises with those 3 hands. This is more of an exercise in probability rather than anything else.

Hyzepher

yaledo

Well you now know he has any two out of 8 cards (aces & kings) rather than any two out of 50 cards...

the chances of him having 2 Aces are: 4/8 * 3/7 = 12/56
ditto for 2 kings
chances of a king and an ace: 4/8 * 4/7 * 2 (AK or KA) = 32/56

so ~57% chance you're leading pre-flop

As you said, this is more of a probability exercise than a poker exercise

Sorry I don't know how to hide the text as in a spoiler

Hyzepher

First of all sorry that I didn't really explain the scenario proberly.

Basically the situation is a simple exercice regarding probability and how perceptions can be misleading. To the uneducated having QQ up against AA, AK or KK looks like you will win only 1/3 of the time. But this is not the case.

We know that the opponent will bet only on AA, KK or AK - this is for simplicity. However, we dont know which - but we do know that we will be ahead if he has AK. So lets look at the probability of each hand.

AA - Out of a deck of 52 there are 6 chances to get AA
KK - as above
AK - Out of a deck of 52 there are 16 chances to get AK

Therefore there are 12 chances that you are losing but 16 chances that you are winning = 57%

Hyzepher

DeVore

yes, but continue the game through and you'll see that you'll lose 8 out of 16 of those times when you are up against AK or KA. You'll also lose almost ALL of the times you go up against AA or KK.... this means you are losing roughly 12+8 times and winning 8 times.

So while technically pre-flop you are ahead (by about 2%) more times then behind (by about 48% ) the odds are not weighted in your favour in this hypothetical game as it proceeds...

DeV.

Hyzepher

Originally posted by DeVore
yes, but continue the game through and you'll see that you'll lose 8 out of 16 of those times when you are up against AK or KA. You'll also lose almost ALL of the times you go up against AA or KK.... this means you are losing roughly 12+8 times and winning 8 times.

DeV.

Not quite - the odds of AK hitting an A or K to the river is about 33% (approx) so AK will beat QQ about 5ish times out of the 16. So played to the end QQ will have an 11 out of 28 chance of winning - presuming AA or KK will beat QQ every time. So that's about 40%.

However, this exercise was to show that some thought needs to go into hand value before you make a decision. Of course QQ against AA, KK or AK is never an ideal situation.

Hyzepher