Paradox or no?

[piki]

[ QUOTE ]
If you knew your opponent hand range was that tight wouldnt the most EV thing to do be to expand your hand range to take advantage of all the blinds he is going to be giving up, or am I missing the point here?

[/ QUOTE ]

This has nothing to do with EV (yet), only equities. Just as if you are in a game with no blinds and your opponent raises those hands anyway. This is purely theoretic, watch out for all 'ifs'.

Ok, continuation from my edit. Let's say opponent opens AA-KK, AKs. What's our equity if we get involved with him with the same range of hands? 50? It is 48,7% because our distribution of hands has changed. I do not know if this was originially considered when defining the 'gap concept', but it definitely supports it. If the opponent takes the best cards and we play looser than him, our disadvantage will be additionally increased by the fact that our hand will include worse cards more often, even if they are evenly distributed in range.

-pix

[AaronBrown]

[ QUOTE ]
If you knew your opponent hand range was that tight wouldnt the most EV thing to do be to expand your hand range to take advantage of all the blinds he is going to be giving up, or am I missing the point here?

[/ QUOTE ]
I don't think you're missing anything. The original question asked which hand to drop to improve your equity, but the discussion seems to assume you're going all-in preflop. The real advantage to playing someone like this is you have so much information about his hand that you will often have a huge edge after the flop, and you'll know when he has you beat.

This may be a theoretical discussion about all-in preflop heads-up play, but if not, if the topic is poker, then your approach makes perfect sense.

[Beermantm]

[ QUOTE ]
[ QUOTE ]
If you knew your opponent hand range was that tight wouldnt the most EV thing to do be to expand your hand range to take advantage of all the blinds he is going to be giving up, or am I missing the point here?

[/ QUOTE ]

This has nothing to do with EV (yet), only equities. Just as if you are in a game with no blinds and your opponent raises those hands anyway. This is purely theoretic, watch out for all 'ifs'.

Ok, continuation from my edit. Let's say opponent opens AA-KK, AKs. What's our equity if we get involved with him with the same range of hands? 50? It is 48,7% because our distribution of hands has changed. I do not know if this was originially considered when defining the 'gap concept', but it definitely supports it. If the opponent takes the best cards and we play looser than him, our disadvantage will be additionally increased by the fact that our hand will include worse cards more often, even if they are evenly distributed in range.

-pix

[/ QUOTE ]

How about making some sence of all this for me?? I have absolutely no idea what your talking about at this point. Are the opponents playing the hand agaisnt each other properly?? Are we assumming you are a better player in the hand? Or is this just about Equities?? WHich I really never learned about so I would be intrested to learn.

Thanks

[piki]

To make this clear for all: I am only considering equity as % of times your hand or range will win against another hand or range of hands on showdown. You can calculate this using PokerStove, which you can google up.

-pix

[Nash_Clown]

[ QUOTE ]

Ok, continuation from my edit. Let's say opponent opens AA-KK, AKs. What's our equity if we get involved with him with the same range of hands? 50? It is 48,7% because our distribution of hands has changed.

[/ QUOTE ]
Our distribution of hands may have changed, but because of our cards, so has our opponent's. If we both play a range of AA,KK, and AKs indiscriminately our equity should still be 50%. PokerStove has it as 50% as well. What am I missing here?

[Andrew Karpinski]

piki : Interesting OP.

[piki]

[ QUOTE ]
[ QUOTE ]

Ok, continuation from my edit. Let's say opponent opens AA-KK, AKs. What's our equity if we get involved with him with the same range of hands? 50? It is 48,7% because our distribution of hands has changed.

[/ QUOTE ]
Our distribution of hands may have changed, but because of our cards, so has our opponent's. If we both play a range of AA,KK, and AKs indiscriminately our equity should still be 50%. PokerStove has it as 50% as well. What am I missing here?

[/ QUOTE ]

I am pretty positive I am not mistaken. I am sorry but I do not know a simple explanation for why it is so, though I am sure it exists. I will try with an example:

Let's say only opponent gets his cards first. He takes a look at his cards and acts accordingly. Then the deck is shuffled and you get your cards. I believe you would agree that in that case, our distribution changes and opponent's is independent of our hand. Is it any different if we're dealt cards at the same time?

EDIT: This is so mind boggling. You take a look at the problem from here, it seems logical it changes, you take another look, it seems logical it does not. Thinking about it again, I confused my self and now I do not know right from left. [img]/images/graemlins/smile.gif[/img]

-pix

[piki]

Nash_clown, I stand corrected. Thank you for your input.

I was mislead from a standpoint of an observer of action in our game. Let's say first opponent raises. Since as observer I know his range, I know that second player's distribution has now changed. This is true and obvious. If tight UTG raises, there are bound to be less Aces in hands of opponents. From here I made my conclusion. But when second player does actually get involved, distributions in both players' hands are equal.

-pix

[AaronBrown]

You have to be careful about your conditioning (not physical shape, logical conditioning).

If both players play the same set of hands, their equity has to be equal. However, suppose the other player plays only AA, KK and AKs, and she opens before I look at my cards. Out of the 1,326 possible combinations of pocket cards, she plays only 16.

I also play only 16 combinations of pocket cards, but since she opened I know that 7 of them are unavailable to me. So out of the 1,225 remaining sets of cards, I will play 9.

Still not looking at my cards, I know if she has AA she wins 80% of the time if I call with the same hand range, KK wins 36% and AKs 35% (counting ties as half wins). Since there are 6 AA's, 6 KK's and 4AKs's, her chance of winning is (6*80% + 6*36% + 4*35%)/16 = 52.2%. Since I call the same fraction of the time when she holds any of these three hands, the computation should be good. I think you are doing something like this to find that I have a slight disadvantage.

We know that logic must be incorrect, because it would say I have the advantage if I look at my cards first. That obviously cannot matter.

The explanation is a bit complicated. She doesn't have the 80% edge every time she holds AA, 1 time in 9 it's 50% (I also have AA), 6 times it's 81% (I have KK) and 2 times it's 88% (I have AKs). If you consider all the possibilities:

1 time out of 6 we have the same cards, 50%
3 time it's AA versus KK, 81%
1 time it's AA versus AKs, 88%
1 time it's AK versus AKs, 66%

each of the last three cases are equally likely to happen with either one of us having the advantage.

[JohnAndersen]

so we are making the assumption that we know his range as a fact? Then, given his known range what the perfect hands to play against him are?