Paradox or no?
 

Let's say we are playing against a very tight opponent. He plays AA-QQ and AKs-AQs. If you play only hands in his range, you break even (equity-wise). You want to do a little better than that. Which one hand in your range of AA-QQ, AKs-AQs should you remove in order to improve your equity the most?

-pix

Re: Paradox or no?
 

AA

Re: Paradox or no?
 

dumb question

Re: Paradox or no?
 

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dumb question

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You should realize that now you are either way ahead and question is really dumb or way behind and you're just trolling. By raising your voice, you took the wrong line.

-pix

Re: Paradox or no?
 

AQs does slightly worse against that range than QQ, but it would be better to remove the 6 combinations of QQ than the 4 combinations of AQs.

This is interesting, but I wouldn't call it a paradox.

Re: Paradox or no?
 

[ QUOTE ]
AQs does slightly worse against that range than QQ, but it would be better to remove the 6 combinations of QQ than the 4 combinations of AQs.

This is interesting, but I wouldn't call it a paradox.

[/ QUOTE ]

I agree, it really is not. It's just that the straightforward answer (AQs) is wrong. Same goes for range of AA,KK,AKs. It's better to remove KK than AKs.

-pix

Re: Paradox or no?
 

I am merely saying that this is question may be paradoxical but is inevetably inpractical and thus i call it stupid

Re: Paradox or no?
 

[ QUOTE ]
I am merely saying that this is question may be paradoxical but is inevetably inpractical and thus i call it stupid

[/ QUOTE ]

If you feel inclined to comment in such manner, you have a surprisingly low post count.

Anyway, this is just a quirk I ran across when doing some more or less practical stuff. When analysing hand ranges in certain manner, this phenomenon is quite prominent and you better be aware of it.

-pix

Re: Paradox or no?
 

Another non-paradoxical and useless quirk for all interested.

Suppose opponent's range is AA and KK. Our best two-hand range vs. him is AA and A5s. Now let's say you want to play best 5 unique hands vs. his range. So you play AA and Ad5d? You can do better - play AA and AdKd instead.

EDIT: Here is a practical consideration. You give your opponent top x% of hands and want to know what is your top y% of hands. Your range will be different from the range you would get by simply taking top y% of all hands because your hands will be weighted. I haven't bothered to figure out what is the actual difference yet. Maybe someone of you has insight in this already?

-pix

Re: Paradox or no?
 

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?