Paradox or no?

[piki]

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