Re: Heads Up Hold\'em question -- Solution
Straight-up answer:
If you deal 26 cards, the odds of dealing exactly 3 of the 6 face-up are
C(6,3)*C(46,23)/C(52,26) = .33205 or so
for an EV of -.0039ish at 2-1 odds.
Tricky answer:
There are 6 upcards in the deck. Deal yourself 6 cards. Of these cards, x are face-up, leaving 6-x face-up in the rest of the deck. Flip over the 6 cards you dealt yourself. Now you've got 6-x face-up cards in each pile, for an EV of lots.
Somebody once told me to think about possible poker situations before you get to the table, so you can make the right play without having to recalculate everything everytime. However, I'm not sure this particular situation quite qualifies -- even though this "move" will guarantee you a pot, it probably not won't show up more than 2 or 3 times over your entire poker life.
PP
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