[bigpooch]

Your opponent played "optimally". OTOH, you played
"suboptimally" because you held a decent pair.

With a medium pair, when HU, you simply draw three since
even one pair is a decent hand when HU. If you held maybe
22 or 33, you could "draw deceptively", but what is the
point? Your opponent could have a pair of fives if he is
playing "optimally". (It turns out he could also have a
pair of fours if he is playing "optimally").

Probably your opponent thought you were making a play and
even if he thought you may not be bluffing a lot, he thought
AA was "too good" to lay down.

Suppose your opponent didn't EVEN play optimally, but folded
a bit more: say he calls with only 90% of the hands he is
"supposed to" according to GT (game theory) if this were a
cash game (which it is not, in any case), but since the
stack sizes are about the same, it won't matter too much.

Predraw, you risk 150+660=810 to win 450
(BTW, how can you make it 960 to go in PL? Seems this is a
NL tourney, not a PL one; normally, you could only call 150
and raise another 600 or 900 to go; also, postdraw you were
able to bet more than the size of the pot)

According to GT, your opponent must AT LEAST call with
450/(810+450) of his hands, but suppose he only calls with
approximately the top 90% of THESE. He would then be at
least calling with 88 or better and some hands that are just
a pair of sevens. [45/(81+45)*0.9 is about 0.321428571 and
when you multiply by C(52,5)=2598960 you get 835380 hands.
There are 198180 hands that are two pairs or better, so that
gives 637200 one pair hands and at 84480 for each rank, you
get 7.5426 ranks or a pair of 88 or just over half of the
hands with a pair of sevens).

Say, he plays only 88 and half of his pair of sevens or
"effectively 7.5 ranks".

After the draw, he automatically checks and after betting
1980 into a 1920 pot, he is to call with a frequency of
1920/(1980+1920) according to GT or about 0.492307692, but
let's say he's a bit of a nit and only calls with the top
90% of THESE. Even then, his calling frequency is about
0.443076923 and if we assume his chances of improvement are
4656/16215 (actually, it IS be a bit higher because it is
MORE LIKELY you have a non-pair type of hand to open, but
the difference won't matter too much because he will be only
calling with about the top 90% of the GT calling hands), he
should be calling with JUST ONE PAIR of the times he does
not improve with a frequency of 0.218746631. That CLEARLY
includes a pair of aces, KKJ+ and you may include some KKT
hands.



Of course, if your opponent were playing "optimally", he
would call with even more hands: turns out he would call
with QQK or better after the draw if the betting amounts
were as above.

Heads up is tough!

I would say that many "regular" players play too tight when
HU or in 3-way situations in draw, because they can't
properly evaluate the strength of hands.