Re: Answers
First of all, thanks to crabbypatty (where from?), schubes,
and TheShootah for their responses.
Second, the games discussed don't have a bug/joker and have
two blinds as in LHE to the left of the button.
Answers:
1) Discarding an ace is best. Your opponent is a 286-1
shot to outdraw your trips and you can get a suspicious
opponent to think you missed your draw. Also, in answer to
crabbypatty, limping in this spot is clearly dependant on
the field. If the blinds defend tenaciously or the button
cold calls with hands like shorts, cathops or draws, you
should punish them with a raise. On the other hand, if your
opponents are quite reasonable and won't often play back
with hands like medium 2-pairs, it is much better to just
limp even though it looks suspicious. Besides, there are
some hands that do seem to play better by limping than
either folding or raising (but I won't say but perhaps you
can think of them!).
In the situation where the players are reasonable to tough,
you can only convince yourself after dealing out this
situation a few hundred (or for the doubting Thomas, a few
thousand) times. One of the most common situations is that
the SB completes for another 0.25 BBs and another common
occurrence is that the button limps or plays a flush draw.
A big chunk of the equity comes from the SB completing and
that swamps other less common situations by a big margin.
I estimate that limping in this spot rather than raising is
between 0.1 and 0.2 BBs better against reasonable but not
pathetic opposition.
I had almost another identical situation with AAA22 and here
the limp is a tiny bit better since I have only 3 key cards
taken up in the hand as opposed to five in the previous one.
2) Quite standard to draw two to AAK since your opponent is
supposedly holding AA or KK according to "Wiesenberg 101".
If you didn't know this, back to the basics! [img]/images/graemlins/smile.gif[/img]
BTW, this is normally a fold in the 3-6 game (do you see
why?).
3) Although schubes mentioned that Wiesenberg mentioned
this in CP, it also comes up in Malmuth's "Winning Concepts
in Draw and Lowball" on p.360 "Examining Kickers". Bear in
mind that the hand discussed there had a deck that includes
a bug.
First of all, your opponent better have AA or KK because if
there is any chance at all he has less, he's blowing some
equity with those "shorts" in this spot and if that were the
case you should draw three because of the postdraw action.
Although drawing one to AAKQ maximizes your chances of
holding the best hand after the draw, I did a little bit of
homework to see if that would translate to a better EV since
the postdraw action is also important. My conclusion was
that drawing one to AAKQ was a tiny bit better from an EV
calculation than drawing three against the typical tough
opponent.
4) If you draw three to a pair, your odds of making a boat
or better is around 210/16215 = 0.01295 (I don't know if
in reality it's higher or lower due to another hand being
pat!). Also, you'll be drawing to a pretty big pair, so
when you get lucky, you have a comfortable raise. Of
course, even if you make Kings full, there is still about a
2% chance your opponent will have better! Now, if you do
raise, some of your opponents will muck their straight
since you "obviously filled or made quads", in which case
you don't get that extra bet all of the time, plus there is
that 2% chance they'll come over the top and you'll be
staring at the nuts.
If you have a three flush, even if it's a small one to draw
to, your chance of making it is a bit higher than C(10,2)/
C(47,2)=45/1081 or about 0.04163 (the reason it's higher is
that often the pat hand is a flush in a different suit) and
you often have a big flush when you make it so you can make
a comfortable raise. Clearly, you should draw to a three
flush if you have one and you don't even have to even raise
unless your flush is king high or better.
What about drawing two to a big straight? (Obviously, you
will draw three to a hand like KK753 which will become
clearer later). You will have either a one-way, two-way or
three-way straight draw (the last kind will be with a hand
like QQJT2) and the probability of completing your hand will
be either 16, 32 or 48 out of 1081. When you complete your
hand, you can't raise (except with AKQJT against opponents
that will always pay off, even with a wheel), so you can
forget about the one-way draw. In the other cases, they are
reasonable since you won't be raising and will be getting
there more than twice as often as compared to drawing three.
The downside is that you'll often end up with something like
QJT98 and you'll just lose another bet. I haven't done the
dirty work for equity calculations but I would guess that
you would draw three to your pair unless you had a QJT hand
to draw to, in which case you would want to draw to that.
Your chance of making this draw is around 0.0444 so you
should be happy with that since you win about 40% of the
times you make it.
5), 6) and 7) later! (Time for dinner!).
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