5CD: free play on BB...i toss 22, keep AK.

[Big Limpin]

Is this dumb? It kinda felt right. Maybe standard play for some of you? I can't recall ever tossing my only pair before:

-5 handed limit draw, I was on the BB, dealt AKx22.
-Fold, Fold, Limp, Fold. Check.
-Hero draws 3 to AK. Button draws 3.
-Hero bricks and checks, button bet, hero fold.

I'm undecided if this was +/-EV, help? [img]/images/graemlins/confused.gif[/img]

Couple thoughts:
When the button limps, most often he has a short - in his mind, "not good enough to raise" but he still wants to play it, so 22<him<KK, usually. He draws after me though, so i wont know for sure. If he limped because he is drawing, then AK and 22 have equal showdown value to me.

I think i improve the AK more often, and it will beat his unimproved hand, but the deuces will make stronger hands, like 222 might beat him if he improves.

I'm torn, thoughts?

[bigpooch]

Let's assume that the button limped in with a pair less than
JJ and bigger than 55 (it's probably not too far off against
most opposition). If you draw to AK, you'll make a pair of
jacks or better with a probability of about 38% whereas if
you draw to 22, your improvement chances are only about 29%.
If somehow you were all-in or your opponent timed out, you
would simply draw to AK (from twodimes.net, your pot equity
is better by 6% to 9% depending on your opponent's pair, the
live cards, and if you are suited on your AK).

It's not that simple though. If your opponent calls after
the draw according to GT (game theory) or close to it
(unlikely, but you need to evaluate your play based on the
theoretical merits and then play exploitively if the
situation warrants it), he will be paying off with not just
any improved hand, but also some unimproved pairs: 2.5/4.5 -
(improvement chances of 29%) is about 27%, so he should be
paying off with unimproved pairs about 0.27/0.71 or 38% of
the time. As the big blind, you can only value bet with
approximately anything that is around the top 40% of the
button's calling hands or about tens-up or better. (If you
bet many more hands than this, you're overplaying the final
round; if you bet much less often, you don't get full value
for your hands.)

Drawing three to AK, you make kings-up or better (kings-up
is the weakest hand you can make that is bettable versus a
three-card draw by the button) about 6.6% of the time (7.6%
if you were suited) whereas you would make tens-up or better
about 18.8% of the time if you drew three to 22. [Also, if
you drew two to A22, you make tens-up or better about 22.3%
of the time, but you would be folding quite a lot after you
drew two to 22A or 33A after you check.]. Your post-draw
betting frequency is very low when you decide to draw to AK,
so you would have fewer bluffing hands (your optimal
bluffing frequency is your legitimate betting frequency
divided by (P+1) where P is the size of the pot before you
bet in terms of the number of big bets).

Also, after you check post-draw, your payoff hands will be
any two pairs from 3s-up up to nines up (or even tens-up if
you choose not to bet tens-up but use it to catch bluffs).
On the other hand, if you have drawn three and somehow end
up with either KKA or AAK, and check, you really are in a
tough spot: although these are both GT calling hands, when
playing against most opposition, you'll be losing a final
bet very often as most opposition (from my experience) won't
be bluffing very often in this case, so you probably only
want to pay off with aces or better. Against a bluffer, you
want to pay off with a pair of jacks or queens and maybe
even as little as TTAKx.

If your opponent will often bluff, you may also want to draw
three to AK to try to make even a pair of jacks to pick off
a bluff. If you were to draw three to 22, you would only
be able to pick off a bluff about 29% of the time.

If your opponent rarely bluffs, but will pay off a lot with
unimproved one pair hands, that sways towards drawing to a
pair of deuces to try to make a bettable hand. You then
probably want to check and fold if your hand isn't bettable.

Against an unknown opponent, I think you prefer to draw to
22 (then the question is whether to keep the ace) since you
want to be able to bet often post-draw. You also avoid the
embarrassment of paying off with KKAxy (and AAKxy, although
this should be an automatic payoff) and losing an extra bet
on the end when you didn't have to if you had drawn to 22
and missed.

And of course, if the button might be limping in with a draw
(flush draws may be typical), you may want to draw three to
AK to pick off a bluff in case you make a big pair. If he
traps a lot (medium trips or better), now you draw to 22,
not just so you don't pay off as often, but to maximize the
chances of making a boat or better.


Another interesting question is this:
-----------------------------------

You are in the BB with the same hand, but now the SMALL
BLIND limps and draws three. Do you now draw three to AK?

If you sense that what you were doing (drawing three to AK
versus the button) was right, you should see that it would
make even more sense to draw three to AK here, as you would
value bet AAK when checked to (and even KKA against the
right opponent in the small blind). Of course, you have to
think about how the small blind plays: his distribution of
hands and how he plays post-draw.

[Big Limpin]

bigpooch, thats alot to think about, i'm still digesting. superb post though! The actual question of keeping 22 or AK isn't really that critical; i know its cents on the dollar EV either way, i know they are close enough to equal.

interesting always to hear your thought processes, it seems i am intuitively playing in a similar manner as you in most places, but often with less mathematical thought. This likely due to quality of opposition. This hand i post from 2/4, but i often play 1/2, my opponents are not game-theory wizards. i;m hesitant to accept GT-dictated actions for my opponent.

So heres a refined opponent: He's a typical loose-passive, this hand will go check-check most of the time. I expect to table A-high or 22 most of the time, his 99 takes it. I just want to mazimize my odds of winning a check-down, secondary consideration is maximizing my chances of winning a big pot when he improves. Agree 55-JJ his range almost precisely; even fish muck 44 OTB, and even nits raise QQ OTB.

This guy is passive, and mostly he will check down all his unimproved pairs *with sporadic spew-bluffs! If he bets (wasnt noted as a maniac), its almost always because he improved. Folding <~TT-up here seems right, if i feel strongly he has improved, which differs from your [ QUOTE ]
Also, after you check post-draw, your payoff hands will be
any two pairs from 3s-up up to nines up (or even tens-up if
you choose not to bet tens-up but use it to catch bluffs).

[/ QUOTE ]Yeah, thats just becasue MY opponent isnt value-betting/bluffing near often enough. I would call him with aces up of course, but not 33-up through at least TT-up or so, and not definately not AA. Then again, I guess i lead at him with >KK-up, 'cause he likes to call. So when i'm checking to him, its usually a check-fold. Remember, this was all a freeplay, and all i'm trying to do is give myself the best showdown hand for our customary check-check post-draw.

Yeah, so where does that refined opponent profile bring us?

On one hand, there will be less bets/calls in this hand, bringing it closer to: [ QUOTE ]
If somehow you were all-in or your opponent timed out, you
would simply draw to AK (from twodimes.net, your pot equity
is better by 6% to 9% depending on your opponent's pair, the
live cards, and if you are suited on your AK).

[/ QUOTE ]
On the other hand, my opponent being a calling station: [ QUOTE ]
Against an unknown opponent, I think you prefer to draw to
22 (then the question is whether to keep the ace) since you
want to be able to bet often post-draw.

[/ QUOTE ]
And also, theres my hesitancy to call him with weak 2pr, which the AK wont be making. Thats maybe why i like the AK intuitevely, i'll make fewer borderline bad folds/calls with it as opposed to 22 making 2pr.

Dunno, great post, bigpoooch, ive got lots to think about now. Anyone else got a voice on this?

[Murakawa]

on a similar note, should you call with any pair on the button when everyone limps for implied odds? What about the SB?

[Big Limpin]

im not sure how thats similar, you mean on the button with a low pair, limping behind UTG, hijack, and CO limps, to go for a set?

No, i wouldnt put in a full-bet to do that, i'm 2nd best ass-[censored] too often, not to mention missing most of the time. For half-bet from SB though....yeah i usually do it!

[Big Limpin]

<u>Update:</u>
After 1 week of tooling around with both lines and noting the results, i've come to a conclusion. Draw to the 22 (/PP), and gun for trips. You will lose less chips on 2nd best hands. Those were the difference, i found, when i kept AK, made even a ~great hand, and was still thumped by his trips. Drawing to the biggest 2pr possible, at all costs, it sooo overrated, from my observations.

*bigpooch, do you ever come back to visit Vancouver?