Nasty pl5cd hand

[List]

I ended up breaking Zeebo theorem and folding. I knew there was no way he was bluffing, and I decided that he wouldn't make the play with just AAA. That said, when I went over the math later I realized that he only has to make the play with AAA a small percentage of the time to make calling profitable. I don't think he ever puts me on a draw that hit btw, he knows I have trips or a full house/quads when I raise him, even if that isn't completely accurate.

[ QUOTE ]
if you had jacks-full instead, it would be much
harder to fold.

[/ QUOTE ]

I'm interesting in seeing the math here. If he only pushes with a full house+, and his preflop range is AA,KK,QQ. What's my equity against his range with JJJ33, given that I dumped a king.

[bigpooch]

IF his worst hand predraw is QQ, you're in terrible shape
because somebody drawing three to XXabc will make X's full
or quad X's MUCH more often than something like yyyXX.
Ignoring other cards (such as the three jacks, two threes,
king and presumed AA or KK in SB's hand), out of the
improvement combinations to make a boat or better when
drawing three to a pair XXabc, there are:

45 for quads
126 for a boat of the form XXXyy
39 for a boat of the form XXyyy

Also, some of the 39 boats of the form XXyyy will be like
AAAXX, KKKXX or QQQXX. Still, the type of hand will be of
the form XXXyy only about 18.6% of the time. Here, you have
a very easy fold (your "pot odds" are only about 1/3).

Suppose instead, the big blind could have TT OR 99 (not
impossible since you were the button and could be on a
semibluff or steal and the SB hasn't shown any strength).
Let's also credit the SB with one of either AA, KK or QQ
(not unreasonable since he doesn't need to defend with TT
and JJ is an impossibility if you end up with JJJ33). Now,
how do you stack up against the BB's range?

So, let's assume the SB has AA (you've pitched a king) and
so we take out two aces, one king, three jacks and two
threes from the deck. [ It won't change the analysis too
much even if the SB has QQ.] Then, the BB could have any
of the following predraw:

AA: 1
KK: 3
QQ: 6
TT: 6
99: 6

(these are only approximate "weights")

With AA, there are only 3 combinations of KKKAA and 6 for
QQQAA and 4x8 = 32 for weaker boats (only eight ranks from
deuce up to ten with three's excluded since you can't get
three of them).

With KK, there are 56 combinations of KKKyy, 4 of QQQKK and
32 weaker boats as before.

With QQ, there are 112 combinations of QQQyy, and 32 weaker
boats, but also 40 combinations of quads (extra card can
only be one of 48-8=40 cards).

With TT, there are 40 combinations of quads, 1 KKKTT,
4 QQQTT, 112 TTTyy and 28 other weaker boats (140 weaker
boats) and similarly with 99.

Effectively, the approximate "weights" are:

quads: 3x6x40 = 720
bigger boats: 9+3x60+6x112+2x6x5= 921
smaller boats: 32+3x32+6x32+2x6x140 = 2000

Here, the approximate chances you have a better boat is
about 54.9% so JJJ33 is just a slight favorite. You had to
call $222.60 in a pot that would total $645.6 minus the rake
so that would be an easy call.


If your opponent's range DID NOT include 99, the numbers
would now look like:

quads: 480
bigger boats: 891
smaller boats: 1160

so you would only have about a 45.8% chance of winning, but
you still call, although now you lose most of the time.

(Hopefully, the math above isn't that far off, but the
summary is adequate!)


SUMMARY
=======

Call if there was some reasonable chance your opponent
started with TT (or worse); otherwise, folding is better.

[AceOfClubs]

Wonderful post bigpooch. [img]/images/graemlins/cool.gif[/img]

[List]

Thanks for taking the time to figure/type all that out. He's never over-calling TT here, and I doubt he calls it with the sb out either. So I guess even JJJ33 becomes an easy fold if he doesn't push AAA.

[spike420211]

[ QUOTE ]

Call if there was some reasonable chance your opponent
started with TT (or worse); otherwise, folding is better.

[/ QUOTE ]

ok, so what would he call 3x BB predraw and draw 3 with? TT?
JJ?
there goes any reasonable chance...

[adrimac]

That is definitely a tough beat List. The odds of boating or better on a 3 draw are about 75-1, no? On another note, you certainly know your players well...Flop is a friend of mine and actually is a full time player...he's very good...you described his game pretty accurately with very few words. Best of luck in the future!

[adrimac]

Also, it's very likely you're dead here, but you guys definitely figured that out...I'm guessing kings full is about the worst he's holding...