Jerrod Ankenman ([info]hgfalling) wrote,
@ 2005-03-24 16:36:00
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Poker Quiz #1...
Maybe I'll do this every once in a while. We'll call this the "useful Yoonies" - Barbara Yoon used to post "test your intuition" all the time about stuff that wasn't that helpful in terms of actually playing poker but was interesting in some combinatoric sense. You know, like Brian Alspach's columns. Hopefully these little quizzes will be the opposite...not that interesting in a combinatorical way, but of some use in thinking about poker. Plus I can ape some of this material for the book.

Test your intuition first, then figure it out:

Let's say UTG makes a moderately tight raise from {AA-99,AK,AQ,AJ,KQs}.
On which of the following flops is he most likely to have top pair or better? On which is he least likely to have top pair or better?

Axx
Kxx
Qxx
Jxx
8xx

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(Deleted post)

[info]oscarmc
2005-03-24 10:21 pm UTC (link)
A,x,x - least likely. 3x the charm.

(Reply to this) (Parent)

[info]entrager
2005-03-24 10:27 pm UTC (link)
My answer: Kxx (having only 24 ways to make top pair or better)

Axx has 39 ways
Qxx has 30 ways
Jxx has 33 ways
8xx has 36 ways

So am I right?

(Reply to this) (Thread)

[info]entrager
2005-03-24 10:31 pm UTC (link)
So I guess it goes without saying that Axx is most likely.

For posterity, the order is:
Axx
8xx
Jxx
Qxx
Kxx

(Reply to this) (Parent)

[info]true_north
2005-03-24 10:37 pm UTC (link)
Most likely - Axx. Least likely - Kxx.

(Reply to this)

My intuition was almost correct
[info]rcfox
2005-03-24 10:57 pm UTC (link)
I though it was in order: Axx, Kxx, Qxx, Jxx, 8xx

But the correct answer is Axx (most likely), Qxx, Kxx, Jxx, 8xx (least likely)

Without giving away the math, 100 plays a role (in one method of solving the problem).

(Reply to this)


[info]jacksup
2005-03-24 10:58 pm UTC (link)
I thought Axx would be most likely and 8xx least likely.

If I've done the math right, turns out Axx is most likely, but Kxx is least likely. Niiiice. It makes sense now that I think about it. Definitely a cool result.

Matt

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[info]prock
2005-03-25 01:02 am UTC (link)
I'm so confused. I would have picked Kxx. But everyone seems to be getting different answers, and I get two cases which are equally the least likely, as well as two cases which are equally the most likely.

Oh woe is me!

That's what I get for trying to do combinatorics after four tabling for five hours.

"I am a poker zombie!"

(Reply to this) (Thread)

[info]prock
2005-03-25 01:23 am UTC (link)
What's a denominator? Is KQo == KQs?

Fuck if I know.

I'm just a poker zombie.

I get Kxx as least likely, clocking in at 28.2%

(Reply to this) (Parent)
answers:
[info]hgfalling
2005-03-25 02:33 am UTC (link)
When the board is Axx, the raiser has TP or better when he holds:
AA (3 times) + AK, AQ, AJ (12 times each) = 39 "does"
KK, QQ, JJ, TT, 99 (6 times each) + KQs (4 times) = 34 "doesn't"
or 53.4%

Kxx:
Does (AA/6,KK/3,AK/12,KQs/3) = 24
Doesn't (QQ-99/24, AQ-AJ/32) = 56
or 30%

Qxx:
Does (AA-KK/12,QQ/3,AQ/12,KQs/3) = 30
Doesn't (JJ-99/18, AK/16, AJ/16) = 50
or 37.5%

Jxx:
Does (AA-QQ/18,JJ/3,AJ/12) = 33
Doesn't (TT-99/12, AK-AQ/32,KQs/4) = 48
or 40.7%

8xx:
Does: (AA-99/36) = 36
Doesn't: (AK-AJ/48, KQ/4) = 52
or 40.9%

So the order is:
Axx
8xx
Jxx
Qxx
Kxx

Now, how might we use this information?

***** Hand History for Game XXXX *****
$15/$30 Hold'em - Thursday, March 24
Seat 1: seat1dude ( $844.5 )
Seat 2: seat2dude ( $625.5 )
Seat 3: seat3dude ( $2165 )
Seat 4: HgFalling ( $1410 )
Seat 5: seat5dude ( $391 )
Seat 7: seat7dude ( $606 )
Seat 8: seat8dude ( $403 )
Seat 9: seat9dude ( $823 )
Seat 10: seat10dude ( $3514.5 )
Seat 6: seat6dude ( $685 )
seat7dude posts small blind [$10].
seat8dude posts big blind [$15].
** Dealing down cards **
Dealt to HgFalling [ 8c 8d ]
seat9dude folds.
seat10dude folds.
seat1dude folds.
seat2dude folds.
seat3dude folds.
HgFalling raises [$30].
seat5dude folds.
seat6dude raises [$45].
seat7dude folds.
seat8dude folds.
HgFalling calls [$15].
** Dealing Flop ** [ 4h, 6d, Kc ]
HgFalling checks.
seat6dude bets [$15].
HgFalling raises [$30].
seat6dude raises [$30].
HgFalling calls [$15].
** Dealing Turn ** [ 7c ]
HgFalling checks.
seat6dude bets [$30].
HgFalling calls [$30].
** Dealing River ** [ Ks ]
HgFalling bets [$30].
seat6dude folds.
HgFalling does not show cards.
HgFalling wins $292
seat9dude has left the table.

(Reply to this) (Thread)
Re: answers:
[info]prock
2005-03-25 04:33 am UTC (link)
Kxx:
Does (AA/6,KK/3,AK/12,KQs/3) = 24
Doesn't (QQ-99/24, AQ-AJ/32) = 56
or 30%


I'm still confused. If a K is on the board, there is only one KQs which matches the board, not three. I think you are mixing p(king on board) with p(hand matches king). But maybe I'm wrong about that. Still zombified.


(Reply to this) (Parent)(Thread)
Re: answers:
[info]prock
2005-03-25 04:37 am UTC (link)
Yes, still clearly confused.

braaaaaaains.

(Reply to this) (Parent)
Re: answers:
[info]jacksup
2005-03-25 05:22 am UTC (link)
On the math: that's what I got too.

On the hand history format (seatxdude): Love it

On the flop check-raise: Like it

On the river bet: Don't like it. Let this guy bet again. With the hands of his that you beat, he's less likely to call your bet than he is to bet himself if you check. And obviously no hand better than yours can be expected to fold. Plus you lose less when your opponent actually has a king. So you lose less when you lose and win more when you win by check-calling, in my opinion.

Matt

(Reply to this) (Parent)(Thread)
Re: answers:
[info]hgfalling
2005-03-25 06:11 pm UTC (link)
When I discussed this hand with Michelle, she and I both agreed that it was more than 50% that this guy folded the best hand. I'm not sure why you think that it's so obvious that no hand better than mine can be expected to fold. I mean, YOU wouldn't fold, but that's hardly emblematic of the population at large.

(Reply to this) (Parent)(Thread)
Re: answers:
[info]actionbobnj
2005-03-25 07:37 pm UTC (link)
OK, I can't help but respond do this one. I am really shocked that you guys would estimate there is a 50% chance the guy folded the best hand here. It really boggles my mind. IMO, any estimate over 5% is high. I'd say its more in the 1-2% range. There is just almost no chance of someone folding a better hand here in a typical online 15 game.

(Reply to this) (Parent)(Thread)
Re: answers:
[info]abostick59
2005-03-26 01:06 am UTC (link)
What hand do you see seat6dude having in this spot that he'd reraise with before the flop, bet and reraise on the flop, bet on the turn, and fold on the river? Do you think he was running a bluff with AQ or AJ?

IMHO, Jerrod was more likely to win the pot by betting than he was to catch a bluff by checking and calling; and the bluff only has to work one time in ten to be profitable.

(Reply to this) (Parent)(Thread)
Re: answers:
[info]jacksup
2005-03-26 03:24 am UTC (link)
Jack-deuce.

In all seriousness, it doesn't really matter what I think he had up until the river. With a board of KK764 and a pot of $300, if a typical player folds for a thirty dollar bet, then the chance that his hand could've beaten two eights is less than eight percent in my opinion. And I actually think it's considerably lower.

But if you want to consider all the action, look at this way. There is a substantial portion of the playing population whose chance of folding better than 88 is zero percent. This portion of the population includes all the good players and all the calling stations. That's A LOT of people. Whereas the percentage of the population who would put in three bets on the flop with better than 88, and then fold when the top card pairs on the end (a SAFE card really), has got to be extremely small. I mean, it has to be an overthinking, sometimes aggressive, but weak-tight on the river kind of player. That player exists, but I would guess he represents less than five percent of the population. And even that guy probably only has a 50 percent chance of folding at most.

IMHO, this is a clear check-and-call. In fact, if I gave this hand on a poker quiz and asked "was the river bet a bluff or a value bet?" I wouldn't even give partial credit for those who answered bluff.

Or maybe you guys are right and I'm crazy. That's always a non-zero probability.

Matt

(Reply to this) (Parent)(Thread)
Re: answers:
[info]actionbobnj
2005-03-26 04:21 am UTC (link)
You're definitely not crazy Matt. I really can't even see this decision as even close. First the chance that someone folds a hand like 99, TT, etc on the river in a typical online 15-30 game is close to zero. I play 1K+ online 15-30 hands per day, and I can assure you it ain't happening except for the *exremely* rare player or possible mouse misclick. If I was real generous I could maybe put that range at 5%.

The other pretty big factor is the same guys with bigger pairs here we know will basically never fold, but sometimes they will check the river through and save you a bet.

(Reply to this) (Parent)
Re: answers:
[info]fich
2005-03-25 07:06 am UTC (link)
I see the problem - seat6dude has moved his chair halfway around the table.

(Reply to this) (Parent)

[info]abostick59
2005-03-26 12:53 am UTC (link)
Have you done the same kind of figuring for different ranges of hands?
Some players won't raise UTG with TT or 99; some "reasonably tight" players will reraise open-raisers with pairs as small as 77 or 66; some players will muck AJ with a raise in front of them; etc.

In other words, how sensitive is the claim "a king-high flop is the least likely to give a tight raiser top pair or better" variations in raising standards?

I could do the work myself, I suppose, but why should I if you already have? ;-)

(Reply to this) (Thread)

[info]abostick59
2005-03-26 04:26 pm UTC (link)
If the raiser is a tight-assed rock, and raises/reraises only with AA, KK, QQ, and AK, then the top-pair-or-better rankings are:

Board   % top pair or better

 Kxx            77.8

 Axx            53.6

 Jxx            52.9

 8xx            52.9

 Qxx            48.4


If the raiser doesn't raise with AK but just the three biggest pairs, then the numbers look like Qxx & lower: 100%, Kxx: 60%, Axx 20%.

It looks like the result is sensitive to the number of raising hands containing kings compared to those containing aces or smaller pairs. Which, when you think about it, ought to be apparent by inspection. Duh.

(Reply to this) (Parent)
King High Flop Theory in Practice
[info]prock
2005-03-26 02:04 am UTC (link) 
holdem       $ 40/80 Eleuthera                          Fri Mar 25 19:57:52 2005
     ante: 0.00 blinds: 20.00 40.00 rake: 2.00  pot:  638 [Js 3h Kd Tc]
 -
Angelina       4238 f                            0    0.0 
 -
 -
LyinBryan      1457 Srr  bc   kr               400  318.0 [Kc Kh] 
 -
Andrew         3231 Brc  r    bf               320 -320.0 [5h 5s] 
iloveparis     1798 f                            0    0.0 
 -
orkids         1746 f                            0    0.0

(Reply to this)

It kills me
[info]freelikebeer
2007-05-29 09:15 pm UTC (link)
I am reading yours and Bill's book and sifting through old headsupclub.com posts from Andrew. Two years ago, you were playing 15/30. Now, uhh, you are playing considerably higher.

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