Collective Outs Challenge

[Louie Landale]

There is considerable belief that the collective outs of bad hands calling in holdem usually turn the high pair "best" but vulnerable hand into an underdog in such a manner that this hand should NOT bet or raise.

I would like to clarify that a hand is a "favorite" if it will win more often than its "fair share" which is 1/n-players in the pot: so if there are 2 opponents (3 players) the fair share of each is 33%; and any hand that will actually win more often than that is a "favorite" and should bet or raise so long as the "underdogs" will call (and probably even if they will fold but I digress...). It can and often DOES happen that more than one hand is a favorite and should raise each other trapping the dog hands.

Here's the challenge. Can anybody please contrive an example of flops and opposing hands where [1] Hero has AK flopping an A or K [2] this pair is the highest on the flop [3] This pair is a favorite heads-up against each opposing hand [4] This pair is an UNDERDOG against the collective field. That is, the "collective outs" of the inferior hands turn Hero's big pair into an underdog and should not bet/raise if all hands were face up.

- Louie

PS. Yes, Heads-up against a straight flush draw the pair is an underdog but that's not a collective-outs issue (it violates condition [3]). And if there is even one more player in the pot Hero is back to being a favorite.

Extra Credit. Lets give hero 88 and its "best"; and I believe you CAN contrive and example where collective outs kill this hand. Even so, such contrived examples will be very rare in real life.

[Nate tha' Great]

http://twodimes.net/poker/?g=h&b=Ac+...+7h%0D%0AJc+Qc

Board A [img]/images/graemlins/club.gif[/img] T [img]/images/graemlins/diamond.gif[/img] 9 [img]/images/graemlins/diamond.gif[/img]

Hero has A [img]/images/graemlins/heart.gif[/img] K [img]/images/graemlins/spade.gif[/img] (23.5%)

Opponents hold
Q [img]/images/graemlins/club.gif[/img] J [img]/images/graemlins/club.gif[/img] (17.6%)
8 [img]/images/graemlins/heart.gif[/img] 7 [img]/images/graemlins/heart.gif[/img] (14.0%)
A [img]/images/graemlins/diamond.gif[/img] 5 [img]/images/graemlins/diamond.gif[/img] (44.9%)

Hero's equity is .235 in a 4-player field, just a hair below par.

[Louie Landale]

We seem to have one winner; thanks to Nate. I wonder if there is any other fundamentally different situation where the "best" hand isn't a favorite: vrs big flush draw, two straight draws, and Hero's kicker is a loser.

So the only case we came up with where the best hand big pair is NOT a favorite results in Hero being just SLIGHTLY a dog, I'm going to conclude that this "collective outs kill the tight player" stuff is donkey-do.

- Louie

[Ilovephysics]

I'm not sure if I'm getting your question correctly, but feasibly someone could hold a pair of Tens like:

Tc Th

...and the flop could come:
9s 6h 5s

In this case, they'd be a favorite against hands like:
1) 3s 2s
2) 9c 7c, perhaps 9c 8c
3) Ac Ks

But against them all, the Tens would win 21%... and yet, I can feasibly see all of these players staying in believing that they have a good shot of winning this hand (or lucked into one).

I'm sure this would happen in other circumstances, too, but I'd agree, it took me about 5 minutes of playing around just to get at this set-up which I felt was somewhat 'reasonable' for people to hang around with... I think you are probably correct for many circumstances.

[Thats Interesting!]

I am of an average intellegance, your question is just too overwhelming for me. [img]/images/graemlins/smirk.gif[/img] Im haveing a hard time understanding what it is ur looking for.

Anyhow, that being said or miss said.

Collective outs do kill a fav hand on the flop sometimes, in some cases all the time. Say if you have top pair top kicker and 9 players call, its not to your advantage to be betting and raising, its to the advantage of the best drawing hand. I know everyone knows this, so ill shut up now. [img]/images/graemlins/cool.gif[/img]

[Ilovephysics]

I suppose, again, another possibility would be that you hold:

Ad Ah
and flop comes:
Js 6s 9c

and you are against:
1) Td 8d
2) 5s 4s
3) Kc Jc

Truthfully, this seems kinda like looking for a needle in a haystack. I highly doubt all of these people hang around... However, I suppose it is still possible that they all do.. In this case, one has a flush draw and backdoor straight draw, one has an open-ended straight draw, and the other has TP with a good kicker and backdoor flush draw.

In a very non-scientific sense, it looks like you are mostly correct.

As best as I can guess on short notice (which may be way off!), it would appear that your 3 opponents against your higher pair (in these cases) basically need something like:

1) an open ended straight draw
2) a flush draw
3) a TP of the flop

I think this pretty much keeps them all in the hand past the flop, too. However, it is all very sensitive to a simple card or two here and there. In other words, if we make the player holding Kc Jc become Ac Jc (a hand a player might otherwise rather have all else being unknown), the Aces are now up to 28% win... and if the hand becomes Qc Jc, (again, perhaps a better hand in this person's mind), now the Aces are at 30%. Note, that in these changes, I doubt someone who was staying in before would all-of-the-sudden drop because of this change... so even if you sensed a flop 'like this', you probably shouldn't change what you are doing.

[bigpooch]

A simple example is for just two opposing hands. To
continue with the theme of one of the posts, let the hero
have A [img]/images/graemlins/heart.gif[/img] K [img]/images/graemlins/club.gif[/img] with the flop as

A [img]/images/graemlins/spade.gif[/img] T [img]/images/graemlins/heart.gif[/img] 9 [img]/images/graemlins/heart.gif[/img]

and let the other two hands be

A [img]/images/graemlins/diamond.gif[/img] K [img]/images/graemlins/diamond.gif[/img]
K [img]/images/graemlins/heart.gif[/img] Q [img]/images/graemlins/heart.gif[/img]


http://twodimes.net/h/?z=239245
pokenum -h ah kc - ad kd - kh qh -- as th 9h
Holdem Hi: 903 enumerated boards containing As Th 9h
cards win %win lose %lose tie %tie EV
Kc Ah 21 2.33 380 42.08 502 55.59 0.300
Ad Kd 0 0.00 401 44.41 502 55.59 0.276
Kh Qh 380 42.08 514 56.92 9 1.00 0.424

[pudley4]

[ QUOTE ]
Collective outs do kill a fav hand on the flop sometimes, in some cases all the time. Say if you have top pair top kicker and 9 players call, its not to your advantage to be betting and raising, its to the advantage of the best drawing hand.

[/ QUOTE ]

But your TPTK hand doesn't have to be the favorite, it just has to be a favorite.

[1800GAMBLER]

It's to both of your advantages if you both bet and raise. Understand the 'if it will win more often than its "fair share" which is 1/n-players in the pot: so if there are 2 opponents (3 players) the fair share of each is 33%;' part.

[shemp]

An interesting aside to some of these hands is that, not only does the "current best" trail, but often ends up being the only hand to pay off on the river -- so it loses fair share wise and reversely -- suggesting that even hands with a lower fair share can be in a better spot given reverse implied odds -- that is, even with lower equity, higher EV.

Also, I think the examples show these aren't pathological events, they may be hard to find, but that may be a feature of how a human searches for them, the hands are not so out of the ordinary.