Ever wonder if you're really a flip with A/K after limpers?

[The Student]

Here's a situation that I've been thinking about lately. Don't have the HH, but the hand went something like this:

UB $11 NLHE MTT
early levels, blinds at 20/40
5 limpers ahead of me, I'm on button with A/Ko. I raise pot to try to get it HU or just take it down. Folded to MP limper who now pushes back at me. We both started with average stacks and it would effectively put me AI too.

Here's the question:
After 5 limpers, assuming this guy has a PP other than As or Ks, is this really a flip? Is it really possible that none of the other limpers have an ace or king, and therefore, do I really have all 6 outs here against a PP?
anyone fold this here?
thoughts?

ts-

[Exitonly]

isn't is almost as likely that someone had limped w/ 89s and the guys 99's (for example) now have only a 1 card redraw?

it all balances out i think.

--

Though, if there were more action like a few raises, ,and you could be fairly sure that there was atleast 1 A or k dead, it might be worth considering..

\You should not be concerned by the fact that there's a pretty good chance that an A or a K's in the bottom half of the deck--probability takes care of that for you. However, if someone shows you all the remaining As and Ks are in the bottom half of the deck, this should affect your decision.

This situation is a mixture of the two examples I just gave. Limpers are slightly more likely to have an A or K then usual, so it's slightly less likely that an A or a K will flop. However, as it turns out, this effect is very negligible. There was an article in card player a few months (or maybe a year) ago that discussed bunching (which is essentially the same topic), and the guy showed through a computer model that it affected hands by less than 1% even in extreme situations. I'm sure you could find it if you want.

[The Student]

[ QUOTE ]

Though, if there were more action like a few raises, ,and you could be fairly sure that there was atleast 1 A or k dead, it might be worth considering..

[/ QUOTE ]

that's what i'm talking about - the possibility that one or more of my A and K outs are already in my opponents' hands. I guess I'm thinking that against 5 limpers, at least one of them is probably playing an A or K, right? but maybe not...maybe I really am still a flip.

friggin' incomplete information!

[The Student]

I'm not sure I understand you, or perhaps I didn't make myself clear in my first post. I'm concerned that some of my A and K outs are already dead because they are in the limpers' hands. So if I assume that even one ace is in someone else's hand, then I am not a true flip against the villian's (probable) pocket pair.

I don't remember the CP article that you're talking about, but I do remember TJ Cloutier writing about bunching. He was saying that sometimes if everyone folds to a LP player, that may mean that someone in tbe blinds is actually holdinga playable hand - that all of the good hands were "bunched" in the blinds instead of being evenly distributed around the table. Is that what you're talking about?

ts-

hmm, ya maybe.. I guess the only thing I can say is that people on the net like to play aces

[Gavagai]

Even if some of your cards are dead, its not as bad as it might seem, because we can also assume that many of your non-outs are dead.

If your opponent has 99, you have AK, and 2 of your outs are dead, on the following rough calculation you have a 38% shot:

1-((42/46)*(41/45)*(40/44)*(39/43)*(38/42)) = 38%

however, if only 2 of your outs are dead, then 6 of your non-outs are dead (there were 4 other limpers), so in fact there is a 43% chance:

1-((36/40)*(35/39)*(34/38)*(33/37)*(32/36)) = 43%

but yes it seems to me somewhat likely that you will be less than a coinflip, for with 6 outs you get:

1-((42/48)*(41/47)*(40/46)*(39/45)*(38/44)) = 50%

(In the situation described you probably had odds to call even if 2 outs were dead.)

Maybe I am looking at things in the wrong way though I dunno.

Gavagai

Edit: thought I should add that, if only 1 of your outs is dead, and 7 of your non-outs are, you get:

1-((35/40)*(34/39)*(33/38)*(32/37)*(31/36)) = 50%

Furthermore, there are many limping hands that don't contain aces of kings, so you certainly aren't entitled to assume that every time in this situation at least 2 outs are dead - often none or 1 will be. So it seems that we shouldn't worry too much about it.

[The Student]

i'm not sure I follow all that you are talking about here. what are non-outs and why should I care about them?

Also, the difference between having all 6 outs left in the deck and only 4 of them left to draw for is a big deal - it's the difference between making the call with correct odds and making this call without the correct odds. I'm still looking for someone to share some of their thoughts with me about making a call getting somewhere between 2:1 and 2.5:1 pot odds with overcards against someone I'm putting on a mid pocket pair when there are a lot of limpers. So far, all I've been able to come up with is this:

Early in the tourney, people are more likely to limp with mid-strength aces (especially sooted) and marginal kings than late in the tourney. The difference being that they are more likely to either raise or fold with those same starting hands in the later stages of a tourney. Seems to make sense? If this is correct, then should it be a factor in my decision in this hand when I'm facing a pot getting about 2.2:1 on my money with A/K?

ts-

[fnurt]

[ QUOTE ]
isn't is almost as likely that someone had limped w/ 89s and the guys 99's (for example) now have only a 1 card redraw?

it all balances out i think.


[/ QUOTE ]

Firstly, most coin flips are 55% for the pp to win and 45% for the two over cards. I'll use Ako vs 77. Losing one out brings you down to 41% and losing two outs brings you to 36%.
You start out with 55/45 or 1.2:1 drawing odds.
One out gone goes to 59/41 or 1.4:1.
Two outs missing goes to 64/36 or 1.8:1.
What you're asking weighs on my mind a lot too, because I'd hate for one of my outs to already be in the muck. I like what one person said that the 77 could have some of his outs mucked too, and it's more likely for someone to fold a 7 then and Ace or King. I've survived not thinking about it too much and assuming that it evens out. But it drives me nuts when I call with AK and then one of the other guys at the table says that he folded an ace.

[Exitonly]

Just a quick pokerstove thing.


AK vs 77 No dead cards.. 45 v 55
...

One K dead .. 60 v 40

One 7 dead .. 50 v 50

one K one 7 ..45 v 55 /images/graemlins/ooo.gif

[The Student]

[ QUOTE ]
Just a quick pokerstove thing.


AK vs 77 No dead cards.. 45 v 55
...

One K dead .. 60 v 40

[/ QUOTE ]

yeah, this is what i'm afraid of and what would make it a bad call in the situation i described in my OP.


[ QUOTE ]
one K one 7 ..55 v 45 /images/graemlins/ooo.gif

[/ QUOTE ]

very interesting. i wonder if this goes back to 50/50 with an A and a K out (or two As or two Ks out) and one 7 out. I don't have pokerstove on this computer or I'd check it myself. this stat alone definitely makes me feel like i shouldn't spend a lot more time worrying about these situations.

thanks exitonly,

ts-

[Exitonly]

whoops, edited my post, i wrote the one K one 7 one wrong...

when two A's or K's are gone and 1 7 gone, it's back to 60/40 for the 7's. (predictably)

edit: so i think unless you have some solid reasons that an A or K is gone, i think it's something to neglect, it balancecse out in time.

You shouldn't be taking situations where it's 'close' for a coinflip anyway.

You can check it at twodimes.net if you'd like. That's how I usually get my preflop %s.

[The Student]

[ QUOTE ]
whoops, edited my post, i wrote the one K one 7 one wrong...

when two A's or K's are gone and 1 7 gone, it's back to 60/40 for the 7's. (predictably)

[/ QUOTE ]

Ahh, that makes more sense - thanks for clarifying.

[ QUOTE ]
edit: so i think unless you have some solid reasons that an A or K is gone, i think it's something to neglect, it balancecse out in time.

[/ QUOTE ]

yeah, it's not like someone said that they had an A or K - so i had no way of really knowing if some of my outs were already in the muck. so hopefully it does all balance out in time.

[ QUOTE ]
You shouldn't be taking situations where it's 'close' for a coinflip anyway.

[/ QUOTE ]

i'm trying out some new things in my MTT strategy - so this time I tried to take a flip early just to see what would happen if I quickly doubled up and was able to bully the table a bit. but yeah, normally i would not call this early in a tourney if i thought i was a flip.

ts-

I kinda came up with the idea of bunching independently, and I do wonder about it sometimes. I don't know if I should be concerned about it or not, so if someone wants to comment on it, that would be great. Of course, it also seems entirely possible that, you could be folded to on the button with JTs or 7s or something like that, and the first four players to act mucked Ax small while the next three mucked Kx medium. In that case, you're holding some very nice cards.

Anyway, responding to the main point of the thread, I think your concern is valid, but I guess I wouldn't worry about it too much. You might want to take a look at Gavagai's post again. Basically, if you assume that you lose one ace or king from the limpers, you lose seven non-aces or kings (i.e. cards that aren't outs for you). So, if you just assumed that all cards were live (except a pp from the villian), you'd be looking at 6 outs out of 48 cards, which is 12.5% of the deck that can help you. If you assume that one ace or king is gone and that the other 7 cards are not aces or kings, you have 5 outs out of 40 cards, or 12.5% of the deck that can help you. If you assume that 2 aces or kings are gone, then you have 4 outs out of 40 cards, giving you help from 10% of the deck. Please note that this isn't your chances of winning but merely the percentage of cards in the deck that will improve your hand. An assumption of two of these cards being held by opponents is probably a bit high, as they could equally as likely be holding QJ or JT, any suited connectors probably down to 56, any small to mid pp, and if they're as donkish as some that I've seen, Q3s (this is just bitterness over my aces getting busted by Q3s calling a pre-flop raise, an all-in on the flop, and then making river trips).

[schwza]

a lot of people have said similar things, but i don't think anyone has really nailed this, so i'll take my shot:

- it's bad if a K or A has been mucked. it's good if a 7 had. but there are 6 A/K's and 2 7's. also, i think that it's much more likely for Ax or Kx to get limped than 7x. 7x is more likely to fold if it gets raised than Ax/Kx, but i think that's easily overwhelmed by Ax/Kx getting limped more and there being 6 vs 2 unaccounted for. therefor, when you see a limp-fold, you should assume the number of A/K's left in the deck goes down (in expectation) much more than 7's (or whatever villain's pair is).

[ QUOTE ]
i'm not sure I follow all that you are talking about here. what are non-outs and why should I care about them?

[/ QUOTE ]

if you were deciding whether or not to call the push and then the limp-folders flipped over their cards to show they had mucked the 12 2's, 3's, and 4's, then your odds of beating 77 goes way up.

no dead cards -
pokenum -h ac kh - 7c 7s
Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
Ac Kh 767723 44.84 938402 54.80 6179 0.36 0.450
7s 7c 938402 54.80 767723 44.84 6179 0.36 0.550

no 2-4's
pokenum -h ac kh - 7c 7s / 2c 2d 2s 2h 3c 3d 3h 3s 4c 4d 4h 4s
Holdem Hi: 376992 enumerated boards
cards win %win lose %lose tie %tie EV
Ac Kh 198967 52.78 174975 46.41 3050 0.81 0.532
7s 7c 174975 46.41 198967 52.78 3050 0.81 0.468

Let me try and do this again in a different way. If one of your aces is missing, it's not the only card that's missing. Making the deck shorter increases your chances of hitting your remaining outs, taking an A out decreases it--they come damn close to canceling.

The more important thing to realize is that cards that you can't see are random and should be ignored. Cards that call are slightly more likely to have As, but the effect is insignificant and should absolutely never effect your play. Please try to understand this and play AK.

[schwza]

oh yeah, sorry, i forgot to make the most important point in response:

this is probably a pretty tiny effect. i've never once considered it and i'm not going to start.

edit: also, if you think there are fewer A's and K's out, you're less likely to run into AA or KK, which helps balance out.

[dmk]

[ QUOTE ]
Here's a situation that I've been thinking about lately. Don't have the HH, but the hand went something like this:

UB $11 NLHE MTT
early levels, blinds at 20/40
5 limpers ahead of me, I'm on button with A/Ko. I raise pot to try to get it HU or just take it down. Folded to MP limper who now pushes back at me. We both started with average stacks and it would effectively put me AI too.

Here's the question:
After 5 limpers, assuming this guy has a PP other than As or Ks, is this really a flip? Is it really possible that none of the other limpers have an ace or king, and therefore, do I really have all 6 outs here against a PP?
anyone fold this here?
thoughts?

ts-

[/ QUOTE ]

you don't need it to be a flip. your pot-raise is 340, assuming the pusher had ~1500 to start the hand, it's 1200 into a 2100 pot. you only need 36% equity to make calling correct. if he doesn't have AA or KK, you easily have that, even if he has a mid-PP and an A or K is dead. however, it can be argued that one of the players that didn't limp could have potentially folded his 2-outs to a set because they had 92, etc. thats why you can't make this type of argument, its possible for anyone to have any-2 cards, so you have to just count on having 6 outs.

[zoobird]

Finally somebody responded to the important part of OP's post...the fact that the cards in a hand that limps are NOT random and in fact are probably more likely to contain A's and K's than other cards. That said, I agree - this is probably a VERY minor effect, and not worth considering.

[The Student]

[ QUOTE ]
[ QUOTE ]
i'm not sure I follow all that you are talking about here. what are non-outs and why should I care about them?

[/ QUOTE ]

if you were deciding whether or not to call the push and then the limp-folders flipped over their cards to show they had mucked the 12 2's, 3's, and 4's, then your odds of beating 77 goes way up.

no dead cards -
pokenum -h ac kh - 7c 7s
Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
Ac Kh 767723 44.84 938402 54.80 6179 0.36 0.450
7s 7c 938402 54.80 767723 44.84 6179 0.36 0.550

no 2-4's
pokenum -h ac kh - 7c 7s / 2c 2d 2s 2h 3c 3d 3h 3s 4c 4d 4h 4s
Holdem Hi: 376992 enumerated boards
cards win %win lose %lose tie %tie EV
Ac Kh 198967 52.78 174975 46.41 3050 0.81 0.532
7s 7c 174975 46.41 198967 52.78 3050 0.81 0.468

[/ QUOTE ]

ahh - okay, thanks for the explanation about the non-outs. that last simulation (where you take out the 2-4) is interesting, not something I had thought about before. when i get back to my regular computer i'm going to play around with these simulations myself.

thanks,

ts-

[The Student]

[ QUOTE ]

The more important thing to realize is that cards that you can't see are random and should be ignored. Cards that call are slightly more likely to have As, but the effect is insignificant and should absolutely never effect your play. Please try to understand this and play AK.

[/ QUOTE ]

my entire concern and point of my thread is what you say right there: Cards that call are slightly more likely to have As , but i can't say that i agree with you that the effect is insignificant. the cards that i can't see here (meaning the original multiple limpers' cards) aren't random - they were good enough to limp but not good enough to raise with PF. sure they could all be small SCs or small PPs or small broadways, but they are not totally random. i still think it's more likely that at least one (if not more) of my A or K outs is already in one of those hands.


[ QUOTE ]
If one of your aces is missing, it's not the only card that's missing. Making the deck shorter increases your chances of hitting your remaining outs, taking an A out decreases it--they come damn close to canceling.

[/ QUOTE ]
Okay, now I understand what the non-outs discussion is about and I understand what you're saying about making the deck shorter helping me out. however, making the deck shorter only helps me if the ratio of my outs:blanks rises. meaning, if there are still 5 outs left out of 40 cards left in the deck, that's okay; however, if there are only 2 outs left in the 40 cards left in the deck - that's actually worse for me. all i'm saying is that i am not yet convinced that you can say that these differences cancel out.

i hope you don't think i'm being a dick, noahsd, because i appreciate your response. i'm just saying that i am still not convinced that i should just assume that the potential loss of my outs and the potential loss of non-outs all balance out and i should stop thinking about this.

once i get back to my regular computer i'm going to play around with some simulations and see if i can come up with anything that convinces me that i shouldn't worry about this anymore.

thanks again for your response,

ts-

[The Student]

dmk - you're absolutely right, i don't need to be a flip here, and this makes a big difference in determining whether or not i should call in this situation.

here's a simulation where i killed some plausible limping hands and put my A/Ko up against JJ. In both of these examples I killed 2 of my outs, but left his remaining Js alive in the deck. Interesting - both examples work out to about the 1/3 pot equity I need to make this call. Still not saying this is a great call early in the tourney, but that even with only 4 outs, I'd still have the odds to call.

In the last example, I killed off one of his remaining Js and of course, my PE now went up to 40% - definitely enough for a call.

ts-

Text results appended to pokerstove.txt

501,942 games 0.005 secs 100,388,400 games/sec

Board:
Dead: Ah 9h Ks Ts Qc Tc 7c 7d 5s 5h

equity (%) win (%) tie (%)
Hand 1: 37.1053 % 36.92% 00.19% { AcKd }
Hand 2: 62.8947 % 62.71% 00.19% { JdJs }


---

501,942 games 0.351 secs 1,430,034 games/sec

Board:
Dead: Ah Ks 6c 6d Th 9s 5h Qs 9c 8c

equity (%) win (%) tie (%)
Hand 1: 37.6944 % 37.49% 00.20% { AcKd }
Hand 2: 62.3056 % 62.10% 00.20% { JdJs }


---
Text results appended to pokerstove.txt

501,942 games 0.005 secs 100,388,400 games/sec

Board:
Dead: Ah 9h Ks Ts Qc 7c 7d 5s 5h Jc

equity (%) win (%) tie (%)
Hand 1: 41.0999 % 40.92% 00.18% { AcKd }
Hand 2: 58.9001 % 58.72% 00.18% { JdJs }

(Note: I've factored in that you have AK in both calculations.)

Let's say a limping range is something like 22-99 (6*8=48 combos), 45s-KQs (35 combos), 9To-KQo (45 combos),A2s-A9s (24 combos). The combos that contain an A or K are KQ (12) and A2s-A9s (24). So, 36/(48+35+45+24) = ~23.7% of limping hands have an A or K in them.

The odds of a random hand having an A or a K is (1 - (46/50*45/49)) = 16%.

So, (I'm going to ignore the effects of cards removed from the deck between limpers and the effects of 2 aces or two kings being out) the expected number of As and Ks missing from the deck considering the limpers holding is about 5 * .237 = 1.185. The expected number of As and Ks in those hands if you ignore the fact that they limped them is 5 * .16 = .8 . This makes for a total of .385 extra outs lost. This costs you a little more than 1% equity in the pot.

Hope this helps. I'm sure if you run your simulation with my numbers you'll get similar results.

[The Student]

awesome - seeing this stuff in actual calculations help me to really understand, so thanks. i can also see that even if we increase the limpers' range a bit to include limped 10/10 and J/J and stronger suited aces like A/10 - A/J, I can see that it really doesn't make much of a difference in the end.

thanks,

ts-

[The Student]

Okay, just thought of something else that makes me ready to stop tossing this issue around in my head and move on to something else (like how I can convince my wife that thinking about poker so much is actually EV+). In addition to the pokerstove #s I just ran showing how the non-outs do really help to make this more of a EV neutral and sometimes even a EV+ call, I just thought of something else.

Two assumptions:
1. The distribution of playable hands that people receive in the early levels of a tourney is the same as the distribution of playable hands they're likely to receive in the later levels of a tourney. To put it another way, people are just as likely to receive weak aces and mid-strength kings early in the MTT as they are in the later levels.
2. People, especially at the cheaper buy-in MTTs, are more likely to limp with a much wider range of hands early in the tourney than they are later in the tourney.

I also think that people may be more likely to limp with a mid-strength ace or a suited K early in a tourney than they are later in the tourney. Later in the tourney they are more likely to either raise or fold with these hands than limp. However, the distribution of the cards remains the same throughout the tourney - meaning that I am just as likely to be missing some of my outs early in the tourney after a bunch of limpers as I am later in the tourney after some folds and one player in the pot. In the later stages of a tourney, however, I never worry about having all 6 outs, even if I can put a guy on a PP below Ks, I always assume that I'm no worse than 45:55 on the hand. So, if I play A/K this way late in a MTT, along with assumptions 1 & 2, I shouldn't worry about whether or not I have all 6 outs when I'm facing a PP with A/K early in a MTT either.

Does this make sense?

ts-