theoretical question: how many callers do you want with aces?

[TStoneMBD]

Assuming you go all preflop, how many callers do you want at a full 10 man table with aces? It is obvious that the more callers you get the less likely it is to win the hand, but the more players you potentially bust. Many players would say you don't want more than 2-3 callers but, wouldn't you want all 9 players to call you because you are clearly getting +EV in the long run and are likely to win the tournament all in 1 hand.

I am not very good with math or game theory so using any sophisticated algebra is above my head.

[Phill S]

if your all in:

in ultimate theory, you want em all to call. you are fave (with several notable exceptions-im sure theres a thread on here somewhere, just scroll down a bit).

however this has huge swings of variance. id rather take a small pay day most of the time, over one big pay day every so often.

you want no more than three or four, and youll rarely get more than one or two.

Phill
ps, for the record, i rarely play aces all in, unless im sure ill get called (ie an early raise and a caller or raiser, or a re-raise to my initial raise. you want to get heads up as often as possible, and ive made my play more profitable from making all in raises and hoping im called to raising to 300+ (blind dependant). if the blinds are big, clearly its all in, but whilst getting it all in rpeflop witht he hand should be one of you goals when dealt it, its quite unlikely youll find someone to oblige

[AleoMagus]

Against nine random hands, I think you certainly make more by getting them all in. You want as many random callers as possible.

The interesting thing though is that poker is not played against random players. Players who will push and players who will call pushes can usually be put on a specific range of hands. Even the crazy nuts have limits.

What this means then is that you are more likely up against other pairs and you are more likely to have your other aces in other people's hands. In some extreme cases, you can even be a huge underdog to win the hand.

I read about one interesting scenario where AA was about 50-1 AGAINST winning a ten player preflop all-in scenario. I forget what the hands were exactly, but experimenting for a minute on my own I came up with a few scenarios where AA was about 20-1 against winning the hand.

These scenarios mostly involved situations where two ther opponents had your extra aces (AK and AQ for example) and where there were a lot of other pocket pairs out

These are just the sort of hands that might theoretically call in a ten player all-in scenario.

In fact, I will suggest here that if nine players go all-in ahead of you, you would rather be holding a hand like 88 than you would AA for this reason. Your other two eights are still probably in the deck.

So, while this sort of thing will never happen anyways, I think I'd sooner have three opponents with pocket aces than ten.

Perhaps someone can find that 50-1 against preflop aces scenario I was thinking about. I'd be interested to see it again.

Regards
Brad S

[TStoneMBD]

[ QUOTE ]

In fact, I will suggest here that if nine players go all-in ahead of you, you would rather be holding a hand like 88 than you would AA for this reason. Your other two eights are still probably in the deck.


[/ QUOTE ]

this is the most ridiculous thing ive ever heard :/

[RayGarlington]

[ QUOTE ]
this is the most ridiculous thing ive ever heard :/

[/ QUOTE ]

Well, it doesn't seem that whacky to me. Remember those 8 players ahead of you are not playing random hands. Short of an harmonic convergence of stupidity, they are not all-in with nothing. In fact, if only half are paying attention, all the aces and kings are spoken for.

[dandy_don]

[ QUOTE ]
this is the most ridiculous thing ive ever heard

[/ QUOTE ]

Think through what is being responded to your post. If you will think about it, these guys will teach you how to think through these situations, and you will profit from the information they share with you. By responding like this, I for one would never respond to another one of your posts if spoken to this way. "Don't bite the hand that feeds you."

What Aleo is trying to get you to rationalize through, is the fact that if 9 callers called an "All-in" bet, then theres more to the story than simply having 9 maniacs calling a solid stating hand.

Although AA is "the" best starting hand, I have to agree with Aleo on this. If there are 9 other callers, then 2 or three have to have some combination of AA, KK, or AK, so the chance of improving your hand is minimal. This while 2 or 3 others will likely have drawing hands (suited connectors and the like) and one of those will likely take down the pot on a straight, flush or trips lower than a painted card.

Personally, (and this is probably coming from my stud play), if I have AA, ideally I want 1, maybe 2 or 3 depending on the table, callers. Anymore than that and I'm going to get outdrawn by a big hand.

[ilya]

An example from the Create-an-Upset thread, courtesy of Durron597:

http://twodimes.net/h/?z=453927
pokenum -h ac ad - 8h 8s - as kc - ah kd - ks qc - kh qd - qs qh - 2c 2d - 3c 3d
Holdem Hi: 278256 enumerated boards
cards win %win lose %lose tie %tie EV
Ac Ad 79140 28.44 196174 70.50 2942 1.06 0.287
8s 8h 81534 29.30 195042 70.09 1680 0.60 0.294
As Kc 2298 0.83 273016 98.12 2942 1.06 0.010
Kd Ah 2298 0.83 273016 98.12 2942 1.06 0.010
Ks Qc 30 0.01 257914 92.69 20312 7.30 0.034
Qd Kh 30 0.01 257914 92.69 20312 7.30 0.034
Qs Qh 0 0.00 276576 99.40 1680 0.60 0.001
2c 2d 40258 14.47 236318 84.93 1680 0.60 0.145
3c 3d 51094 18.36 225482 81.03 1680 0.60 0.184

This is pretty mild, too. I just thought it was droll that it happened to have 8s as the favorite.

[TStoneMBD]

Im sorry that I came off as rude but I find it odd that noone is siding with me against his comment that 88s are better than AAs in this situation. Maybe if you run the math there will come up a situation very rarely in which 88s are actually a favorite to beat a field of 10 over AA, but this is few and far between. Just because yours aces are covered and you cannot catch a set does not mean 88s are better. Remember you will only catch a set with 88s once in 5, not to mention set over set possibilities while the odds of aces winning against a field being 20% or lower is not the norm.

Maybe I am taking his comment a little too literally in thinking he really advised that 88s are better than aces, but they clearly arent. If he was just trying to make a point that aces dont hold up very often with using a little bit of sarcasm, I apologize.

[Tosh]

[ QUOTE ]

In fact, I will suggest here that if nine players go all-in ahead of you, you would rather be holding a hand like 88 than you would AA for this reason. Your other two eights are still probably in the deck.

[/ QUOTE ]

I see what you are saying but if you are giving them credit for vaguely decent hands, then all of their cards are out too so your aces will win unimproved a lot. The problem is its tough to prove either way though I guess.

You might well be right, I'm just suggesting a counter argument.

[tubbyspencer]

As for the 88 being better, I agree. And by the same token, wouldn't 22 be just about the best? Somebody's more likely to have the other 88 out than the other 22; and they're more likely to be playing something like 98s than 32s. 8's are more likely to be out than 2's; and with a ten way all in, you'll almost certainly have to improve to win - no matter what you hold.

Of course, if this were the first hand, I might fold to a 9 way all in - and settle for second place /images/graemlins/smile.gif

[Lori]

Just turning this on it's head for a moment.

If all nine other players go in before you on the first hand, and you have to decide whether to play or fold.

You are somewhere in the region of 30% (If memory serves, It's been a while since I looked this up) to win this pot, and therefore the tournament.

30% of the time you will win $50 = $15 EV, the other 70% of the time, you will get a one-ninth share of the $50 for second and third prizes = $5.56.

Total EV = $20.56 for playing.

If you fold, you will always (neglecting split pots again) come second, apart from the one time in ten that you win the heads up battle that ensues.
$30 90% of the time = $27 EV, $50 10% of the time = $5 EV, total fold EV = $32.

In a ring game, however, you should always call here.

It is possible I've remembered incorrectly about the odds of aces winning a ten-way pot, but even if it's near 50% you are still better off folding!

Lori

Edited to make clearer.

[ilya]

[ QUOTE ]
Of course, if this were the first hand, I might fold to a 9 way all in - and settle for second place /images/graemlins/smile.gif

[/ QUOTE ]

Well, if everyone has gone all-in and you have last action, folding has gotta have the highest EV no matter what you have.

Especially since, even though the other player will have a 9-1 chip lead on you, the blinds will still be at level 1 and you will have plenty of play. Therefore you can probably count on winning heads-up more often than the 10% suggested by only looking at chip counts.

[dandy_don]

[ QUOTE ]
As for the 88 being better, I agree. And by the same token, wouldn't 22 be just about the best? Somebody's more likely to have the other 88 out than the other 22

[/ QUOTE ]


Well, I believe the 8's being middle pair, will have more straight possibilities than the 2's. So for hitting trips or quads, yes the will be equal or slightly better than the 8's, but when considering the straights that could land, the eights open up a few more opportunties.

FWIW, if I'm not the first to go all-in, I'm not calling with either 8's or 2's /images/graemlins/grin.gif.

[Tosh]

I think that was looked at before Lori. As far as I'm aware there is no error in your calculation at all, if all 9 players go all in first hand your EV is higher folding.

[mackthefork]

[ QUOTE ]
I think that was looked at before Lori. As far as I'm aware there is no error in your calculation at all, if all 9 players go all in first hand your EV is higher folding.

[/ QUOTE ]

Correct, if all 9 go in not only is it correct to fold, its not even close, you would be lucky to have a 25% chance of taking down the pot. A number of people want to call in this situation but it makes no sense, however since the situation has never come up and is unlikely to do so it seemed to me pointless to argue.

Regards Mack

[Gandor]

Just what I could come up with quickly.

Result
http://twodimes.net/h/?z=459282
pokenum -h ad ah - as ks - ac qc - jd jh - td th - 9d 9h - 8d 8h - 7d 7h - 6d 6h - 5d 5h
Holdem Hi: 201376 enumerated boards
cards win %win lose %lose tie %tie EV
Ad Ah 5350 2.66 195463 97.06 563 0.28 0.027
As Ks 27816 13.81 172997 85.91 563 0.28 0.139
Ac Qc 27623 13.72 173190 86.00 563 0.28 0.138
Jd Jh 31831 15.81 169534 84.19 11 0.01 0.158
Td Th 28363 14.08 173002 85.91 11 0.01 0.141
9d 9h 23051 11.45 178314 88.55 11 0.01 0.114
8d 8h 18419 9.15 182946 90.85 11 0.01 0.091
7d 7h 14968 7.43 186397 92.56 11 0.01 0.074
6d 6h 12840 6.38 188525 93.62 11 0.01 0.064
5d 5h 10552 5.24 190813 94.75 11 0.01 0.052

Gandor

[WarmonkEd]

TA DA! 50:1

http://twodimes.net/h/?z=459381
pokenum -h ah ad - ac 2c - as 2s - kh kd - qh qd - jh jd - th td - 9h 9d - 8h 8d - 6h 5h
Holdem Hi: 201376 enumerated boards
cards win %win lose %lose tie %tie EV
Ad Ah 3845 1.91 197151 97.90 380 0.19 0.019
Ac 2c 23847 11.84 173810 86.31 3719 1.85 0.127
As 2s 23847 11.84 173810 86.31 3719 1.85 0.127
Kd Kh 32452 16.12 168688 83.77 236 0.12 0.161
Qd Qh 26488 13.15 174652 86.73 236 0.12 0.132
Jd Jh 21402 10.63 179738 89.25 236 0.12 0.106
Td Th 17386 8.63 183754 91.25 236 0.12 0.086
9d 9h 14276 7.09 186864 92.79 236 0.12 0.071
8d 8h 13322 6.62 187818 93.27 236 0.12 0.066
6h 5h 20792 10.32 180348 89.56 236 0.12 0.103

[SossMan]

MAKE IT STOP!!
MAKE IT STOP!!

THESE THEORETICAL AA HANDS ARE GETTING WORSE THAN THE BAD BEAT POSTS!!!

**KILLING MYSELF NOW**

-SOSSMAN

[AleoMagus]

Wow... It isn't that often that I wake up on a saturday to see that about 15 people jumped into a thread I posted about in the early hours of the previous night(morning)

Interesting discussion but here are this morning's thoughts after a bit of research

Straight away I decided to run the AA preflop all-in scenario by defining a range of hands that the opposition could have and not just by concocting crazy all-in scenarios designed to make aces an underdog

Holding aces, if all other players are playing only sklansky hand ranking groups 1-2 or pocket pairs, aces are still making money (In a ring game, not a tourney as Lori correctly points out. Or actually, they are making money in a tourney too, just not as much as by folding. Don't ever actually fold pocket aces before the flop)

If, however I predetermine that the other two aces are in people's hands, and throw 88 in the mix, the 88 does actually win more often. Aces still win over 15% of the time, so they should theoretically still be played.

As a side note, hands like AK and AQ are usually about the biggest underdogs in scenarios like this - where the likelihood that someone has AA seems like a certainty (10 all-ins)

What I find sketchy about this kind of reasoning however is thgat it somewhat overlooks bayes theorem. This theorem (in essence) states that if you are holding aces, you can correctly infer that the odds of another player holding AK, AQ or any hand with an ace in it go down. If I pre-specify the prescenc of the other two aces in player holdings I'm contriving a situation to meet my own purposes - showing that 88 is actually better under these circumstances.

So what am I actually saying? Theoretically, is 88 really better that AA if nine players push all-in? I honestly didn't expect it would be such an incendiary comment.

No. The skilled NLHE player in me has to say no, but it's actually a strangely close call and does point to sort of what I was getting at - As the number of players increase, the EV of aces does not necessarily keep going up.

In another extreme example, consider a situation where 22 players are playing a game of hold'em and all of them push. If they can be put on a range of hands for those pushes, aces might almost certainly be beat because there may simply be no possible remaining cards that will have the aces as a winner.

Now, this is all theoretically interesting, but it bears repeating that it's completely stupid in a way. I'd be surprised if I ever actually even considered folding aces preflop in my lifetime. Even then I'd still probably be unable to resist playing them.

Then there is one last thing to consider... I know players who if they saw five players push ahead of them, would push with anything just because 'it's fun to have big huge confrontations and watch the cards come out'. Maybe in the extremely unlikely scenario that a lot of players all pushed, some of them may well be playing random hands.

Regards
Brad S

[AleoMagus]

Honestly I feel your pain... I really do

I just can't stop myself. It's a problem

Regards
Brad S

[znup]

I've really enjoyed your posts and will miss you. Condolences to your family.

Here lies SOSS mAAy he rest in peace.

[Tosh]

LOL c'mon SossMan, if you can't beat them, join them. /images/graemlins/tongue.gif

[UncleRemus]

Not sure if this is "as bad as it gets" for rockets, but this is about as bad as I could get it. Brutal!

Result
http://twodimes.net/h/?z=459616
pokenum -h ac as - ah 2c - ad 2s - qc qs - jc js - ts tc - 9c 9s - kc ks - 8h 7h - 4d 5d
Holdem Hi: 201376 enumerated boards
cards win %win lose %lose tie %tie EV
As Ac 3900 1.94 196406 97.53 1070 0.53 0.021
2c Ah 3139 1.56 193139 95.91 5098 2.53 0.027
2s Ad 3253 1.62 193025 95.85 5098 2.53 0.028
Qs Qc 27579 13.70 173792 86.30 5 0.00 0.137
Js Jc 21809 10.83 179562 89.17 5 0.00 0.108
Ts Tc 18137 9.01 183234 90.99 5 0.00 0.090
9s 9c 16465 8.18 184906 91.82 5 0.00 0.082
Ks Kc 34401 17.08 166970 82.91 5 0.00 0.171
8h 7h 33306 16.54 168065 83.46 5 0.00 0.165
5d 4d 34289 17.03 167082 82.97 5 0.00 0.170


(Yes, I'm really bored)

[AleoMagus]

[ QUOTE ]
I wake up on a saturday

[/ QUOTE ]

... is it friday today?

LOL. You know that you are a poker player when you don't know what day of the week it is

That 52:1 against scenario IS brutal. Thanks all who dug around trying to come up with those. Crazy stuff.

Regards
Brad S

[MikeGuz]

I have this theory I am sure shared by others that a lot of players means the deck is rich in smaller cards - this does work for me - say I'm on the button with a lot of limpers or say 1 or 2 raises ahead I may play a hand like 56 or 45.

Anyway if I were in a hand and I knew some how all the players would be all in I'd have to assume there was a bunch of big cards out there so I would not be afraid of a hand like 56 - It would be fun to run some sims with a bunch of hands like 99-88-AK-AQ-JJ-ATs-KK-QQ-TT and 56o and 56s - se what hands do best.

[KJ o]

This is fun! My take:
Twodimes simulation (http://twodimes.net/h/?z=463287)
pokenum -h ah as - ac 2c - ad 3d - kh ks - qh qs - jh js - th ts - 8h 9h - 6s 7s - 4h 5h
Holdem Hi: 201376 enumerated boards
cards win %win lose %lose tie %tie EV
As Ah 805 0.40 200500 99.56 71 0.04 0.004
Ac 2c 27513 13.66 173792 86.30 71 0.04 0.137
Ad 3d 29487 14.64 171818 85.32 71 0.04 0.147
Ks Kh 31619 15.70 169746 84.29 11 0.01 0.157
Qs Qh 25624 12.72 175741 87.27 11 0.01 0.127
Js Jh 20777 10.32 180588 89.68 11 0.01 0.103
Ts Th 17385 8.63 183980 91.36 11 0.01 0.086
9h 8h 14443 7.17 186922 92.82 11 0.01 0.072
7s 6s 20460 10.16 180905 89.83 11 0.01 0.102
5h 4h 13192 6.55 188173 93.44 11 0.01 0.066

Now, If I had 5h 4h and nine people were all-in ahead of me, I'd probably fold. Unless this was a huge freeroll...

[Jason Strasser]

I hope no one misreads this. I have to say, this situation will happen hardly ever. Maybe never. In general you will not be folding aces pf under any situation.

[Lori]

In general you will not be folding aces pf under any situation.

Worth clarifying. I have NEVER folded aces preflop in a single table tourney and have only once been in position where I should have (and didn't realise until after I hit call... of course they managed to lose which was distressing when I had already realised my error)

For what its worth, the situation was.

Limit Holdem, blinds 150-300

CO: 400 chips
Lori: (Button) 10 chips
Other TWO players: lots of chips

CO folds, lori has aces.

Lori

[t_perkin]

I folded AA preflop once.

My wireless mouse batteries went dead 5 pixels to the right of the call button.

AAAAAAHHH

Tim

[Fiery Jack]

Suppose you are last to act and 7 people have gone all-in in front of you already.

You hold AA. What now?

[Robert Ezzo]

Early in a tourney? As insane as it sounds, I'd rather fold there. Let 6 out of 7 people get knocked out of the tournament immediately - AA maybe the best starting hand, but against 7 other all-ins it doesn't look that hot. I'm more focused on getting ITM, and the odds are too dicey with that much action. If it is later in the tournament (e.g. 100/200 blinds), then I'd push and pray.

[Moonsugar]

280:1! Check it out:

http://twodimes.net/h/?z=464114
pokenum -h ah as - ac 2c - ad 3d - kh ks - qh qs - jh js - th ts - 8s 9h - 6s 7s - 4h 5h
Holdem Hi: 201376 enumerated boards
cards win %win lose %lose tie %tie EV
As Ah 716 0.36 200589 99.61 71 0.04 0.004
Ac 2c 27528 13.67 173777 86.29 71 0.04 0.137
Ad 3d 29502 14.65 171803 85.31 71 0.04 0.147
Ks Kh 31704 15.74 169661 84.25 11 0.01 0.157
Qs Qh 25701 12.76 175664 87.23 11 0.01 0.128
Js Jh 20862 10.36 180503 89.63 11 0.01 0.104
Ts Th 17396 8.64 183969 91.36 11 0.01 0.086
8s 9h 13908 6.91 187457 93.09 11 0.01 0.069
7s 6s 18646 9.26 182719 90.74 11 0.01 0.093
5h 4h 15342 7.62 186023 92.38 11 0.01 0.076

[hummusx]

Didn't someone already calculate the EV of this? I can't remember where the post was. Personally I think I'd fold and figure I'm a better player than whover emerges from this mess with most of the chips. I'm (almost) guaranteed second, and I should have time to try to get some of the big stacks chips before the blinds are big enough to cause major problems.