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

[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 [img]/images/graemlins/smile.gif[/img]

[/ 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 [img]/images/graemlins/grin.gif[/img].

[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