TripJax

Question
Wednesday, November 01, 2006

I've been working on a post recently that I should have up soon, but while writing the post a question crossed my mind that I'm wondering about. It could be a stupid question, but whatever...

In a 10 handed Hold'em poker game - assuming all players remain in the hand until all community cards have been dealt, and all betting is complete - is it possible for a player to have a hand that is drawing dead pre-flop, based on the cards that all other players hold?

Does that make any sense? Further, does anyone care? I'm just looking for someone who has more time on their hands than me to put some thought into it and find the answer.

Get your notepads out and get to work. Or, maybe you know the answer right away. Lets see some comments people!

posted by TripJax @ 4:00 PM,

27 Comments:

At 5:00 PM, AlCantHang said...: It's got to be possible. Let me get my drinking shoes on here in a few moments and figure it out.
At 5:04 PM, Anonymous said...: I won't spoil the suspense. It's actually pretty easy 10 handed. I believe that the minimum is seven handed. And for a spoiler, but one that you'll have to work for, it was discussed in the 2+2 forums recently.
At 5:10 PM, ScurvyDog said...: There have to be many, many possibilities, but here's one, with as few as just seven players.

Player #1 is drawing dead pre-flop.

Player #1: 2d3d
Player #2: 4d5d
Player #3: 2c2h
Player #4: 3c3h
Player #5: 7h8c
Player #6: AcAd
Player #7: AhAs
At 5:14 PM, Anonymous said...: The possability that one of the players hole cards will make a straight flush prevents it from being possible.
At 5:18 PM, Anonymous said...: Example:

Player #1: 3d 6d

While improbable, the possability exists that the flop will come 4d, 5d, 7d which prevents Player #1 from drawing dead preflop.
At 5:21 PM, Anonymous said...: Ahh. Just figured out the straight flush possabilities can be prevented by the other players hole cards. Whoops.
At 5:29 PM, Tommy said...: Two players each with pocket deuces would both be drawing dead to two players each holding (the same) pocket 3s, 4s, or 5s.
At 5:30 PM, Tommy said...: On second thought, they wouldn't be drawing dead... they could tie.
At 5:34 PM, Tommy said...: http://twodimes.net/poker/?g=h&b=&d=&h=2c+2s%0D%0AAs+2d%0D%0AAc+2h%0D%0AAh+3s%0D%0AAd+3c%0D%0A5h+4d%0D%0A7s+6c%0D%0A9h+8d%0D%0AJs+Tc%0D%0AKh+Qd
At 5:35 PM, Tommy said...: Meh, now I read the better examples in above... there goes that 5 minutes.
At 6:08 PM, Anonymous said...: 8 players -

http://twodimes.net/h/?z=2159237
pokenum -h 2h 2s - 2c 2d - 5c 5d - 5h 5s - th ts - tc td - ac ad - ah as
Holdem Hi: 376992 enumerated boards
cards win %win lose %lose tie %tie EV
2s 2h 0 0.00 376992 100.00 0 0.00 0.000
2c 2d 0 0.00 376992 100.00 0 0.00 0.000
5c 5d 124 0.03 366212 97.14 10656 2.83 0.014
5s 5h 124 0.03 366212 97.14 10656 2.83 0.014
Ts Th 250 0.07 354470 94.03 22272 5.91 0.030
Tc Td 250 0.07 354470 94.03 22272 5.91 0.030
Ac Ad 6682 1.77 40358 10.71 329952 87.52 0.455
As Ah 6682 1.77 40358 10.71 329952 87.52 0.455
At 6:12 PM, Anonymous said...: As for 7 players... Are we defining drawing dead to mean no chance to win or tie, or are ties allowed? If ties are allowed, you can do it in 7 by dropping one pair of Aces - everyone ties on KKKKA types of boards, then.
At 6:57 PM, Anonymous said...: My favourite 7 hand solution because it has two dead hands, and they're mighty good ones:

Dead: KdKh, KcKs
Other: AcAs, AdAh, 9d9s, 9c9h, 8c7c

As we say in the math biz, details left to the reader.

And the conditions are the strong ones, the KK's are dead, with no possibility of even taking part in a split pot.
At 7:10 PM, Anonymous said...: There are 6 possible boards where the Kings chop (2-6 and 3-7 non-club straight flushes)...

http://twodimes.net/h/?z=2159330
pokenum -h kd kh - kc ks - ac as - ad ah - 9d 9s - 9c 9h - 8c 7c
Holdem Hi: 501942 enumerated boards
cards win %win lose %lose tie %tie EV
Kd Kh 0 0.00 501936 100.00 6 0.00 0.000
Ks Kc 0 0.00 501936 100.00 6 0.00 0.000
As Ac 7893 1.57 134545 26.80 359504 71.62 0.374
Ad Ah 11794 2.35 130644 26.03 359504 71.62 0.382
9s 9d 266 0.05 487615 97.15 14061 2.80 0.015
9c 9h 133 0.03 487748 97.17 14061 2.80 0.014
8c 7c 108297 21.58 393639 78.42 6 0.00 0.216
At 7:14 PM, Anonymous said...: Oops, time to rummage around in my memory a bit more.
At 7:47 PM, Anonymous said...: Memory fixed ... I think ...

Dead: KcKd
Other: AcAd, AsKh, AhKs, QcQd, 7d7h, 7c7s

7's block the 2-6 straight flushes, and
the 8-Q straight flushes in H and S are blocked by the AK hands.

Likewise, ordinary straights no good for a split either.

I know I should check this mechanically to avoid (further) embarrassment.
At 7:55 PM, Anonymous said...: That one works. :)

http://twodimes.net/h/?z=2159404
pokenum -h kc kd - ac ad - as kh - ah ks - qc qd - 7d 7h - 7c 7s
Holdem Hi: 501942 enumerated boards
cards win %win lose %lose tie %tie EV
Kc Kd 0 0.00 501942 100.00 0 0.00 0.000
Ac Ad 336892 67.12 158936 31.66 6114 1.22 0.675
As Kh 5137 1.02 480611 95.75 16194 3.23 0.024
Ks Ah 5137 1.02 480611 95.75 16194 3.23 0.024
Qc Qd 114756 22.86 387186 77.14 0 0.00 0.229
7d 7h 297 0.06 478413 95.31 23232 4.63 0.024
7s 7c 297 0.06 478413 95.31 23232 4.63 0.024
At 10:05 PM, TripJax said...: I like how so many people begin with the strong hands and find a way that they can be drawing dead. I on the other hand thought of this question with the idea that everyone would start with 7 2 off-suit and figure out how all the hands could ultimately create a dead hand. Wild how different strokes, different folks. Keep at the discussion...it's phenomenal.
At 1:02 PM, Unknown said...: All poker life surrounds 7 2 off suit.
At 2:54 PM, slb159 said...: Looks like you can just win with any two cards at any time.

Best poker advice I ever got (keeping the source anonymous), "When in doubt, PUSH!"

Hope that helps in the discussion.
At 2:57 PM, Jordan said...: Player 1 has a dead hand:

Player 1: 7c2h
Player 2: 5h7d (ruins straight flush for 2h, and takes a pair away from the 7)
Player 3: 8c6c (ruins straight flush for 7c)
Player 4: 77 (can't pair the 7)
Player 5: 22
Player 6: 23 (can't pair the 2)
Player 7: 55
Player 8: 58 (no 5s for a A-5 or 2-6 straight)
Player 9: 88 (no eights for a 6-T or 7-J)

And done... Did I miss anything?
At 3:37 PM, TripJax said...: The only thing you missed is that the question prescibes 10 players instead of 9. 10 was not really the main part I guess, I was just going with the most you will normally see in a hold'em game...

Very well done peoples...I appreciate putting your mind into this question and working it out. I'd be interested to see the calculations done via a program to see if we aren't missing something. I have not checked the 2+2 forums (can't from work, but I'll check it out sometime).
At 3:54 PM, Iakaris aka I.A.K. said...: Hey-Zu Kris-Toe!

Have you been hooked up with some primo peyote I need to know about?

Fascinating post that made even an egomaniac like myself feel like an idiot.
At 4:05 PM, Anonymous said...: Before I read any replies, I had also thought of the Aces and Kings example someone listed above.
At 4:39 PM, Anonymous said...: All the intelligence in here makes my head spin.
At 7:01 PM, Dawn Summers said...: Wow. My head hurts. Now I'm always goingto be scared that my kings are dead pre-flop.
Dawn
At 9:55 AM, Astin said...: High - In your example, there are, in fact, 4 players who can't win, and one more who has a less than 1% chance of winning. However, a tie is still possible for everyone.

Higher pairs, two pairs, sets, or quads with a kicker higher than 8, or straights, flushes, full boats, quads or straight flushes on the board would lead to 9-way split, so nobody would be knocked out.

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