Mulitple Pocket Pairs

jjflash · #1 03-16-2007, 05:49 PM

My girlfriend was recently playing online and chatting with the table when the following question came up. I am sure that this has probably been asked and answered on this forum but I am a little new here so I appreciate any help. What are the odds of AA, KK, and QQ being dealt in the same hand in a nine handed holdem' game? I have actually seen this happen once (the kings flopped a set and won a huge pot by the way). I tried to do the math and I think that my numbers are pretty close. I think that it is around 0.02% or about 1 in 5000. Can some of you math wizards tell me if this is about right? Thanks for all your help.

jay_shark · #2 03-16-2007, 06:14 PM

What is the probability players 1 ,2 and 3 have a's , k's and q's in some order ?

akq , aqk , kqa , kaq , qak , qka in which there are 3! different arrangements of these letters.
The probability is 6/1326*6/1225*6/1128 *3!

However , there are 9c3 ways of picking three players from 9 . Now we use the principle of inclusion/exclusion and we may disregard the negative term since it's unlikely there will be two players sharing the same pocket pair .

Multiply that number above by 9c3=36 to give you 0.000059414 or 0.00594%

LionelHutz00 · #3 03-17-2007, 12:00 AM

Here's a hand I played the other day. No AA involved but it's the same idea:

PokerStars No-Limit Hold'em, $2 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

Button ($223.40)
Hero ($204.90)
BB ($170.50)
UTG ($142)
UTG+1 ($268)
MP1 ($317.15)
MP2 ($319.35)
MP3 ($244.75)
CO ($34)

Preflop: Hero is SB with J[img]/images/graemlins/diamond.gif[/img], J[img]/images/graemlins/spade.gif[/img].
UTG calls $2, 1 fold, MP1 raises to $10, 4 folds, Hero calls $9, 1 fold, UTG raises to $30, MP1 raises to $317.15, Hero folds, UTG calls $112 (All-In).

Flop: ($471.15) 2[img]/images/graemlins/diamond.gif[/img], A[img]/images/graemlins/spade.gif[/img], 9[img]/images/graemlins/spade.gif[/img] (2 players, 1 all-in)

Turn: ($471.15) 2[img]/images/graemlins/spade.gif[/img] (2 players, 1 all-in)

River: ($471.15) 8[img]/images/graemlins/club.gif[/img] (2 players, 1 all-in)

Final Pot: $471.15

Results:
UTG has Qc Qs (two pair, queens and twos).
MP1 has Kh Kc (two pair, kings and twos).
Outcome: MP1 wins $471.15.

kerze · #4 03-17-2007, 02:29 AM

A little bit differnt but a memorable hand i played.

6 players NL Cap on Full TIlt.

one player min raises and 3 call

Flop comes 589

Pot is capped by one player and 3 call

Hands turned over 55, 88, 99, KK

Would have loved to seen the KK guys face when he realized he had the worst hand post flop.

The set of 9's held. (I was 88)