Two Plus Two Poker Forums If I have a pocket pair, are other pocket pairs more likely?
 Register FAQ Search Today's Posts Mark Forums Read Video Directory TwoPlusTwo.com

 Notices

 07-13-2012, 10:02 AM #1 Carpal \'Tunnel     Join Date: Jan 2011 Location: Polishing crystal football brb Posts: 12,652 If I have a pocket pair, are other pocket pairs more likely? I have a buddy who insists that anytime one player at a table has a pocket pair, the odds of others at the table also having pocket pairs are increased. Is he full of **** or is there validity to this claim?
 07-13-2012, 10:10 AM #2 Pooh-Bah     Join Date: May 2008 Location: prolly ATF Posts: 3,537 Re: If I have a pocket pair, are other pocket pairs more likely? This is probably a good question for the Probability forum. I'd say that if your friend IS right, it's not a mathematically significant difference to influence any decision you're making at the table, so it doesn't really matter.
 07-13-2012, 10:36 AM #3 Carpal \'Tunnel     Join Date: Jan 2011 Location: Polishing crystal football brb Posts: 12,652 Re: If I have a pocket pair, are other pocket pairs more likely? Right. Mods feel free to move if appropriate.
 07-13-2012, 11:09 AM #4 journeyman   Join Date: May 2012 Posts: 385 Re: If I have a pocket pair, are other pocket pairs more likely? Looks like your friend is right. The odds of having a pocket pair dealt to you with all other cards being unknown are 52/52 * 3/51 = 5.88% (any card as first card, and one of the 3 of the same rank for the second card). Let's say you're heads-up and you have a pocket pair. What are the odds of your opponent having a pocket pair? We know 2 cards so there are 50 left. 48 of those cards have 3 mates, 2 are the mates to your pair. (48/50 * 3/49) + (2/50 * 1/49) = 5.96% Not a big difference. Don't really feel like working out the math for 3 players and up though I would expect that it gets slightly higher for each added player.
 07-13-2012, 12:09 PM #5 Carpal \'Tunnel     Join Date: Jul 2007 Location: on top of Manhattan Chase Posts: 6,638 Re: If I have a pocket pair, are other pocket pairs more likely? Your friend is definitely correct. If you start with a full deck, it's possible to deal a pair of any rank in 6 ways. If someone is dealt a pair of, say, 3's, there's one pair of 3's left in the deck, so the number of pairs possible has gone down by 5. However, if someone is dealt, say, 75, then the number of pairs of 7s or 5s - which is 12 in a full deck - has gone down to just 6 (3 pairs of 7's and 3 pairs of 5's) which is a reduction of 6. Long story short, dealing a non-pair hand, reduces the number of pairs still possible by more than if you deal a pair.
 07-13-2012, 12:27 PM #6 Pooh-Bah     Join Date: Aug 2011 Location: Essex, UK Posts: 5,388 Re: If I have a pocket pair, are other pocket pairs more likely? Yes, but the difference is so small that it's not significant. It's like when you get KK at a full ring table. There's about a 4% chance that someone will have aces, but you can't be scared of that. They are just as likely to have QQ or worse.
 07-13-2012, 12:50 PM #7 old hand   Join Date: Oct 2007 Posts: 1,921 Re: If I have a pocket pair, are other pocket pairs more likely? Your friend is correct. There are 78 unique ways to make a pair (since AdAc And AcAd are the same). If the two cards we remove are both the same, there are 73 ways to make pairs with the remaining cards (6 for each of the cards not in our pair, and the one remaining pair of whatever we removed). If the two cards are different, there are only 72 (6 for each of the 11 we haven't removed, plus 3 for each of the two that are missing one card). It's about .08% more likely any given hand will be a pair if you have a pair. At a six max table, it's .32% more likely there's at least one other pair out there when we have a pair. Really doesn't seem worth bothering about.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are Off Pingbacks are Off Refbacks are Off Forum Rules

All times are GMT -4. The time now is 07:02 PM.

 Contact Us - Two Plus Two Publishing LLC - Privacy Statement - Top