Odds on Pocket Pairs

[RammerJammer]

This is a spin-off of Diabloblanco's thread "Questions for the more advanced players", which is one of the liveliest we've had in a while. Let me say up front that I'm a math idiot. Don't get numbers, never have, never will. I defer to others for my statistical poker information, as long as it's documented by a reliable source and not just something thrown into a forum post.

Here's one I don't get and have wondered about for some time, but have never asked. Can someone explain these very basic odds to me? The source is Mike Caro's table "The Probability of Being Dealt Specific Hold 'Em hands Before the Flop" which appears in the appendices of "Super System". Here are the odds Caro gives for being dealt pocket pairs:

AA - 220 to 1
KK, QQ, JJ - 72.7 to 1
TT thru 66 - 43.2 to 1
55 thru 22 - 54.3 to 1
ANY pair - 16 to 1

Why are the odds of being dealt AA any higher than being dealt 22? Shouldn't the odds of being dealt any pair be exactly the same? There are no more of any one rank in the deck than another. 52 cards, 4 each of 13 ranks. If there were 4 Aces and 12 deuces, I could see the disparity. But there's not.

Can someone enlighten me, please?

 

[Grumbledook]

right then ;]

the odds for being dealt any specific pair are the same

that table though the only single pair is AA with odds of 220 to 1

the odds next to 22 of 54.3 to 1 is not JUST 22 its getting 22 or 33 or 44 or 55

hopefully that should have cleared it up for you, if not just say and I will try and elaboate some more on it

 

[icepari]

Just think for a second if you change the cards lets say draw 2 over the A cards and draw A on the deuces will the odds change.You either didn`t undrestand something or the one that wrote this is a complete idiot.Just to know how to chech the combinations 52.51/2=1326 different combos of cards this is AqAh is different than AhAq when i have more time i will explain how to count what =s the chance of being dealt a pocket pair

AqAh is diffetent to AhAs i meant

 

[RammerJammer]

I see what you're saying, Grumble. The odds that you will be dealt EITHER KK, QQ, or JJ (3 possible combos) are 72.7 to 1. But the odds of being dealt EITHER TT, 99, 88, 77, or 66 (5 possible combos) are much better at 43.2 to 1. I was interpreting his table as saying that the odds of drawing Aces were much higher than drawing any other given pair, when in fact the odds of drawing any random pair is a constant at 16 to 1.

If I follow you, then another way to phrase it would be that I should see, based upon probabilities, a pocket pair once in every 16 deals. I should see AA (or ANY OTHER SPECIFIC pocket pair) once in every 220 deals.

 

[Four Dogs]

Good explanation 'dook. I just checked out the math and it works out.

AA = 1 hand 1/221
KK, QQ, JJ = 3 hands = 3/221 = 73.67 to 1
TT thru 66 = 5 hands = 5/221 = 44.2 to 1
55 thru 22 = 4 hands = 4/221 = 55.25 to 1
I'm not sure why I'm getting the slight difference between my numbers and and the ones posted by RJ but I guess I can't argue with Mike Caro.

 

[Grumbledook]

correct there are 4 aces in the deck and 4 dueces in the deck

so the odds of drawing any 2 of those 4 will be the same

you are just as likely to get 2 aces as you are to get 2 2s


The tables at the back of supersystem are gospel ;]


The reason your odds are slightly out is because you can't just do the calculations as you did, its slightly more complex ;]

good enough for a rough guide though

 

[icepari]

I said he didn`t get it right .Why don`t you read of course the chance to get 1 of 3 pairs i larger than gettin one specific pair.I meant That the biggest stupidity is to think that AA will come rare than 22.

 

[RammerJammer]

I said he didn`t get it right .Why don`t you read of course the chance to get 1 of 3 pairs i larger than gettin one specific pair.I meant That the biggest stupidity is to think that AA will come rare than 22.

I try not to take offense with icepari because there is often an obvious language gap that puts us on different pages. He english is not good too alway. No problem.

 

[Four Dogs]

Way to take the high road RJ. Too many short fuses here, me included. Your right of course.
Icepari, where are you from and what's your first language?

 

[icepari]

Well i am From Bulgaria ,i know spanish (not very good) i know deutch (quite well), and english i know it perfectly i think (just typing all the posts long after midnight 3-4 in the morning ) And i am not so focused.Sorry for the mistakes! There will be no more.
Best regards

 

[Four Dogs]

Deutch or Dutch? I speak german but probably not well enough to avoid offending people.

 

[diabloblanco]

German sounds like you're blessing someone out when you say something complimentary. Its a great cursing language.

 

[woodsy44]

A pair of pocket cards e.g. 55, 66, 77, 88 are always bad for me.
You feel confident and probably raise. But if a higher card comes out, then....
if you had 66 then A,10 and 7 come out on the flop, odds are someone will have that ace or 10 etc.
If your card comes then wooooo.
probably just me and my bad experiences.

 

[Four Dogs]

German sounds like you're blessing someone out when you say something complimentary. Its a great cursing language.

Everything in French sounds like a come on.
Everything in Italian sounds like an argument.
Everything in German sounds like an order.
I wonder what English sounds like?