2 card possibilites

[kimmyk]

I am wondering how many possible 2 card hands you can be dealt. Suited, unsuited, pp's, good, bad, the whole works.

[biggambler]

169 Assumeing that we count duplicates as only one. KQ of clubs is = to KQ of spades.

[switters]

there are a total of C[52,2] hands, which is equal to 52*51/2 = 1326 hands -- many of these hands are equivalent, however...

you might be dealt one of the 13 possible pairs. there are 6 ways to get dealt each pair, accounting for 13 * 6 = 78 hands.

there are C[13,2] = 78 other combinations (23, K6, AK), and you can get each of these suited (4 ways, i.e. 6[img]/forums/images/icons/heart.gif[/img]7[img]/forums/images/icons/heart.gif[/img] = 6[img]/forums/images/icons/club.gif[/img]7[img]/forums/images/icons/club.gif[/img]) or unsuited (12 ways, 6[img]/forums/images/icons/club.gif[/img]7[img]/forums/images/icons/diamond.gif[/img] = 6[img]/forums/images/icons/spade.gif[/img]7[img]/forums/images/icons/heart.gif[/img])

the 78 suited hands * 4 ways each = 312 hands
the 78 unsuited hands * 12 ways each = 936 hands

so there are 78 + 78 + 13 = 169 possible hands, which can be made 936 + 312 + 78 = 1326 ways!

it's also interesting to note that you are exactly 4 times as likely to get dealt suited cards as a pocket pair, and exactly 3 times as likely to get dealt unpaired, unsuited cards as suited cards!

-switters

[kimmyk]

So to get this straight. There is a 1 in 1326 chance of getting for ex. Ah Ad?

[Cyrus]

"So to get this straight. There is a 1 in 1326 chance of getting for ex. Ah Ad?"

Yes. AhAd (or AdAh) is a unique combination among the 1326 unique 2-card combinations that can be made from the 52-card deck. C(52,2)=1326 as you know.

So the odds against being dealt any pocket Aces is 220:1 , since 1326/6=221. (The 6 represents the 6 ways that the 4 Aces in the deck can be combined, in other words there are 6 ways that pocket Aces can be dealt.)

[All the above has been posted here lots of times.]