odds question

[hansdebelge]

hi there.
i was wondering if anyone could tell me how many two-card starting hands there are total. is it something like 260?
and also, how many total boards are there? (starting hand plus five community cards) am i right in thinking around 2 million. i think ive heard around there but does anybody have the exact numbers for me?
thanks a lot.

[uuDevil]

[ QUOTE ]
hi there.
i was wondering if anyone could tell me how many two-card starting hands there are total. is it something like 260?
and also, how many total boards are there? (starting hand plus five community cards) am i right in thinking around 2 million. i think ive heard around there but does anybody have the exact numbers for me?
thanks a lot.

[/ QUOTE ]

Hey.

If you consider AsKc distinct from AsKd, there are C(52,2)= 1326 hands. If not, there are 169.

If you've been dealt a hand and you looked at it, there are C(50,3)= 19,600 possible flops and C(50,5)=2,118,760 possible 5 card boards.

[hansdebelge]

thanks a lot, man. that really helps.

[AaronBrown]

To expand a little on uuDevil's excellent answer:

There are 13 pocket pairs you can get (Ace to 2).

If you don't have a pair, one card can be any of 13 and the other can be any of 12. But you have to divide this by 2, because K-9 is the same as 9-K. So 13x12/2 = 78.

You have to multiply the 78 by 2 because the hand can either be suited or unsuited.

So there are 2x78 + 13 = 169 starting hands.

The hands are not equally likely. There are six ways to get each pair, four ways to get each suited hand and twelve ways to get each unsuited hand.