Hand combinations

[JonLines]

Hi there, I have this written somewhere at home, but just trying to prove something to a colleague at work.

Can someone tell me how many possible hole card hand combinations there are?

And also how many possible hand combinations are left after you have been dealt your hole cards?

Would be a great help.

[Cobra]

In a deck of 52 cards there is 1326 different combinations of two cards you could be dealt.

=(52 c 2)=52*51/2*1=1326

After you have your two cards there are now 1225 combinations left in the deck of 50 cards.

=(50 c 2)=50*49/2*1=1225

Your two cards eliminated 101 possible combinations of the cards for your opponents.

Cobra

[JonLines]

Cheers Cobra, that was quick!

/images/graemlins/grin.gif

[William Notell]

[ QUOTE ]
In a deck of 52 cards there is 1326 different combinations of two cards you could be dealt.

=(52 c 2)=52*51/2*1=1326

[/ QUOTE ]
Yes, 1326 unique combinations. However, only 169 of them are distinct in Poker. That is, for example, AhAd is essentially the same as the other five pocket aces.

13 (pairs) + 13*12/2 (suited non-pairs) + 13*12/2 (unsuited non-pairs) = 169
[ QUOTE ]
After you have your two cards there are now 1225 combinations left in the deck of 50 cards.

=(50 c 2)=50*49/2*1=1225

Your two cards eliminated 101 possible combinations of the cards for your opponents.

Cobra

[/ QUOTE ]
For the 169 essentially unique combinations, there are still 169 combinations possible for a second hand. That is, none of the combinations are completely used up, although some are less likely (e.g., one possibility left for a matching pocket pair).