Starting hands - what am I missing?

[Beck]

Please let me know where my calculations do not hold up anymore:

In Hold'Em there's 52*51=2652 different ways to deal the pocket cards.
If I decide to only play pairs (6*13=78), AK(16) and AQs(4)I get a total of 98 possible staring hands or a VPIP of 3,7%. But I also know that I will be dealt a pocket pair once in 17 hands, which alone is 5,9%.

It's probably pretty obvious were I went wrong.....just not to me.
Been wondering whether I actually should double 3,7% to 7,4% since for instance the holding AhKh both could be dealt as AK and KA?

[elitegimp]

[ QUOTE ]
Please let me know where my calculations do not hold up anymore:

In Hold'Em there's 52*51=2652 different ways to deal the pocket cards.
If I decide to only play pairs (6*13=78), AK(16) and AQs(4)I get a total of 98 possible staring hands or a VPIP of 3,7%. But I also know that I will be dealt a pocket pair once in 17 hands, which alone is 5,9%.

It's probably pretty obvious were I went wrong.....just not to me.
Been wondering whether I actually should double 3,7% to 7,4% since for instance the holding AhKh both could be dealt as AK and KA?

[/ QUOTE ]

yes, you should double it -- because when you say "total hands to be dealt = 52*51" you are implying that Ah Kh is a different hand than Kh Ah. Yet when you say "4 ways to get AQs" you imply that Ah Qh is the same as Qh Ah.

Most people prefer to just divide 52*51 by two to get the number of unique starting hands at 1326 (because order you are dealt the cards doesn't matter). This has the same effect as multiplying the number of hands you play by two.