I am a (semi-)proffecional poker player with a penchant for practical maths. When i calculate the odds of certain things i often get discrepancies between what various website quote and what i get. some help would be apreciated. In texas hold 'em you get delt 2 cards and another 5 on the board. I argue this:

if i am dealt A,K (in the hand), what is the chance of hitting either an A or a King in the next 5 cards to hit the board.

Texas Holdem Odds - Probabilities for Poker Hands
quotes it as being 50% (just under half way down the page). However, i calculate this:

3 aces left in deck + 3 kings left in deck = 6 cards the satisfy my outcome. assuming a normal 52-card deck (so there are 50 cards left in the deck i get):

(6/50)+(6/49)+(6/48)+(6/47)+(6/46)=62.5%.

which is a huge difference.

please tell that website has it wrong?! If not help me work out this VERY SIMPLE calculation

thanks,

Morlaf