In an honestly programmed game, if you kept a pair and drew three cards, the probability of getting none of the remaining two of that rank is 14190/16215 or about .875, the probability of getting exactly one more of that rank is 1980/16215 or about .122, and the probability of getting both of the other cards of that rank is 45/16215 or about .003.
This is the same for keeping a pair of aces, a pair of kings, and so on, regardless of the pair you keep.
If you believe that the game is not programmed honestly, then you should definitely not play it.
Note to poker players: The probabiities above do not tell you the final hand, just how many of the same rank (of the pair you kept) that you get. So the 14190/16215 where you get no more 6's when drawing to 66 includes such diverse hands as 66AKQ, 66AA4, and even 66AAA.
