I have been looking at the way people calculate the odds of poker hands for a few hours and i think there is a HUGE flaw. In poker a player is never dealt two CONSECUTIVE cards. This in my view changes the odds, while also making the number of people at the table as well as the players position a material factor. For example
2 handed: first player dealt; odds of getting pocket aces = (4/52)x(3/50) = .46% or 1/217
2 handed: second player dealt; odds of getting pocket aces = (4/51)x(3/49) = ~.48% or 1/209
correct me if I'm wrong but this infers that the greater the number of players and the further in the action you are (closer to the button) the higher the probability of being dealt aces. Assuming that no other players have been.
or to be exact
The odds of being dealt pocket aces at a ten handed table on the button = (4/43)x(3/39) = .72% or 1/139
Where as the odds of being dealt pocket aces at a ten handed table on the small blind =(4/52)x(3/42) = .55% or 1/182
for this reason i believe the answer to "what is the probability of being dealt pocket aces" can not possibly be greater then 1/217 and should from here forward be described as the least likely ratio. that is in a heads up match being dealt the first card or 1 in 217 times.