Quote:
let's say I have pocket Deuces at a 9 handed table, how often will one of the other 8 players have a deuce?
Probability 101: When confused about a probability think of the opposite (because all probabilities must add up to 1)
I.e.:
"Probability that someone else has a deuce (or two)" + "Probability that no one else has a deuce" = 1
In other words:
"Probability that someone else has a deuce (or two)" = 1 - "Probability that no one else has a deuce"
Now we can easily figure this one out:
"Probability that no one else has a deuce"
There's 8 other players holding 16 cards and 50 unknown cards of which 48 are non-deuces.
So the probability is:
48/50 for the first of those 16 cards to not be a deuce
its then
47/49 for the second of those 16 cards to not be a deuce
etc.
48/50 * 47/49 * ... * 33/35
= 0.46 (roughly)
So the probability that someone is holding a deuce (or two) is
1 - 0.46 = 0.54