Question about probability in stud

[DMSNI]

I am trying to calculate the probability of having a particular hand by 5th street in 7 card stud. If i know the probability of having it on 4th and the probability on having it on 5th (after 1 card each time) how do you combine the two to find the probability of getting that hand by 5th street. For example with 8 players, starting with a pair the probability of having 3 of a kind on 4th is 1:21 (42 cards /2). How does one calculate the probability over more than 1 street?

[tshort]

There are various ways of doing so.

Say you are dealt a pair of 5's. The probability of getting trips by 5th street is the sum:

P(getting trips on 4th street)

+ P(getting trips on 5th street) given you did not get trips on 4th street

In the example of being dealt say 55A, the probability of trips by 5th street:

2/49 + 47/49 * 2/48

Probability by 6th street:

2/49 + 47/49 * 2/48 + 47/49 * 46/48 * 2/47

You are adding up the all possible cases of reaching trips. This method gets cumbersome and there are easier methods if you're familiar with basic combinatorics.