This is a discussion on Not sure about this within the online poker forums, in the Learning Poker section; Does anyone have any idea what the odds are of someone winning 3 straight hands with the same straight?
First: For five card stud, which is a simpler problem, I submit to you the answer is 5.70 X 10^(-20) to three significant digits.
Second: For seven card stud, or probably of more interest to you,Texas Holdem, I submit to you the answer is 5.28 X 10^(-16) to three significant digits. Now, you did say the same straight, which is an important qualifier. I took the easy route and made the assumption that you meant exactly the same cards in the straight, as I am a little tired tonight.
Final Note: My calculations do not take into account the possibility of the straight being beaten by a better hand.