Re: Odds of 3 in a row?
The "correct" answer is as much psychological as mathematical. This type of question is inspired by some unusual occurrence, and only afterwards does someone say "Wow, what were the chances of that?"
Well to answer the question correctly from a mathematical standpoint, "that" must be specified precisely.
It is correct to answer the question "What are the chances that my next three hands will be Q4o?" with (12/1326)^3, or 0.00000074 (the odds being 1,350,000-to-1 against). But perhaps a better question would be "What are the chances of being dealt the same hand in three particular deals?" (definining "same hand" as same two ranks, suitedness mattering, but the actual suits themselves not mattering: approximately 0.000061; 16,350-to-1 against); or "What are the chances of being dealt Q4o the next two times after it was dealt once?" ((12/1326)^2=0.000082; 12,209-to-1 against).
Perhaps an even better question would be "What are the chances of being dealt three of the same hand in a row sometime during a 4-hour session of hold 'em?" Assuming 150 hands in 4 hours, the answer would be close to 1 in 1000, which is not really all that remarkable. It should happen to you on average once every 4000 hours of play.
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