Doubts about the calculation of the probability.

Nobles, I ask for help in calculating probabilities to verify that I have done the math correctly.



The probability that a player has a chance to get a quad, regardless of his cards, is one in 4,200.

1 - First doubt, is this proportion correct?

2 - Second doubt: in this case, at a table with 9 players, can we consider that, in each hand, there are 9 possibilities to form a court? That is, each hand has 9 possibilities out of 4,200 (or approximately one in 467) of ending with a court (assuming that all 9 players reach the showdown)?

3 - Third question: Is this account valid? In a hypothetical live tournament with 27 players, where the average number of hands played is 1 every 2 minutes (calculated based on the agility - or lack of - of the dealers who work in our club) and which ends with 6 hours, fantasizing that all 27 players remain in the tournament during those 6 hours, and that everyone reaches the showdown in all hands, so we will have 180 hands played per player X 27 players = 4,860 hands per tournament. That is, the probability in the long run is that there will be a little more than one court per tournament, on average. (More precisely 1.1571 blocks per tournament)

I await the return of the most experienced.
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