[BruceZ]

[ QUOTE ]
There is no one "correct" way to interpret probabilities, and your example doesn't even work.

Assuming all the 10,793,861 people's hands are being dealt from different decks, there's actually a 37% chance that someone won't get aces all three times, by my estimate:

(10,793,860/10,793,861)^10,793,861 = about 37%

So either the interpretation is wrong, or the math is wrong, and I trust the math in this case.

[/ QUOTE ]

He said in the long run, meaning that if we repeated this experiment a large number of times, each time dealing 3 hands each to 10,793,861 players, then on average 1 player would get 3 AA. That is, the expected value of the number of players getting 3 AA is 1. This is correct.

Another correct interpretation is that if we were to deal 3 hands to each player until some player gets 3 AA, then on average we would need to deal hands to 10,793,861 players. That is, the expected value of the number of players dealt hands before a player gets 3 AA is 10,793,861.