"My" variance v "My accounts" variance?

[schroedy]

Please consider the difference between these two statements:

"Poker is all luck."

"Most players underestimate the luck factor in poker."

Poker players can run very bad for a very long time (or very good for a very long time) due to simple randomness. And that's the rub.

There is another story about randomness -- a statistics professor leaves a class of 35 students. Before he leaves he asks the class to write down a series of results for a hypothetical 50 flip trial with a coin. And to select one student to actually flip the coin and record the results for 50 trials. The professor almost ALWAYS is able to pick the actual trials from the hypotheticals. Know why?

[GMontag]

[ QUOTE ]
There is another story about randomness -- a statistics professor leaves a class of 35 students. Before he leaves he asks the class to write down a series of results for a hypothetical 50 flip trial with a coin. And to select one student to actually flip the coin and record the results for 50 trials. The professor almost ALWAYS is able to pick the actual trials from the hypotheticals. Know why?

[/ QUOTE ]

A run of 50 coin flips will likely have 5 in a row of either heads or tails, something which almost no student would intentionally put in the fake runs.

[AKQJ10]

I guessed more simply that the fake ones will turn out 25-25 or 26-24, but I like your answer too.