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Re:What is ergodicity? (2016) by mturmon on Thursday June 27, 2019 @03:18PM (#20297627)
This is well-stated.

In fact, an even stronger statement is possible: If you start with $1MM, eventually you will fall below $1 and never go above $1 again no matter how long you keep playing.

And all of that not just on a fraction of sequences, but with probability 1.

Re:What is ergodicity? (2016) by kgwgk on Thursday June 27, 2019 @03:37PM (#20297805)
True, as I said in a previous comment we have “almost sure” convergence to zero (i.e. the sequence will converge to zero with probability one).