Re:What is ergodicity? (2016)
by kgwgk on Wednesday June 26, 2019 @05:56PM
(#20289648)
For any threshold (say $1, assuming you start with $1mn) and any confidence level (say 99%) there is a number of flips n such that you have over 99% probability of holding less than $1 after playing n times. On the other hand, the expected value of your wealth at that time is 1.05^n million dollars.
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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.