One side effect will be that random set of people will run out of money in that case. If 0 wouldn't be issue, then I'd expect normal distribution around the starting point? (I'm not 100% sure I understood your question though, also I'm not that smart...)
The absolute risk (X dollars) for the coin flip in these games is decided by the poor person (20% of their "wealth").
If the poor person could tolerate the absolute risk of the rich person, I wonder if the outcome changes.
I think you understood me. Some people would probably run out of money sooner, but I have a feeling the distribution would be a little more even.
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