I didn't calculate manualy last post, here is the detailed calculation:
each person has a 92.224% winning 1000, but 7.776% losing 31000. This is a simple calculation.
I really cannot see any point in Part III, the "I" in the story seemed very stupid. I think everyone should hate him. I would hate him if he asked me to play. I didn't see any gain for him, he even lost his $500, how stupid he was! He , he lost trust, he lost friendship and he even lost money.
If he tried to help most people, then that not only decided by him, but casinos as well. It depends the minimum and maximum betting amount. If the min is 1000, and the max is 20000, he also should not double in each round, he should bet like this:
First round: 1000
second round: 1001
3rd: 2002
4th: 4004
5th: 8008
6th: 16016
This way, by adding 1 more round, he can help 95.3344% instead of 92.224%, but half of winner win 1000, the other half win 1 dollar, but this is a win anyway.
Adding more rounds, averagely, will lose more money, but will have a bigger winning percentage.