If he is betting 1 btc each time, the expected profit in the long term is 0, how is he able to make 200.000 bitcoins? How is he able to win 200.000 more than loosing when the chances are 50/50? Makes no sense
He'd only need to double his coins 17.6 times to earn more than 200K coins starting from 1. The probability of that happening is 0.5^17.6 is 1/200000. Which means 1 out of 200000 people will encounter this. Doesn't seem too far fetched to me.
It is far fetched if you consider the total number of total possibilities that exist and he would have to hit that streak on the first bet.