The whole point of the paradox is that if you keep playing it’s impossible to end with anything but nothing. Sam laid out no exit point, not sure how he comes to the conclusion that he can end with an enormously valuable existence.
It is extremely risky and ill-advised, but as SBF said, it’s possible to end up in a very (very!) good position. The crux is that infinity doesn’t exist. You will place the bet at most a finite number of times.