The situation the article explores was interesting, but made the jump to something mathematically complex before I sunk my teeth into the fundamental bit.
If you added some effects on what kind of gambles are available to players at different levels, you can create several different attractor states.
Ergodicity is a nice property of models like molecules of gas bouncing around a room, which means that statistical mechanics is practical. If one percent of the molecules tended to end up with all the kinetic energy, while the other molecules gradually one by one reached a complete standstill, then statistical mechanics wouldn't work.
Since the very simple process shown in the article doesn't have this property, it means some familiar statistical tools can't be used naively with these models, or to extrapolate a little bit, to any model of any human activity that tends to these kinds of capturing, fixed-point, attractor outcomes.
So in fact regardless of the initial run of luck, every player still goes to zero with probability one. The youtube video that another commenter linked to actually explains the 40% and 50% example much better.