Mankiw's logic seems a little circular... education buys you the golden ticket, but then the process for determining the winners is stochastic. What determines

Mankiw's logic seems a little circular... education buys you the golden ticket, but then the process for determining the winners is stochastic. What determines the distribution of the stochastic process? If more people get educated, and the stochastic process stays the same, doesn't the distribution of outcomes stay the same? So in what sense is the distribution related to education? If in some areas network effects got more important, and Windows became ubiquitous, or Mankiw's textbook... and then industry got pretty powerful and able to defend the cash streams, without worrying about taxes or checks on market power... then the stochastic process became more winner-take-all.