  We study the computation contests where players compete for searching a
solution to a given problem with a winner-take-all reward. The search processes
are independent across the players and the search speeds of players are
proportional to their computational powers. One concrete application of this
abstract model is the mining process of proof-of-work type blockchain systems,
such as Bitcoin. Although one's winning probability is believed to be
proportional to his computational power in previous studies on Bitcoin, we show
that it is not the case in the strict sense.
  Because of the gaps between the winning probabilities and the proportions of
computational powers, the Matthew effect will emerge in the system, where the
rich get richer and the poor get poorer. In addition, we show that allowing the
players to pool with each other or reducing the number of solutions to the
problem may aggravate the Matthew effect and vice versa.
