The new algorithm is so awkward. There is an easier way to divide the cake for n people (n>=2). For a rectangular cake move the knife with a slow uniform velocity, for a circular cake, cut to the center, and start rotating the cake with a slow uniform rotational velocity. The first person to yell stop will get the part of the cake that is split by the knife's current position. The process continues until there is only one person who doesn't get a cake. Although not every piece is guaranteed average, the game is fair.