  A division of a cake by n people is envy free if everyone thinks they got the
biggest pieces. Note that peoples tastes can differ. There is a discrete
protocol for envy free division for n=3 which takes at most 5 cuts. For n=4 and
beyond there is a protocol but the number of cuts it takes is unbounded. In
particular the number of cuts depends on peoples tastes. Given any number N
peoples tastes can be set so that the algorithm takes over N cuts. There are
three such algorithms known. Which is better?
  We have devised a way to measure the number of cuts even though it is
unbounded. We use ordinals; therefore, a statement like "this protocol takes at
most 2omega steps" makes sense. We analyse all three discrete algorithms for
envy free cake cutting with this measure.
