  It is known that any open necklace with beads of $t$ types in which the
number of beads of each type is divisible by $k$, can be partitioned by at most
$(k-1)t$ cuts into intervals that can be distributed into $k$ collections, each
containing the same number of beads of each type. This is tight for all values
of $k$ and $t$.
  Here, we consider the case of random necklaces, where the number of beads of
each type is $km$. Then the minimum number of cuts required for a ``fair''
partition with the above property is a random variable $X(k,t,m)$. We prove
that for fixed $k,t,$ and large $m$, this random variable is at least
$(k-1)(t+1)/2$ with high probability. For $k=2$, fixed $t$, and large $m$, we
determine the asymptotic behavior of the probability that $X(2,t,m)=s$ for all
values of $s\le t $. We show that this probability is polynomially small when
$s<(t+1)/2$, it is bounded away from zero when $s>(t+1)/2$, and decays like
$\Theta ( 1/\log m)$ when $s=(t+1)/2$.
  We also show that for large $t$, $X(2,t,1)$ is at most $(0.4+o(1))t$ with
high probability and that for large $t$ and large ratio $k/\log t$, $X(k,t,1)$
is $o(kt)$ with high probability.
