  In frequently repeated matching scenarios, individuals may require
diversification in their choices. Therefore, when faced with a set of potential
outcomes, each individual may have an ideal lottery over outcomes that
represents their preferred option. This suggests that, as people seek variety,
their favorite choice is not a particular outcome, but rather a lottery over
them as their peak for their preferences.
  We explore matching problems in situations where agents' preferences are
represented by ideal lotteries. Our focus lies in addressing the challenge of
dividing chances in matching, where agents express their preferences over a set
of objects through ideal lotteries that reflect their single-peaked
preferences.
  We discuss properties such as strategy proofness, replacement monotonicity,
(Pareto) efficiency, in-betweenness, non-bossiness, envy-freeness, and
anonymity in the context of dividing chances, and propose a class of mechanisms
called URC mechanisms that satisfy these properties. Subsequently, we prove
that if a mechanism for dividing chances is strategy proof, (Pareto) efficient,
replacement monotonic, in-between, non-bossy, and anonymous (or envy free),
then it is equivalent in terms of welfare to a URC mechanism.
