  Much work in the parimutuel betting literature has discussed estimating event
outcome probabilities or developing optimal wagering strategies, particularly
for horse race betting. Some betting pools, however, involve betting not just
on a single event, but on a tuple of events. For example, pick six betting in
horse racing, March Madness bracket challenges, and predicting a randomly drawn
bitstring each involve making a series of individual forecasts. Although
traditional optimal wagering strategies work well when the size of the tuple is
very small (e.g., betting on the winner of a horse race), they are intractable
for more general betting pools in higher dimensions (e.g., March Madness
bracket challenges). Hence we pose the multi-brackets problem: supposing we
wish to predict a tuple of events and that we know the true probabilities of
each potential outcome of each event, what is the best way to tractably
generate a set of $n$ predicted tuples? The most general version of this
problem is extremely difficult, so we begin with a simpler setting. In
particular, we generate $n$ independent predicted tuples according to a
distribution having optimal entropy. This entropy-based approach is tractable,
scalable, and performs well.
