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.

翻译：在博彩平价投注文献中，大量研究探讨了事件结果概率估计或最优下注策略，尤其针对赛马投注。然而，某些投注池不仅涉及单一事件，还涉及事件元组。例如，赛马中的六选一投注、“三月疯狂”小组赛挑战、以及随机比特串预测，都需要进行一系列独立预测。尽管传统最优下注策略在元组规模极小（如预测赛马胜者）时效果良好，但对于更高维度的一般性投注池（如“三月疯狂”小组赛挑战）则难以处理。因此，我们提出多视角池问题：假设我们希望预测一个事件元组，且已知每个事件每种潜在结果的真实概率，如何以可处理的方式生成一组 $n$ 个预测元组？该问题的最一般形式极其困难，因此我们从简化场景入手。具体而言，我们依据具有最优熵的分布生成 $n$ 个独立预测元组。这种基于熵的方法具有可处理性、可扩展性且表现良好。