# Entropy-Based Strategies for Multi-Bracket Pools

## TL;DR

This paper introduces a new approach for making multiple event predictions using entropy-based strategies, which is efficient and effective for complex betting scenarios like March Madness brackets.

## Contribution

The novel contribution is applying entropy-based methods to generate optimal multi-event predictions in high-dimensional betting pools.

## Key findings

- Entropy-based strategies are tractable and scalable for multi-bracket prediction problems.
- The approach performs well compared to traditional wagering strategies in high-dimensional settings.

## Abstract

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.