# Probabilistic prediction and context tree identification in the Goalkeeper Game

## TL;DR

This paper investigates how features like context tree shape, entropy, and deterministic patterns affect the predictability of stochastic sequences in a game setting, and compares different learners' methods for identifying sequence structures.

## Contribution

It introduces an analysis of factors influencing sequence predictability and models learners' procedures for structure identification in probabilistic sequences.

## Key findings

- Context tree shape impacts prediction difficulty
- Lower entropy sequences are easier to predict
- Best learners rely less on their own past choices

## Abstract

In this article we address two related issues on the learning of probabilistic sequences of events. First, which features make the sequence of events generated by a stochastic chain more difficult to predict. Second, how to model the procedures employed by different learners to identify the structure of sequences of events. Playing the role of a goalkeeper in a video game, participants were told to predict step by step the successive directions -- left, center or right -- to which the penalty kicker would send the ball. The sequence of kicks was driven by a stochastic chain with memory of variable length. Results showed that at least three features play a role in the first issue: 1) the shape of the context tree summarizing the dependencies between present and past directions; 2) the entropy of the stochastic chain used to generate the sequences of events; 3) the existence or not of a deterministic periodic sequence underlying the sequences of events. Moreover, evidence suggests that best learners rely less on their own past choices to identify the structure of the sequences of events.