Three competing patterns

TL;DR

This paper extends existing formulas for calculating the probability of one pattern winning over another in Bernoulli trials to the case of three competing patterns, providing a broader theoretical framework.

Contribution

It introduces a generalized theoretical approach for analyzing the probabilities of three competing patterns in Bernoulli sequences, expanding prior two-pattern models.

Findings

Derived formulas for three-pattern competition probabilities

Extended the theory from two to three patterns

Provided a comprehensive mathematical framework

Abstract

Assuming repeated independent sampling from a Bernoulli distribution with two possible outcomes S and F, there are formulas for computing the probability of one specific pattern of consecutive outcomes (such as SSFFSS) winning (i.e. being generated first) over another such pattern (e.g. SFSSFS). In this article we will extend the theory to three competing patterns.