Comparing $n$-dice fixing the sum of the faces

TL;DR

This paper explores how changing the face values of n-sided dice while keeping the total sum constant affects their comparison, providing insights into dice behavior under face value modifications.

Contribution

It introduces new results on dice comparison when face values are varied with a fixed total sum, expanding understanding of dice probability distributions.

Findings

Identifies conditions for dice equivalence under face value adjustments

Provides criteria for comparing dice with fixed total face sums

Analyzes the impact of face value changes on dice comparison outcomes

Abstract

These notes describe some results on dice comparisons when changing the numbers on the faces while the sum of all the face stay the same.