Bertrand's Ballot Problem: Have you seen the gorgeous GRAPHICAL solution?
Channel: Aha Problems
Date: 23/04/2024

Indian elections are right around the corner and we have to study a bit of election mathematics. So we will celebrate the election by learning a famous historical puzzle, Bertrand's Ballot Problem:
"In an election where candidate A receives p votes and candidate B receives q votes with p bigger than q, what is the probability that A will be strictly ahead of B throughout the count?"

This problem has a celebrated bijection proof due to Desire Andre which will be exposed in this video using a geometric method. Note that although we say "Andre's reflection trick", the original solution by Andre never used any reflections.

00:06 Dhruvanarayana's historic 1-vote win!
01:01 The main question of the video: What are the chances that Mr Dhruvanarayana ties at some point?
01:14 The mathematical setup
01:55 Bertrand's Ballot Problem
02:35 Geometric presentation
07:37 Andre's reflection trick
07:52 Solving Bertrand's problem
09:06 Solving the main question of the video.