MathDB
2021 Combo Div 2 P5

Source:

March 2, 2021
combinatorics

Problem Statement

Bill Gates and Jeff Bezos are playing a game. Each turn, a coin is flipped, and if Bill and Jeff have m,n>0m,n>0 dollars, respectively, the winner of the coin toss will take min⁡(m,n)\min{(m,n)} from the loser. Given that Bill starts with 2020 dollars and Jeff starts with 2121 dollars, what is the probability that Bill ends up with all of the money?
Proposed by Daniel Li
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