The M&M Game: From Morsels to Modern Mathematics

To an adult, it's obvious that the day of someone's death is not precisely determined by the day of birth, but it's a very different story for a child. We invented what we call the M&M Game to help explain randomness: Given k people, each simultaneously flips a fair coin, with each eating an M&M on a head and not eating on a tail. The process then continues until all M&M'S are consumed, and two people are deemed to die at the same time if they run out of M&M'S together. We analyze the game and highlight connections to the memoryless process, combinatorics, statistical inference, and hypergeometric functions.