Efron's Dice: Where Mathematics Beats Luck
During a Friday meeting with friends, I pulled out four inconspicuous dice from my pocket. With a mysterious smile, I asked if anyone wanted to play a simple game. Robert, known in our group as a lucky person, immediately took up the challenge. "The rules are simple," I said. "Whoever rolls more pips wins. To keep it fair, choose your die first." Robert confidently chose one of the dice, and I calmly took another from the remaining ones. We rolled several times. To everyone's surprise, I consistently rolled higher numbers. "Would you like to try with a different die?" I innocently suggested. "You can change to any of the remaining ones at any time." Robert, feeling that luck had abandoned him, eagerly took up the offer. I also reached for a different die. To his growing frustration, the situation repeated itself. He changed dice several more times, trying all possible combinations, and I picked a different one to pair each time. My ...