Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

The second probability game you can use to trick humans was invented by mathematician James Grime. He developed a set of nontransitive dice, which now bear his name: Grime dice (which is now the second-best boy-band name in this book). They come in five colors (red, blue, green, yellow, and magenta), don’t have the normal numbers 1 to 6 on them, and you can use them to play a game of highest number wins. You and your opponent choose a dice* each and roll them at the same time to see who gets the highest number. But for every dice there is a different-colored dice that will beat it more often than not. On average: red beats blue; blue beats green; green beats yellow; yellow beats magenta; and then magenta beats red. My contribution to the dice was to wait for James to work the numbers out and then suggest a range of colors to help remember the red-blue-green-yellow-magenta order; each color is one letter longer than the previous one. Now, you let your opponent choose their color first, and you pick the dice with one fewer letters. Red (3) rolls over to magenta (7). If you use these dice to win drinks and money off your friends and family, you may eventually have to come clean about their nontransitiveness. Maybe even teach them the order of the dice. But then suggest doubling the dice up and rolling two of each color together. Because rolling the dice in pairs perfectly reverses the order of which beats which. Instead of red beating blue, blue now beats red more often than ...