When two or more people roll a die each in order to see who scores highest – what you do, for example, when deciding who goes first in a board game – there is always the chance of a tie. In the event of a tie, of course, you roll again. But then there is still the chance of a tie. And this can go on ad infinitum.
In other words, the process is not as efficient as it could be. Eric wondered if he could come up with a set of fair dice such that one roll of each die is enough to establish an absolute winner. In devising a solution – and thus saving the board game players of the world hours and hours of lost time – Eric and a friend have made the greatest innovation in dice technology in recent years.
Their set of four "Go First" dice (pictured above) are such that when two, three or all four of the dice are rolled together:
1) no ties are possible.2) each die has an equal chance of displaying the highest number.
Eric's friend is Robert Ford, a mathematics professor at Dalton State College, Georgia. Initially they were considering a set of eight cubic dice, but Robert worked out that it was impossible to have a set of cubic dice that satisfied the two conditions. He then looked at a set of four dodecahedral dice – the 12-sided dice that are used in Dungeons & Dragons – and after a week found a solution, which include all the numbers from 1 to 48 with no repeats:
Die 1: 1, 8, 11, 14, 19, 22, 27, 30, 35, 38, 41, 48
Die 2: 2, 7, 10, 15, 18, 23, 26, 31, 34, 39, 42, 47
Die 3: 3, 6, 12, 13, 17, 24, 25, 32, 36, 37, 43, 46
Die 4: 4, 5, 9, 16, 20, 21, 28, 29, 33, 40, 44, 45
These dice satisfy Eric's requirements: if you roll any subset of them, each die has an equal chance of winning.