During excavations in Ur, a town in southern Iraq, archaeologists found an early Stone Age game. In order to move the figures around the board, you have to throw dice. However, the faces of the tetrahedral dice do not have a number on each face like today’s dice. Rather, each face is marked with a dot in one corner. If you throw four dice you get the sum of the dots in the top corner between zero and four. The chances of throwing a four in this game are 1 to 256. But how high are the chances of throwing a one, two or three? This is harder to calculate. But you can figure out the probability if you take a closer look at the symmetrical properties of a multi-faced dice and thus visualise the potential number of ways to throw a one, two or three. For example, if you want to know what the chances are of throwing a one, you have to consider the ways in which the dice could fall to achieve this result. Assuming only one of the dice lands with its dot at the top, then the other dice must all land with one of their three dot-less corners at the top – which means there are 3x3x3 = 27 possible outcomes to this throw. Within this scenario, however, any of the four dice could be the one to land with its dot at the top. Thus, in total, there are 4x3x3x3 = 108 possible ways of throwing a one. With a total of 4x4x4x4 = 256 different potential outcomes the chances of throwing a one are therefore 108 to 256. (abe)

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