Since 2004, more often than not, while teaching with Dofin ASE I kept assigning the class homework involving a nonstandard 6-die problem. The reason could be related to a remembrance since my times with Oxford University when one of my teachers realized that Romania did not have a border with Germany.
The real reason is that in order to understand finance one needs to span many mathematical branches including probability and combinatorics. “Playing” with an n-die is a good starting point.
A standard 6-die refers to a fair, six-sided die, whose faces are numbered 1 to 6.
The homework asks to find an alternative pair of 6-dice, with faces labeled with positive integers different from the standard 6-dice. The new pair should have the same odds for throwing every number as a normal pair of 6-dice.
Moreover it must be proved that there is precisely one pair of nonstandard 6-dice with the same probability as a pair of standard 6-dice.
The answer is known as Sicherman Dice and is represented by a pair of 6-dice labeled with (1,2,2,3,3,4) and (1,3,4,5,6,8).
For unicity one can check Proposition 9, here.
One of the first instances when the problem was mentioned was in M. Gardner, Penrose Tiles to Trapdoor Ciphers.