Now it gets much more interesting. That is because we find a radical change of the probabilities.
But first, let’s see some examples:
When playing with 2 inverted dice, you can achieve any result from 10 to 20 (that is 11 possible results).
We realise that there is only one way of getting the result 20, and that is when both the dice show the number 1. However, we also see that for instance the result 18 can be achieved in several different ways.
It is time to make a complete table to get an overview. We have 36 possible outcomes to look at:
We can now without difficulty create two tables showing the odds of all possible results, in the case of both two normal dice and two inverted dice:
With two inverted dice, the two highest numbers are also those most difficult to achieve. This is usually not the case, since it’s normally just as hard to roll 2 as 12.
There are several uses for this. For example, try playing Monopoly with inverted dice instead of regular dice (or change the rules and add the possibility of a player having to use inverted dice in certain situations). Feel free to invent new games of your own.