Here it gets more interesting. This is caused by the fact that with 3 inverted dice you don’t have the same number of possible results as with 3 normal dice.

With 3 normal dice, the sum is always between 3 and 18 (i.e. 16 possible results), but with 3 inverted dice, the sum is always between 6 and 20 (i.e. only 15 possible results).

We can easily deduct this, since we get the lowest result when only the three largest dice values, being [4], [5] and [6], are shown. The sum is then 1+2+3 = 6. In the same way we see, that we get the largest result when only the number [1] is shown, i.e. 2+3+4+5+6 = 20.

We could create a table showing all possibilities of achieving the results between 6 and 20 using three inverted dice, but to do so would be a rather tedious task.

As an example, we see that the result 11 can be achieved with the following combinations:

Let us leave it to the readers to calculate all the odds for dice rolls with 3 inverted dice. This can be done manually with the help of a table similar the one shown in the post about two dice, but it’s quite a lot of work (some programming skills would be useful). There are 6 times 6 times 6 possible outcomes, so the table consists of 216 rows.

#### Links:

Playing with 1 inverted die [1]

Playing with 2 inverted dice [1] [2]

Playing with 4 inverted dice [1] [2] [3] [4]

Playing with 5 inverted dice [1] [2] [3] [4] [5]

Playing with 6 inverted dice [1] [2] [3] [4] [5] [6]

Playing with *many* inverted dice