Welcome Forums The principle of inverted dice Playing with 3 inverted dice

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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 ,  and , 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  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.