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

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    Inverted Dice

    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:


    Playing with three dice
    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.


    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

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