Non-transitive Grime Dice, via Mathematica

Here is what may surprise some people. Here is an expectation table (i.e. just averages):

    | :olive | :magenta | :blue | :yellow |  :red |
    |--------+----------+-------+---------+-------|
    |  4.167 |    4.333 |   4.5 |   4.667 | 4.833 |

Generated by this Clojure code (`exp` means expectation):

    (print-table (order-keys-by exp dice) [(exp dice)])

I'm surprised that the two (very good!) articles ([1] and [2]) I've read did not point that the non-transitive property [3] holds on the dice even though the expectation are transitive:

    E(olive) < E(magenta) < E(blue) < E(yellow) < E(red)

Of course the expectations have to be transitive; they are scalars.

When you apply a function to pairs (e.g. compare one die against another), you can get non-transitive behavior. This is not earth-shattering, but it is interesting.

Put another way: this is yet another reason to not trust a single summary statistic (e.g. the average in this case) when you really should look at the distribution.

My code is here: https://gist.github.com/xpe/30ae93b107c91ec2ccf5

(Edited at 12:57 PM EST.)

[1] OP: http://latkin.org/blog/2015/01/16/non-transitive-grime-dice-...

[2] http://www.singingbanana.com/dice/article.htm

[3] Actually, there are multiple cycles; the 'secondary' cycles are not as 'strong'.

Not non-intuitive at all. Reminds me of Rock-paper-scissors-lizard-Spock but in dice form.