Can we derive a non-contextual inequality from a simple game?

Have you ever thought about whether we can derive an inequality, like the ones used in quantum information science, from any classic game? These inequalities help us identify the boundaries between classical and quantum behaviors.
Everybody knows the classic game, Rock-Paper-Scissors. It can be extended such as Rock-Paper-Scissors-Lizard-Spock, which was shown in “The Big Bang Theory”, one of the US TV network comedies. From this classic game, we can derive one of the non-contextual inequalities, i.e., KCBS inequality [PRL 101, 020403 (2008)].
Here is the rules:
1. Rock crushes lizard.
2. Lizard poisons Spock.
3. Spock smashes scissors.
4. Scissors cut paper.
5. Paper covers rock.
6. Rock breaks scissors.
7. Scissors decapitate lizard.
8. Lizard eats paper.
9. Paper disproves Spock.
10 Spock vaporizes rock.
The rules are referred to Wikipedia Rock-Paper-Scissors-Lizard-Spock. For two persons playing the game, we find that any fair player will win 2/5 of the time on average. If a player has only five different selection cards, then on average one person can defeat the other twice, i.e. 2/5 are multiplied by 5 selections. The scenario of winning the classical game gives us the same classical bound on a pentagram inequality in KCBS inequality. Coincidentally, the Rock-Paper-Scissors-Lizard-Spock game has a pentagram shape due to the relations (1-10) above.
What do you think? It might be some controversial; but it is interesting that we can try to derive another inequality from a game in our daily life :). To find out more about these contextual inequalities check out our latest review. Come out, come out, wherever it is!