Here an interesting riddle:

The Terrible Twins, Innumeratus and Mathophila, were bored. “I know”, said Mathophila brightly. “Let’s play dice!”
“Don’t like dice.”
“Ah, but these are special dice”, said Mathophila, digging them out of an old chocolate box. One was red, one yellow and one blue.

Innumeratus picked up the red dice. “There’s something funny about this one”, he said. “It’s got two 3’s, two 4’s and two 8’s.” “They’re all like that”, said Mathophila carelessly. “The yellow One has two 1’s, two 5’s and two 9’s – and the blue one has two 2’s, two 6’s and two 7’s.”

“They look rigged to me”, said Innumeratus, deeply suspicious. “No, they’re perfectly fair. Each face has an equal chance of turning up.”

“How do we play, anyway?”

“We each choose a different one. We roll them simultaneously, and the highest number wins. We can play for pocket money.” Innumeratus looked sceptical, so his sister quickly added: “Just to be fair, I’ll let you choose first! Then you can choose the best dice!”

“Weeelll … ” said Innumeratus, hesitating.

Should he play? What is so special about the dice?

Ian Stewart: “Professor Stewarts mathematisches Sammelsurium”, Rowohlt Taschenbuch Verlag, 2011.

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