Two players play a dice game with one another. The winner is the person who throws the highest value. Three different dice are available. Each has different face values but the total always amounts to 57:
Would you like to choose or would you prefer to let your opponent take first choice?
To evaluate the probability of winning, we must compare the dice with one another. The illustration to your right shows that you have more chance of winning with the green dice than the blue dice.
However, the blue dice (illustrated at bottom right) has the upper hand over the red dice. We can therefore assume that the green dice is better than the red dice (transitivity) …
However, the last illustration shows that the green dice is disadvantageous compared to the red dice. We are dealing with a non-transitive situation here, similar to the "rock, paper, scissors" game.
For this reason, you should always allow your opponent to select the dice first.