Miwin's dice its 2 lowest numbers. The dots on each die are colored blue, red or black. Each die has the following numbers: Numbers 1 and 9, 2 and 7, and 3 and 8 are on opposite sides on all three dice. Additional numbers are 5 and 6 on die III, 4 and 5 on die IV, and 4 and 6 on die V. The dice are designed in such a way that, for every die, another will usually win against it. The probability that a given die in the sequence (III, IV, V, III) will roll a higher number than the
Miwin's dice against IX, and IX against XI. Third set: fourth set: The probability that a given die in the first sequence (5, 3, 1, 5) or the second sequence (6, 4, 2, 6) will roll a higher number than the next in the sequence is 5/9; a lower number, 4/9. The dice in the first and second Miwin sets have similar attributes: each die bears each of its numbers exactly once, the sum of the numbers is 30, and each number from 1 to 9 is spread twice over the three dice. This attribute characterizes the implementation of intransitive dice, enabling