The concept of transitivity is often perceived as something natural, as we encounter it in everydays life. In probability, however, this is often not true. We will deal with this problem in the thesis. The aim of the introductory part of the assignment is, first of all, to present and describe the basic problem to the reader and to further support it with examples. In the continuation of the thesis, when the reader is already familiar with the paradox of intransitive dice, we devote ourselves to an in-depth analysis of some mathematical facts related to intransitive dice. We take a closer look at the basic set of three intransitive dice and also expand the dimensions to a set of four dice, which also includes Efron’s dice. Similar to the number of dice in the set, we also increase the number of sides of each dice. From a mathematical point of view, the most complex part of the thesis is represented by theorems that are directly related to the probability of the dice winning against the others in the set. We limit these probabilities more precisely under various conditions and we also support the listed facts with mathematical proofs. An important finding, in connection with the limitation of probabilities between intransitive dice, is certainly the direct connection of the results with the ratio, which is well known among mathematicians and is also called the golden ratio.
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