  The problem of creating a three-sided dice with the probability of it landing
on each of its sides being equal to 1/3 has been around for many years. Various
approaches have been attempted, but as different authors achieved at different
results, no uniform answer has been found. In this paper, the probability of a
cylinder-shaped coin landing on its side is investigated, aiming to predict the
final position of the coin, based on the starting physical and geometrical
parameters of the coin. Pure physical methods and computer modeling have been
used to find the parameters of a "fair" coin and to determine which parameters
of the system affect the probability of the coin landing on an edge, and in
what way. Statistical analysis of the situation has been made, to ensure that
the probabilities we are trying to find, correspond to the appropriate physical
events. Overall, two main possibilities for modeling the situation are
considered: single-axis rotation (flat rotation) and the superposition of
rotation against multiple axes (volumetric rotation). For each, a model was
built and it was compared with computer modeling and real-life experiments.
Dynamical and energetic approaches have been considered, and a model of the
coin during its impact with the ground has been created. A robot that is
capable of launching cylindrical coins, picking them up, and recording the
result of the experiment, controlling starting parameters precisely, and
distributing them to our needs, and automatically record the results of the
experiment, was created. In conclusion, the parameters of a "fair" coin are
provided, which have even probabilities landing on all its sides, as well as
the dependencies of the probability of a coin landing on its edge, on different
parameters.
