  It is known that quasiperiodic hypermeander of spiral waves almost certainly
produces a bounded trajectory for the spiral tip. We analyse the size of this
trajectory. We show that this deterministic question does not have a physically
sensible deterministic answer and requires probabilistic treatment. In
probabilistic terms, the size of the hypermeander trajectory proves to have an
infinite expectation, despite being finite with probability one. This can be
viewed as a physical manifestation of the classical "St. Petersburg paradox"
from probability theory and economics.
