When dealing with problems, like aging, or playing games, like Tetris, it
is
tempting to use probability distribution over the intake materials or
falling
bricks. However, just having a probability distribution does not
guarantee,
that a specific type of falling brick will ever occur, it
just says that it's
highly
unlikely for it to not occur.
To solve for infinite lifespans, or infinitely long playing of Tetris, what's
needed, is a guarantees of the frequencies, or even patterns. Hence,
the
idea of a "Determinity Distribution" or "Deterministic Probability
Distribution", which sounds like an oxymoron, but could be defined
simply.
Suppose we have an algebra of events (e.g., like when defining a
random variable), and add
a
requirement, that the events have to repeat at no rarer or more often
than threshold
frequencies. That automatically implies that only specific periodic or
aperiodic patterns of event can qualify.
Surely, you may think a periodic pattern already has a "Determinity
Distribution",
because we have frequency guarantees. However, it is not a probability
distribution, because we already know the pattern with certainty.
However, given the
inequalities
(e.g., thresholds, or upper / lower bounds) for frequencies, it may be
possible to construct many patterns, and even aperiodic patterns (just
like aperiodic fractions, like irrational numbers with
proofs), that guarantee those frequencies, and at the same time are not
exactly predictable (!).
Thus, a determinity distribution would define an equivalence class for all
patterns, that the constraints of the probability distribution with
frequency
guarantees.
This also may be applicable to lottery games. For example, lottery
makers
may claim specific probabilities about their games, but not guarantee
them,
so
that the winning prize actually is never really won. However, giving legal
requirements for determinity distribution would change the games...
And yes, determinity distribution would imply, that the more
observations we have, the more certain other events are, but not
completely certain (until the last event before threshold). It's kind of an
interesting concept mathematically, that you can have such interplay of
indeterminism and determinism.