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The theory of fair gambling devices
The theory
of fair gambling devices makes an inference to an unobserved state-space whose states are the ways
in which an outcome can occur in a game of chance.
This inference is from an observed state-space
containing a single state; this state is abstracted
from the states in the unobserved state-space.
Values are
assigned to the probabilities of the ways in which an
outcome can occur by maximization of the missing
information about the way in which an outcome will
occur. Maximization of the missing information assigns equal values to the
probabilities of the ways.
The
following example illustrates the concepts. In a throw of a pair of dice, each way in which an
outcome can occur is a pair of faces facing upward, where each face belongs to
a different die. There are 36 different pairings of faces; thus, there are 36 ways in which an outcome can occur. Maximization of the
missing information about the ways in which the outcome
will occur assigns the value of 1/36 to the probability of each way.