Now: consider a game of
Fizzbin
played against an extraterrestrial
The ET deals a series of five-card hands,
from a
deck with unknown numbers of cards, suits, cards /
suit, & ranks
and
declares which of you is the winner after each deal
Probability theory cannot predict
p(winning) because the necessary data are lacking
Likelihood
(Bayesian) theory can estimate L(winning)
based on accumulated data
on the composition of hands, and which win or lose
E.g.,
after the first game the minimum number of suits &
cards / suit is known
After N games,
a reasonable model of the maximum numbers is
possible
The model might
assume [be conditioned on the expectation]
that all suits contain equal
numbers of cards, as in Poker
Additional data might
indicate that there is a less common suit, or rank
Analysis of the distribution of
events could estimated
E.g., a Chi-Square
test might reject the hypothesis that all suits are
equally common