If the dealer is Ricky Jay, the odds of my
being dealt a straight flush are whatever Ricky wants.  In this
problem we'll suppose that Ricky Jay is my confederate and that to
avoid suspicion, he'll deal me a straight flush in just 1 hand out
of 100.

As we'll talk about in class, we can reason about probabilistic
unknowns by using logarithms of probabilities.  One of those
ratios is called the *Bayes factor*.   Using the logarithm of the
Bayes factor gives a quantity called the *weight of evidence*.
Turing was the one who suggested that weight of evidence be
measured in *decibans*.  The unit is by analogy with the
deci*bels* used in acoustics: a deciban is ten times the base-10
logarithm of the ratio.  So 10 decibans is a ten-to-one ratio, and
20 decibans is a 100-to-one ratio.

We often use weight of evidence to adjust our beliefs about unseen
information.   For example, suppose you are playing poker with me
and with Ricky Jay, and you learn that I am dealt a straight
flush.  What is the weight of evidence in favor of the hypothesis
that Ricky is cheating?
$$
W(cheating:straight flush) = 10 \log_{10}
\frac{P(straight flush given cheating)}
     {P(straight flush given fair play)}
$$
Which is
$$
W(cheating:straight flush) = 10 \log_{10}
\frac{1/100}
     {1/64972.9} = 10 \log_{10} \frac {64972.9} {100}
$$
Which by the algebra of logarithms is
$$
W(cheating:straight flush) = 10 (\log_{10} 64972.9 - \log_{10} 100)
  = 10 (4.8 - 2) = 28\, dB
$$
Most people would consider 28 decibans very strong evidence for a
hypothesis.  (But notice that the likelihood of what happens when
Ricky cheats is a number I pulled out of thin air.)