There are two forms of the SB problem currently being discussed, one
with rather small numbers, and one with very large numbers.  Here I give
a form of the problem with moderate numbers, which may be easier to
understand intuitively.

You were present when a crime was committed, but you took no part in it.
You have been arrested, and are tried for this crime.

After you have given your evidence, the judge sentences you (this
country has an unusual judicial system).  Her sentence is "You will now
be taken from this court and locked in a prison cell.  Meanwhile the
trial will continue and we will hear the evidence of the witnesses.  If
we find you not guilty, you will be released from prison at 10 p.m.
tomorrow - this short sentence will be for your failure to prevent or
report the crime.  But if we find you guilty, you will be visited at 10
p.m. tomorrow by someone who will administer a soporific and 24-hour
memory-wipe.  This treatment will repeated until you have passed 100
nights in prison, and then you will be released at 10 p.m.
Psychologists advise us that this will have a reformatory effect on
you."

You know that you are innocent of the crime.  But there is a chance that
the witnesses will lie and the court will reach an unjust verdict - you
estimate this chance as 20%.

Some time later, you wake up in prison.  How do you rate your chance of
being released the same evening?

As a thirder, I know that the answer is 5/104.  But my gut feeling is
that it is .802 (ok, my guts aren't that precise - let's say somewhere
around 0.8).  I am finding it hard to reconcile this at present.

Nick
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Nick Wedd    n...@maproom.co.uk