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But, if it makes you happy, I'll also show how you SHOULD post your version:
If A is right (1/3 chance of that):
then the host reveals B (1/2 of 1/3)
and switching does NOT pay off
or
the host reveals C (1/2 of 1/3)
and switching does NOT pay off
If B is right (1/3 chance of that):
then the host reveals C
and switching does pay off
If C is right (1/3 chance of that)
then the host reveals B
and switching does pay off
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/(bb|[^b]{2})/
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