Wait... the Switcher is only going to win 1/2 the time against the show and get the car or other Grand Prize.
1/2 is better than 1/3 but switcher won't win 2/3 the time.
Eh, no when a door is opened odds are 50:50 to get it right but first picker is stuck with their choice 1/3 chance, so Switcher takes up slack 2/3's.
So show wins 2/3 of time against a First picker and 1/3 time against a Switcher.
1/2 is better than 1/3 but switcher won't win 2/3 the time.
Eh, no when a door is opened odds are 50:50 to get it right but first picker is stuck with their choice 1/3 chance, so Switcher takes up slack 2/3's.
So show wins 2/3 of time against a First picker and 1/3 time against a Switcher.
b = b + ...