IMAGINE THAT YOUR ON A GAME SHOW HAVE 3 DOORS TO PICK FROM. ONE HAS A BRAND NEW CAR, THE OTHERS HAVE GOATS. SUPPOSE YOU PICK DOOR A, BUT BEFORE YOU OPEN IT, THE SHOW HOST REVEALS THAT DOOR B HAS A GOAT. YOU CAN NOW ETHIER SWITCH TO DOOR C OR STICK TO DOOR A. YOU MIGHT THINK THAT IT'S JUST 50/50, BUT ITS NOT. THE 2 REASONS WHY ARE THAT 1. THE DOORS CONTENTS NEVER CHANGE. IF DOOR A WAS WRONG 2/3 TIMES AT THE START, IT'S WRONG 2/3 TIMES AFTER B IS REVEALED; AND 2. THE HOST KNOWS THE CONTENTS OF EACH DOOR AND WILL ALWAYS REVEAL A WRONG OPTION. SO, THE RESULT IS, 2/3 OF THE TIME YOU PICK A WRONG DOOR, THE HOST IS FORCED TO OPEN THE OTHER WRONG DOOR, SWITCHING WINS. THE REMAINING 1/3 IS WHEN YOU PICK THE RIGHT DOOR AT THE START, WHICH MEANS THE HOST WILL SIMPLY REVEAL ONE OF THE 2 WRONG DOORS. SO EVEN THO IT SEEMS LIKE 50/50, SWITCHING TO DOOR C IS TWICE AS LIKELY TO WIN AS STAYING WITH DOOR A.
