You will fail

Correct answer! The chance of initially choosing the car is one in three, which is the chance of winning the car by sticking with this choice. By contrast, the chance of initially choosing a door with a goat is two in three. If the player originally picked the door hiding the car, the game host has shown one of the two goats. If the player originally picked the door hiding Goat A, the game host has shown the other goat. If the player originally picked the door hiding Goat B, the game host has shown the other goat. Thus, if the player chooses to switch, the player wins the car in the last two cases. So choosing to switch doubles your chances to win, from one third to two thirds.

You are wrong. The chance of initially choosing the car is one in three, which is the chance of winning the car by sticking with this choice. By contrast, the chance of initially choosing a door with a goat is two in three. If the player originally picked the door hiding the car, the game host has shown one of the two goats. If the player originally picked the door hiding Goat A, the game host has shown the other goat. If the player originally picked the door hiding Goat B, the game host has shown the other goat. Thus, if the player chooses to switch, the player wins the car in the last two cases. So choosing to switch doubles your chances to win, from one third to two thirds.

If you bet 40% each time, your probable payout after 100 flips will be $4,700. This is seven to eight times less than the optimal choice, but you might find comfort in knowing that most people choose this answer.

If you bet 51% each time, your probable payout after 100 flips will be $31, or 1,161 times less than the optimal choice. Are you a gambler?

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