“You are the contestant on a game show that has 3 doors. One of them conceals a big prize. After picking a door (either A, B, or C), the show’s host reveals an unpicked losing door. He then asks if you’d rather change to the remaining unopened door, or stick with the one you had initially selected.”
Do you switch, or do you stick with your original door?
Contrary to what some may think, this classic “Let’s Make a Deal” probability puzzle proves that IF the contestant chooses a different door than the one picked first, they increase their probability of winning to two-thirds. No tricks. I’m serious.
(Let’s say that Door C is the winner.)
Scenario 1: Choose Door A. Door B is revealed. SWITCHING WINS.
Scenario 2: Choose Door B. Door A is revealed. SWITCHING WINS.
Scenario 3: Choose Door C. Door A or B is revealed. SWITCHING LOSES.
Switching your initial choice has a higher chance of landing the ultimate prize!
It boils down to this: when the contestant makes the original choice, they have a 1:3 chance of picking correctly. But then the game changes. After the host removes an option, you’re down to one good answer of two total doors. (It WOULD be simple probability if the contestant was presented with only two doors from the get-go.) If the player DOESN’T SWITCH, they’re assuming they’ve picked the prize accurately in round 1…. which isn’t likely. SWITCHING acknowledges this and effectively reverses the player’s chances. In fact, picking a dud door with this method isn’t likely.
Don’t believe it? Get a friend and 3 playing cards to see if you can’t statistically debunk the theory. If a “wrong” card is revealed and a contestant switches cards during phase two every time, I predict they’ll have a 66% success rate of getting the big prize…. as opposed to 33% probability if never switching answers. Strangely, the contestant is likely to win if they choose wrong in the first phase. Your odds are initially slim, then double in the player’s favor upon flipping answers. Cool, huh?
The big question is: how many would naturally switch choices without this knowledge?!