The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is equipped with three doors. Behind two are goats, and behind the third is a shiny new car. You are asked to pick a door, and will win whatever is behind it. Let's say you pick door 1. Before the door is opened, however, the rules require the host (Monty Hall), who knows what's behind the doors, to open one of the other two doors revealing a goat and to offer you the choice of switching to the remaining unopened door, regardless of your initial choice. The Monty Hall problem is deciding whether you do.
The correct answer is that you do want to switch. If you do not switch, you have the expected 1/3 chance of winning the car, since no matter whether you initially picked the correct door, Monty will show you a door with a goat. But after Monty has eliminated one of the doors for you, you obviously do not improve your chances of winning to better than 1/3 by sticking with your original choice. If you now switch doors, however, there is a 2/3 chance you will win the car (counterintuitive though it seems).
 |  | winning probability |
| pick | stick | 1/3 |
| pick | switch | 2/3 |
The Season 1 episode "Man Hunt" (2005) of the television crime drama NUMB3RS mentions the Monty Hall problem.
The problem can be generalized to four doors as follows. Let one door conceal the car, with goats behind the other three. Pick a door 
. Then the host will open one of the nonwinners and
give you the option of switching. Call your new choice (which could be the same as
if you don't switch) 
. The host will then open a second nonwinner, and
you must decide for choice 
if you want to stick to 
or switch to the remaining door. The probabilities
of winning are shown below for the four possible strategies.
 |  |  | winning probability |
| pick | stick | stick | 2/8 |
| pick | switch | stick | 3/8 |
| pick | stick | switch | 6/8 |
| pick | switch | switch | 5/8 |
The above results are characteristic of the best strategy for the 
-stage Monty Hall problem: stick until the last choice, then
switch.
