1. The Monty Hall Simulation
in Excel

2. The Rules of the Game Do you switch?? There are 3 doors to choose from
Randomly placed behind one of the doors is a NEW CAR!
Behind each of the other two doors is a donkey
You are asked to choose a door
The host then opens a door you did not choose and shows you a donkey
You are then asked if you would like to switch to the remaining closed door
Do you switch??

3. Useful Excel Functions
=randbetween(lower_bound, upper_bound)
generates a random integer between and including the bound numbers
=rand()
generates a random decimal number between 0 and 1
=if(condition, value_if_true, value_if_false)
tests for a logical condition; returns specified value if condition is true or an alternate specified value if condition is false
this is our “decision maker” function
=sum(cell:cell)
sums up all cells specified; the colon is used to express a range of cells

4. Divide and Conquer
We are going to break our larger problem down into sub-problems for easier coding
We will consider three cases
In each, the car will be known to be behind a particular door
Combining the results of the three cases will provide an understanding of the larger situation

5. Case 1: Car Behind Door #1 Contestant Chooses a Door
Our main usage of random numbers will be for the contestant’s random selection of a door, as the first step of the game
Use a formula to generate a random number for the contestant’s selection of door #1, 2, or 3

6. Case 1: Car Behind Door #1 How does the host decide which door to open?
The host will never open the door the contestant selected, so we know Door #1 cannot be opened. However, this might be a good condition to logically check for…
These True/False questions can be coded with the “if” function

7. Case 1: Car Behind Door #1 So, do you switch doors?
It is simpler to code the logic that determines whether the contestant would have won if he/she stayed with the original door selection
use the “if” function to do this
Logically, if the contestant would have won by staying with the original door selection, he/she would have lost having switched doors
use the “if” function to code this based off of the win by staying value

8. Case 1: Car Behind Door #1 (formulas for first game played)
Remember to add sums at the bottom of the win columns to total the number of games won either staying or switching

9. Write the coding for the other two cases, where the car is known to be behind Door #2 and Door #3