User:Swampf0etus/sandbox

Scenario simplification matrix
Some find it easier to understand the solution when shown all scenarios in a matrix. Both matrices below shows all possible positions of the car against all possible choices by the contestant. A win outcome is shown as a 1 and loss as a 0.

The following matrix shows all possible outcomes where the contestant chooses to switch;

The following matrix shows the inverse, where the contestant chooses to stick with their choice;

As can be seen, the contestant is twice as likely to win the car they choose to switch than if they choose to stick with their original decision (six wins against three).