You’re probably familiar with the 3 door problem, made famous by Marilyn Vos Savant. I have tried to add a new twist to the problem to show its implications for some real life issues.
First consider the original problem:
- You’re a contestant on a game show. There is a prize behind one of three doors (the other two doors don’t have prizes). You are told to pick one door, so you do.
- However. . . before your door is opened, the game show host intervenes. He opens one of the other doors and shows you that there is no prize behind it. He then gives you the option of staying with your original pick or switching to the other unopened door.
- Should you switch doors
You should always switch, because the probability of getting the prize is more if you switch (66.67%) – more precisely its double than if you do not switch (33.33%).
A simple php program by Fane Henderson which simulates it, confirms the results.
case 1. If the contestant picks a door, his chances of winning are 1/3
case 2. If the contestant is offered to pick two doors, his chances of winning are 2/3.
If the contestant picks a door and sticks to it this is case 1
If the contestant is offered to switch after picking a door, and showing an empty door is exactly the same if he picks a door exchanges the selected for the remaining two doors and then the host opens the door, from his just exchanged doors, with no prize behind it. This is case 2 and hence the chances of winning are 2/3
A Little Twist
Assume that God is the Host and He has offered three doors namely J,
C and I to you. You have selected a one (though generally its not an active choice). Then God opens a door from the remaining to reveal that reward is not behind that door. He then offers you to switch the door. Will you switch?
What we can not do is to choose a door (which all of us actively or passively, already had) and then ask God to show us the door behind which there is no reward and then decide to stick or to switch, but what we can easily do is:
- Assume that the Switching gives us the 2/3 chances of winning (the popular 3door problem result)
- Do the iterations for all of the population associated with any of these “Doors”.
- Assume a simple chronological order J => C => I which means that:
- No one can choose J
- J can choose C
- C can choose I (b. & c. implies J can choose
I as well)
- I cannot choose any
- While doing these iterations actually assign the number of persons lining up for J, C and I to make these statistical analysis close to real, and keeping in mind the constraints of No. 3 (or by assigning it a
weight-age (from 0 to 100% for different case studies) to make the decision of switch.
- Check out that which of the Door after performing this switching iteration process (No. 4) have most of the people lined up behind it.
- God’s design can not push the most to take His wrath and hence most of the people will be standing behind the “God’s Door”
I am not writing any simulation code to do it for you. You are at liberty to do the simulations the very way you like them with whatever constraints you like. I am not closing the chapter here, rather its just a prelude to another way of knowing His Thoughts.
Author: Irfan R. Toor