Yo Adrian.!

This post presumes you are familiar with the Monty Hall Problem and the associated post/article. If not, first read the Monty Hall Problem posting and then come back to this. Now we can begin…

**Lock The Gates!**

While ruminating on Monty Hall I came up with this * Gedankenexperiment. * It’s doubtful that what is here is unique/new but here it is anyway. Enjoy.

First, let’s restate the problem and refresh our memory.

You’re on the *Let’s Make A Deal* game show. You’re given the choice of three doors: Behind one door is a shiny new car!; behind the other 2 doors are goats (which you don’t want!). You pick a door, say No. 1, and the host (Monty Hall), who knows what’s behind the doors, opens another door, say No. 3, which has a goat. Monty then says to you, “Do you want to switch and instead pick door No. 2?”

What should you do?

**1. Should you stick with your original choice of door No. 1?**

**2. Should you switch to door No. 2? **

**3. Or… as a whole lotta people believe, it wouldn’t matter whether you stick with door #1 or whether you switch to door #2. All you know is that one door has the prize and one doesn’t so you would have a 50/50 chance of winning either way. ****This is the part of the problem we will now focus on.**

**Let’s ****think**** about this…**

**When we initially picked door#1 our odds of winning the car were 1/3 (33.3%). Now, when Monty shows us a “goat” behind door#3, all of a sudden we think our odds of winning increased to 1/2 (50%) even if we stick with Door#1. But think about it… ****Did Monty really do anything that would change our initial odds of winning?**

**I like this one… What if Monty shows us the goat behind door#3 and then closes it, and then, 5 seconds later a meteor falls from the sky, hits us in the head, and as a result we forget what was behind the door!!….. And then we are given the chance to switch from our initial door#1 to door#2. If we stick with our original choice of door#1, what are our odds of winning the new car? Are they still the original 1/3 or have they increased to 1/2 ? Did the odds of the car being behind our original choice of door#1 go from 1/3 to 1/2 when we realized a goat was behind door#3? And did the odds then revert back to 1/3 when we forgot what happened?**

**Or how about this. What if we have a personality disorder that makes us ****always stick with our first choice no matter what.**** If Monty shows us the goat behind door#3 are the odds of the prize being behind door#1 and door#2 the same (50/50)? If we will always stick with our original choice will our odds of winning always be 1/3? That would seem to conflict with the notion that *** “All you know is that one of the 2 remaining doors has the prize and one doesn’t so you would have a 50/50 chance of winning either way.”*

**As we can now see, there are too many holes in choice #3 above. Or in other words, it ****does**** matter whether we stick with our original choice vs whether we switch to door#2 !!!**

**Open The Gates!**