Comments on: Let’s Make a Deal

By: Evil1

Evil1 — Wed, 25 Jan 2012 18:01:22 +0000

If there were 1 Billion doors to choose from, and I picked one randomly that I thought may contain the prize, I would have a 1 in 1 Billion chance of picking the right door first time (very little chance of success). If the host then opened 999,999,998 doors that HE knew did not contain the prize (leaving my original picked door and only one other door), that would mean that either my door was right (on first choice) – or the only remaining door he has left unopened is right and the odds would suggest I should swap to his door. Much better odds than the three doors but the principle is the same, unless someone sees a flaw in my reasoning?

By: cornflower

cornflower — Fri, 29 Apr 2011 01:02:35 +0000

*rather than the first

By: cornflower

cornflower — Fri, 29 Apr 2011 01:01:47 +0000

I’d like to point out what I think about the coin tossing question. The question “What are the odds that…” is the key here, and is what may make the problem misleading.
It makes a difference when you say: “What are the odds that the coin will come up heads on the next (100)th flip?” and when you say: “What are the odds that you will get a series of 1oo coin flips that come up all as heads?” The illusion is in that we tend to think of the second formation of the question rather first, as our brain tends to recognize stark patterns more quickly, as the article says.

By: Alucin Veritas

Alucin Veritas — Sat, 26 Dec 2009 08:23:27 +0000

An inversion of thought might provide clarity. Instead of having the probability of being right, look at the probability of being wrong. Initially, there is a two thirds probability of being wrong. Then, in the switch there is a one in two probability of being wrong. Since the two probabilities are connected, they are multiplied. The result is that if a switch has occurred, then there is a one in three probability of being incorrect.

By: Bob Nesbo

Bob Nesbo — Mon, 09 Nov 2009 09:48:30 +0000

I believe Edgar Allen Poe had an entire dissertation regarding something similar to this. I read it years ago, and I will have to search it…

By: sulkykid

sulkykid — Sun, 19 Apr 2009 00:53:05 +0000

Previous odds and outcomes ARE relevant as any horseplayer knows.

By: tactilejones

tactilejones — Sat, 18 Apr 2009 23:05:46 +0000

Okay, head hurts, nausea setting in, and yet I’m compelled to exacertbate the situation by tediously registering, logging in, and commenting via T9 text from my cellphone!! So, I think I get the concept, initially… switching to the 2/3 odds from the 1/3 odds and all that. But then, consider this scenario: No previous gameplay. Two doors, one contains a prize, one contains nada. You “own” one door. You’re given the choice to switch doors, or not, before the prize-containing door is revealed. Whether you switch or not, your chances are 1/2. Other than the “no previous gameplay”, this is the scenario you’re presented with in Monte’s game, no? So if previous odds and outcomes are not relevant, as according to the Gambler’s Dillemma (as presented here), shouldn’t “pick one of two doors randomly containing a prize” remain at 1/2 odds, regardless of whatever silly game you were playing a moment before? HELP!! I will not eat or sleep until I understand this!

By: howardfrankfort

howardfrankfort — Sat, 14 Feb 2009 17:42:19 +0000

The least likely senario oddswise is you have chosen the winner @ 1 of 3 choices. If the odds favor you have chosen a goat in step 1, accept that you probably have. What doors would this senario leave Monty? A winner and a looser. He cannot choose the winner, so if odds are your only indicator, and they favor you have chosen a goat, HE had no choice to make, you forced him to eliminate the other goat. So if odds are you chose a goat to begin with, and you know what that would have forced Monty to do, what door would you pick? The switch takes into account your choice and Montys choice. Instead of using your odds of 33% getting the prize in step 1, use your odds of 66% of picking a goat in step 1 plus if that happend, 100% odds of Monty picking the other goat for you.

By: tikigod4000

tikigod4000 — Mon, 05 Jan 2009 17:57:14 +0000

MY BRAIN!!! MY BRAIN!!

By: BenKinsey

BenKinsey — Wed, 01 Oct 2008 14:07:25 +0000

Very interesting I didn’t understand at first but due to the many excellent examples I get it. Thanks Alan.