Monty Hall Problem Pt 2/3: Practical Application

The point: When it comes to matters-of-fact, logic/evidence-based positions are superior to intuition-based positions and this can be exploited for profit.

The rant that goes with it:

In Part 1 of this 3-part series, we saw how learning to intuitively appreciate the “Monty Hall Problem” demonstrates that intuition alone is not a reliable means of determining the way things actually work. In this part, I anecdotally will show how this knowledge can be used to really screw people over. Remember: with such great power comes great responsibility, not to mention the chance of getting your teeth smashed-in, so wield this weapon with respect and care!

The beauty of the “Monty Hall Problem” is that although it is just as easy to come to the wrong conclusion as it is difficult to accept the correct conclusion, the right answer can be proven, in court if necessary, making it a perfect tool for a con artist. The idea is simple: If the wrong answer is so intuitive that someone will remain committed to that wrong answer, even AFTER you’ve TOLD them the correct answer, the opportunity to convince them to place a high-stakes wager against the answer that you can ultimately PROVE to be correct is very difficult to resist to any self-respecting swindler. It is the timeless story of using someone’s greed against them. Case and point:

In 2009 while I was working under an expat contract in Qatar, I aspired to attend The 7th Amazing Meeting (TAM7) conference on critical-thinking in Las Vegas with my son Adrian. Unfortunately, I was unable to go because the project was at a critical stage and the Area Manager refused to grant any leave during that period. This was doubly-unfortunate because I had chosen to split my one annual business-class ticket entitlement into two economies, one of which I had already used to go to Canada (for far less than the value of ½ a business-class) and the right to use balance towards the value of second ticket was about to expire. In short, I wanted to go ½-way around the world to Las Vegas and if only the ADM would sign-off, I would get there and back for free.

Like a kid repeatedly asking his dad for a cookie before dinner, I asked him three times to authorize the trip and like the prick that my dad could be, he continually refused to provide a cookie…er…his signature. Finally, he asked me, “What’s this conference all about anyway?” I told him, “it’s about skepticism and critical thinking”, to which he replied, “what’s critical thinking?”

I explained to him that critical thinking is all about the application of high standards of introspective analysis when forming or considering ideas and that this includes the very challenging tasks of filtering out personal bias, recognizing fallacious logic, questioning dubious premises, learning to accept evidence-based conclusions even if they are inconvenient to you, etc. Considering his perplexed look, I decided to give him an example. I described the “Monty Hall Problem” to him and told him that the techniques of critical thinking help to cut through the intellectual noise that prevent one from not only coming to, but appreciating the correct solution.

When I gave him the question of whether to switch, stay or tell me it doesn’t matter, he came to the intuitive-based conclusion “it doesn’t matter whether I stay or switch” and then scoffed at the correct answer of “best to switch” when I gave it to him. Both of these are common responses, however, even as I explained the logic behind the reason for switching doors, he continued to stand by his original conclusion, becoming very distressed in the process. He apparently had trouble dealing with someone so deluded by such pseudo-math and misguided thinking.

Seeing an opportunity, I proposed, “If you are so sure that I’m wrong about this, then ‘Let’s Make a Deal’, shall we? If I can get you to admit that your answer is wrong and mine is right in less than 10 minutes, you sign-off on our trip to Las Vegas. If I can’t do this in 10 minutes then I will stop asking for your signature and you’ll never hear of this again.”

“You’re on!” he exclaimed, certain that he couldn’t possibly lose.

In the first 2 minutes, I explained the 10-ticket Scratch-&-Win analogy to him, but he wasn’t impressed (I said that it was a good teaching device; I never said it worked EVERY time).

Having failed at the theoretical, I went for the practical in the form of repeated trials: I dug through my desk (typically a pig-sty, iso that cost me another 2 minutes) and found a deck of cards. I took out 9 red-suit cards and one black-suit card to represent losing and winning tickets respectively, shuffled them and put the 10 cards face-down in a row front of him such that I knew where the black suit was. I had him select a card and then I turned up 8 red cards, leaving his card and the 10th face down on the table. I then asked him, “stay or switch?” True to his belief, he said, “It doesn’t matter”. When he turned over his card, it was a loser. Of course, we know there was a 90% chance that it lose, no surprise there.

10 unscratched tickets
10 unscratched tickets, 1 selected
10 tickets, 8 scratched, 1 selected and 1 unselected, each unscratched
10 scratched tickets
We repeated the exercise 10 times over the next three minutes (for those of you who have lost track of time, we are now 7 minutes towards the 10-minute deadline). I recall that through all these trials, he held the winning card only twice, which although one better than chance according to theory, was enough for him to eventually look up in shock as though he had just realized that he left a baby at the grocery store, then face-palm and utter through his sweaty fingers, “oh, f**k me!”

Yes, he got it eventually, and fully 2 minutes before my time was up. He signed and I sent him a postcard from Las Vegas.  TAM was awesome, by the way.

I have since been tempted to run this sure bet for cash, but I just can’t bring myself to do it because I have a terrible poker-face and I just can’t bring myself to take advantage of people in such a way (…very often). Perhaps you are not so principled as I am. Good luck with that.

In the final Part 3 of this series, I propose an alternate version of the problem that both eliminated the 50/50 conundrum with the added benifit of being more counter-intuitive than the original.

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