Be Smart: Change Your Choice
Your choice was reasonable and logical. Yet now it sucks.
Hmm. Quantum mechanics. Weird like magic and complicated. Is there anything weird like magic that is less complicated so we can all harness its power right now — without understanding quantum mechanics? Yes. Yes, there is.
The road to the weird thing started with …
An introduction to Quantum Computing, where we did some basic operations on real equipment, amazed me! The event demonstrated we are already harnessing quantum effects to solve logical problems.
Quantum effects produce statistically coherent results almost instantaneously in ways that seem impossible from a natural human experience perspective. The strange statistical behavior of very small things is now, in machines, answering questions of our choosing.
And this got me wondering if there are some exotic statistical facts right in our faces that we can use to solve real-life logical questions now, today, this minute, without using this rare and complex esoteric lab equipment and without having to do math.
And then I remembered the disgusting irrational truth which is the Monty Hall problem. This thing is offensive.
Monty Hall and Arguing with a PhD in Statistics
So about a dozen years ago a brilliant professional engineer and professor of statistics, George Michelov, who I had the privilege to work with on software projects asked me over lunch to answer the Monty Hall problem. I did not remember hearing about it before that day. A good description is on a Wikipedia page dedicated to the topic and I’ll copy it here …
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say №1, and the host, who knows what’s behind the doors, opens another door, say №3, which has a goat. He then says to you, “Do you want to pick door №2?” Is it to your advantage to switch your choice?
I answered wrong.
The right answer IS ALWAYS CHANGE YOUR INITIAL CHOICE. Let me explain how this works: CHANGE YOUR INITIAL CHOICE AFTER THE HOST SHOWS YOU WHICH OF THE REMAINING DOORS HAS A GOAT.
I could not believe that answer even when George explained it to me. Seemed like a number trick; a trick I was not seeing. So that night I wrote a simulation to prove that answer could not be right. The simulation told me I was wrong too. George and the program were right and my brain could not wrap around it.
If you are unfamiliar with this problem and are a smart thinking person then THIS ANSWER MAY MAKE NO SENSE. THERE IS NO WAY THE UNIVERSE WORKS LIKE THAT. However, it does.
Is this magic?
Yes. Okay, not really. It is math applied to the science of statistics. This math lights up a path that is normally hidden from us. Read the wiki page if you want to study and understand the most popular probabilistic explanation that your first choice had a ⅓ chance of being right and changing your choice gave you a ⅔ chance of being right. Crazy. Yes. So is quantum mechanics. Both are real whether you believe in them and work to understand them or not. Real.
And this choice change advantage applies for any number of choices from three to just shy of infinity.
So what, I’m not on a game show.
Yes you are. Except on this game show there are a nearly infinite number of doors and you are asked to choose doors probably EVERY DAY. Possibly MANY TIMES EVERY DAY. Life is complex.
So, what do we learn from the crazy choice insight exposed by the Monty Hall problem?
Don’t stay the course in dynamic situations. Open a different door when life, your host, shows you a bad door after you already chose a door and have not yet opened it. Give yourself that edge.
What is a Dynamic Situation?
Well, much of real life is about dynamic situations. According to Stephanie Borgert (see her terrific book “The Complexity Trap” published 2017), working with people, depending on people, is the definition of a complex dynamic situation. The Learning for Sustainability website has a pretty good explanation on the distinction between complex and complicated and I’ll copy part of their explanation for a complex system here:
complex systems are based on relationships, and their properties of self-organisation, interconnections and evolution. Research into complex systems demonstrates that they cannot be understood solely by simple or complicated approaches to evidence, policy, planning and management.
Dynamic situations are complex systems and no amount of sweat and intellect will produce a complete plan of action with as much chance of success as well thought-out action and discovery iterations. The study of complexity teaches us that step-by-step decision making, as facts are discovered, is the best way forward.
And how does the Monty Hall insight apply to complex business and life situations? I see it like this …
When we decide yesterday what we will do tomorrow and we refuse to reconsider that choice we are cheating ourselves of an advantage. The odds are against us having made the wisest choice yesterday before our host, life, showed us a few new things today.
There is a significant nuance here beyond just being “agile” in our approaches to problem-solving and solution engineering. That nuance is that for seemingly equal choices, it is important that we pick a new choice from the remaining set sometimes for no other reason than we know from the math that it will give us a better chance at winning that car.
So, change my mind all the time?
No, not every choice situation fits the Monty Hall problem. The Monty Hall insight applies to situations where you don’t have inside knowledge to THE right answer. The insight applies when there are several choices that for us, in our moment, appear of equal value. The magic edge applies to complex situations.
Taking advantage of the edge looks something like this …
- You are taking an educated guess at the best way forward (make a choice)
- Afterward, circumstances reveal specific other choices that were bad (goats)
- Now, apply the insight and CHANGE your original choice to pick from the set of equivalently rational choices still available. (looking for that car)
In the software domain, where I spend most of my time, these scenarios avail themselves often. We plan, because that’s the smart thing to do; and then by the time we are about to invest in building a new thing we have generally learned that some earlier possibilities no longer look as shiny as before. Should we re-evaluate the next step at that point? The math says yes.
The Practical Take Away: Maybe this is already happening
I believe these opportunities to pick a better door present themselves organically when people are working together, and collaborating on activities.
The re-evaluation of doors chosen probably happens naturally in productively meshing groups; in part just because different people bring different ideas and safe environments encourage them to speak up and share them. Authentic energized conversations lead to better choice opportunities.
Better outcomes depend on us changing our minds.
The smartest cookies are actively looking for and finding the opportunities to change their choices — and then changing their choices because they want that edge.
