How reliable is your decision-making?
Part 2 of ‘Mind Stretching’: a series aiming to debunk game theory concepts, whilst encouraging you to expand your creative horizons.
How often do you change your mind? And why? Or why not? Are you satisfied with your decision-making? Let us find out through the following exercise.
You’re at a game show. All the lights are on you. You’re happy you reached this far; the crowd is calling your name & you feel more confident than ever. In front of you, there are 3 doors. Next to them, holding a clipboard, there is a charismatic presenter. She tells you one of the doors is hiding the car of your dreams. The other 2 are each hiding a kitten.
You are allowed to choose a door and keep whatever you find behind it.
Let’s say you’ve chosen door number two.
The presenter congratulates you with a cheeky smile. You’ve made an excellent choice, she says, for the producers of this game show. She glances at her clipboard, and tells you that out of her generosity, she’ll allow you to change your mind. But before that, to make your life more difficult, she will open door number three for everyone to see a cat purring behind it.
What do you do? Why did she do that? The pressure is mounting. The crowd is silent, and everyone is staring at you.
Think about it. Are you keeping your initial door - number two? Are you swapping it for door number one?
What’s your choice? Take a moment to decide what to do before you read further.
….
A first thought could be “hmmm she’s playing a mentalist’s malarky on me. She knows I picked the right door and she’s trying to persuade me to change my mind. She’s working for the producers, not me. Why would she help me? Now that I know behind door number three there was a cat, my chances of getting a car are even higher, right?
Our first instinct would be to keep door number two. But it’s impulse, not logic. The mathematical choice would be to accept her offer and swap door number two for door number one. Let me explain.
When you’ve chosen door number two, your chances were 1/3 – that is 33%. After the third door opens, if you keep your door (number two), your chances are still 33% but if you swap, your chances increase to 66% (2/3).
You’re going to ask: What’s the logic in that, shouldn’t my chances be 1 in 2 (50%)?
And that’s an excellent question, well done!
Your chances would’ve been 50% if you would’ve started with 2 doors. But you started with 3. And if you ignore the fact that the presenter opened door number three, you’re actually being asked if you want to swap door number two for door number one AND three, thus doubling your initial chances – to 66%.
Getting the other door opened by the presenter is a distraction – the presenter will always know which door does not contain the car and will always open it. Ignore this aspect.
This situation becomes more obvious if you have to choose between one hundred doors.
If you choose door number two again, and the presenter asks you if you want to swap door number two for ALL other ninety-nine doors; is this an easier choice? Mathematically, you are trading a 1% chance for 99%.
Of course, if you like your cats, keep your initial door. But if you want to increase your chances of getting your dream car – always accept the trade.
This exercise is called “The Monty Hall problem” and when it was first published it was disputed by many mathematicians. So, if it makes sense to you, well done! You’re officially smarter than some mathematicians. If it’s still a bit unclear, don’t worry about it, think about it one morning, when you’re rested, and you’ll get it.
Now, coming back to the initial question, how often do you change your mind?
How often are you taking an emotional decision, and how often are your decisions grounded in logic? How do you distinguish between helpful information and “noise”? If you gain access to more information, will you re-evaluate your initial decision?
