Today I’m looking at how our gut feel for numbers – probability/chance in particular – is inaccurate.
This is important because trading is a game of chance. We should trade only when we have the highest expectation of success.
I’m going to look at the Monty Hall game. If you’re not already familiar with it, Monty Hall can be a surprising introduction to how we misjudge our chances of winning.
Gut Feel Misjudges Chances of Winning a Game
Another well-known example of how our gut feel gets confused about probability is the Monty Hall Game – named after the host of the 1960s television quiz show Let’s Make a Deal.
Each week, Monty Hall would offer the contestant three doors. Behind one door was a big prize and behind the other two doors was nothing. Obviously, the contestant had a 1 in 3 chance of choosing the winning door.
Let’s imagine that you are a contestant.
You pick a door – the blue one – hoping to win the prize.
Then Monty has a bit of fun with you. Monty knows which door the prize lies behind. After you tell Monty your choice, he opens one of the doors to show you that the prize isn’t there.
Monty then asks you if you want to change your mind.
So what do you do? Stick with your first choice or change?
I’ll give you a moment to make your choice – try to choose without reading ahead.
Made your mind up? Good.
The correct answer is that you should accept Monty’s offer and change your selection to the yellow door. Doing so increases your chances of winning the prize.
Now, I must admit when I first heard this puzzle, my initial instinct was to stick with my original choice – I didn’t think it would make any difference switching doors. Surely, after Monty had shown me one empty door, I would have a 50/50 chance of winning the prize whether or not I switched my choice of doors. But, no, that’s not the case. In fact, after Monty has shown you one empty door, there’s a two-thirds likelihood that the prize lies behind the door you did not originally pick. Let’s see why.
First, you are presented with a choice.
You have a one in three chance of choosing the right door.
Second, you choose a door.
There is a one in three chance the prize is behind this door. There is a two in three chance that it lies behind another door.
Now Monty opens a door.
In doing so, he changes your chances, if only you realized it. There must still be a two in three chance that the prize lies behind one of the doors you haven’t chosen. You have now been shown which of these doors doesn’t have the prize behind it. This means that choosing the final door – the yellow door on the right – has a two-thirds chance of winning the prize.
Gut Feel Misjudges Shared Birthday Probabilities
Our intuition fails most of us badly on shared birthdays.
How many people do you think would need to occupy a room for a 50/50 chance that two of them share the same birthday? The answer is 23.
For a 99%+ chance that two people share a birthday, only 57 people are needed.
These results are counterintuitive. Our gut feel is that more people should be needed.
If we rely on gut feel in activities involving probabilities we are likely to make big mistakes.
There’s a stock market saying that bulls can make money, bears can make money but the pigs get slaughtered. Make sure you leave gut feel to the pigs and write your trading plans using predefined, objective criteria.