By CAITLIN SMART.
Caitlin studies statistics and computer science at a tertiary level, and promises us that maths and logic can be fun. Let's kick off her new column with a look at game shows.
Before Deal or No Deal, before Who Wants to be a Millionaire, there was Let’s Make a Deal, an American game show that now looks wackier than Wipeout.
The original format of the show is that there are several doors behind which are goats – and a car. It’s your job to pick the correct door and win a car instead of a room full of poop.
Suppose you're on the show, and you're given the choice of three doors. You pick a door, say number one. The host, who knows what's behind the doors, opens another door, say number three, behind which is a goat. The host then says to you: “Do you want to pick door number two?” Is it to your advantage to switch your choice?
Well, what do you think? Should you stay or should you switch doors? Most people, myself included, think that it’s a 50/50 chance. You have two doors. One has a goat behind it, one has a car behind it. So what will it be: Stay, or switch?
Interestingly, people tend to stay with their original choice; a psychological effect that basically says people trust their gut instincts a little too much. As it happens they are making the wrong choice.
If you ever happen to be on Lets Make a Deal, if you switch, there is a ⅔ chance that you will win the car. If you stay, it’s only a ⅓ chance.
Amazing, huh? It’s really hard to explain how this works, so difficult, in fact that it’s caused a lot of controversy among statisticians, mathematicians and economists for decades. Let’s see if we can explain this another way.
Suppose you’re on a game show, and you’re given the choice of 1,000 doors. Behind one door is a car, behind the others, goats. You pick a door, say number one.
The host, who knows what’s behind the doors, opens doors number three to 1,000, all of which have goats behind them. The host then says to you: “Do you want to pick door number two?”
Now would you rather pick the door that you chose out of 1,000 random doors with no knowledge, or should you pick the host’s door, door number two? Remember, he has just filtered out 998 goats to make sure that you have the best possible options.
The Monty Hall problem, as it is now known, relies on you updating your choices as you get more information. As the host throws out one of your options, the other door becomes less and less likely to have a goat behind it.
Of course, modern game shows are even more complex than this. But hopefully this at least shows you that numbers can be incredibly messy and our brains and ‘gut instinct’ aren’t always right.