Today’s puzzle is about dating strategy.
You’re single and looking for love. In front of you are three doors. Behind each door is a prospective partner. Your mission is to couple up with your best possible match.
Imagine you chose a door at random. If you couple up with the person behind it, the chance you get your best match is 1 in 3. (You can assume that of the three people who are waiting behind the doors, there is a best match, a not so good match, and a least good match for you.)
Thankfully, I’m going to let you open some doors. But there are rules:
To start, you select a door. Any door. It will open to reveal one of your potential suitors. If you want to choose this person as your match, you can. Job done. You couple up with them. But if you decide to go with the first person, you don’t get to see either of the others. Risky! The person might be just your type, but maybe the others are even more so…
(You can assume that you are able to correctly judge the person’s suitability for you as soon as you see them.)
If you decide to move on, you discard the first person. They’re history. You select one of the two remaining doors. It opens to reveal someone else. Again, you can choose this person as your match. But just like before, if you choose this person, you don’t get to see who is behind the final door. Nor are you allowed to return to the person you discarded behind the first door.
If you decide to move on a second time, you select the final door. You must choose the person behind it as your match, whatever you think of them. Also risky!
To summarise: you only have one chance to decide on each person. If you decide to reject someone, you can’t return to them after. If you choose the first, you don’t get to see any of the others. If you want to see them all, you must choose the last.
What strategy gives you the best chance of finding your best match? Can you improve your odds from 1 in 3?
(Further clarification: You must assume that you know nothing about the average attractiveness of the group that the suitors are selected from. If you see the most attractive person you have ever seen behind the first door, there is still a 50 per cent chance that the person behind the second door is even more attractive. The question is not psychological or sociological: you can’t settle with the first one you think is acceptable. The puzzle is mathematical: it asks you to maximise your chance of getting the best possible match of those three on offer.)
I like this puzzle because even though it is a massive simplification of modern dating, the underlying idea is relevant to many situations in real life. If you get to see many things (not just suitors) in sequence, and choosing one means you don’t get to see what comes after, nor are you allowed to return anything earlier in the sequence, when is it in your best interests to commit?
I’ll be back at 5pm UK with the solution, and a discussion of the well-studied mathematical problem on which the puzzle is based.
Meanwhile NO SPOILERS.
I also co-write Football School, the children’s book series that explains the world through football. The third volume (left) is just out. In it there are chapters on the maths of the coin-toss, the chemistry of pitch markings, the biophysics of dribbling, the biology of footballers’ feet, the history of the first football club, the design and technology of trophies, the politics of Spain, and much much more.