The other day, I played "Guess Who?", the classic game for children from about 6 to 9 years, with my six-year-old son. While we were playing, we both tried to work out the best way to win the game. This article series is the result of our search for an effective game plan. Part 1 is aimed at the whole family; the second part is intended for grown-ups (and near-grown-ups!) with an interest in data science. OK - let's find out how to win!
"Guess who?" The rules
"Guess who" is a game for two people. Each player takes one of 24 face cards and places it out of sight of the other player. The aim of the game is to find out what face is on your opponent's card. Each player takes a turn to ask a yes-no question about the character's appearance, e.g. "Does the person have glasses?".
As a memory aid, each player has a board with cards showing all 24 characters (see picture). After each question, you turn over the cards that have been eliminated by the answer to your question, e.g. all those with a face wearing glasses. The first to guess which card the other person is hiding is the winner.
Simple guidelines for winning: the lucky number
If you want to win the game, you must be sure to ask the right question when it is your turn. What questions can you ask? Well, you might try one of the following:
- Is the person a man/a woman?
- Does the person have white/blond/brown/black hair?
- Is the person bald?
- Do they have a small/big nose?
- Does the person have a beard?
- Is the person wearing something on their head?
No doubt you can think of plenty more. You could ask about eye color, for example, or whether the person has a full beard, a chin beard, or a moustache.
If you want to know whether to ask a particular question, you should first count the number of cards that would be left for each of the two possible answers. Let's say there are five cards (all in the picture below right) of people with blond hair right at the start of the game. That means that the other 19 don't have blond hair, of course. The smaller of these two numbers, the five in this example, is the one we need. I call it the "lucky number". It's a lucky number because – if we are lucky – it narrows the number of potential solutions right down. The other, bigger number leaves the identity of the mystery card much more open.
To win, you simply have to pick the question with the best lucky number every time. It's important that you only count the cards that are still showing. Unfortunately, it still involves a lot of counting. In a best-case scenario, however, the lucky number could be as large as half of the cards still in play. So if you can think of a question that has the potential of taking half of the cards out of contention, it will always be your best option. It won't always be possible, of course.
Justus' trick, or how to shift the odds slightly in your favor
To improve your chances just a little without having to try too hard, here's another trick: don't count your own card (the one your opponent has to guess). Because you already know that your opponent hasn't selected it. Particularly toward the end of the game, this gives you a slight edge that you wouldn't otherwise have. My son Justus drew my attention to this trick when we played the game recently. It didn’t take long before he was able to gain an advantage from using it.
The trick works even better if you play the game several times and don't shuffle the cards before each new game. You don't have to count all the cards that came up during the last few rounds, because you know they won't turn up again in the current game.
Would you like to know how a data scientist would approach this game? Then I recommend you read part 2 of this article.