Guess Who board game question/poll

The Game Room
1

My kids were playing the Guess Who board game last night. The goal is to guess who your opponent picked among about 24 choices – each choice has some distinguishing characteristics or attributes. So, there may be two males, both with brown hair and ties, but only one will have glasses. There will never be two characters with all of the same attributes.

You pick a character and your opponent picks a character, and, through a series of yes/no questions, you try to figure out who your opponent picked. For example, you may ask:

Is your person a man?
Does your person have facial hair?
Does your person wear glasses?

…and so on.

An argument broke out between my kids – can you ask a question that has more than one feature? In other words, can you ask, does your person have black or brown hair? A “yes” answer would mean that the person has either color, but doesn’t have blond or red hair, or no hair at all. Then, there are subtle ways to ask about two features – Is your person a man with facial hair? “Yes” would narrow it down pretty significantly, and even “No” would narrow it down a lot.

My question is:

Are dual attribute questions acceptable?
(1) Yes, any yes/no question is OK
(2) Yes, but only if they are subtle
(3) No, only single attribute questions are allowed

The results will settle a dispute at home.

2

I don’t think actual two part questions ever came up back when my sister and I played. But we definitely had the more specific questions. The thing is, they aren’t that advantageous. Sure, if you get a yes, you can eliminate two sets of traits, but if you get a no, you can only eliminate the intersection of that set. Assuming the same number of people with each trait, you would eliminate twice as many with a yes, but half as many with a no.

So I really don’t see any reason to eliminate them. They are high risk high reward plays.

3

I don’t see any problem with combo questions. It’s all geared around the same decision process - do you go for the safe approach and ask questions that will eliminate half the group, or do you go for the riskier approach that will eliminate either 25% or 75% (if you’re lucky) of the options.

4

I think it could add something interesting to an otherwise boring game. (Boring to me, kids understandably love it).

5

You’d think that, but from what I understand, most attributes are in a minority of characters. At least according to wikipedia, most of the time, 5 characters will have an attribute and 19 will not. So, on average, when you ask a question, you eliminate 5 at a time. By asking combo questions, you can whittle the field in half with each question.

Or, something like that. I didn’t write the wiki page.

I thought it was cool that one of my kids came up with the idea of asking inclusive-or questions – she’s destined to be a programmer, I guess. I haven’t played the game much, but I never thought of doing that.

6

I remember playing Guess Who, and I’d have to say no, combo questions are not okay. Not even “facial hair”; you have to ask “beard” or “mustache” (nobody has both).

The thing is, I think BigT has it backwards. As far as I can tell, the game is designed so that until you get down to just a few people, each “trait” appears on roughly 25% or less of the people. You’re supposed to be taking a risk. If you can ask about more than one trait, you can avoid the risk, and just eliminate half of the group each time.

For instance, it looks like there are 18 (or maybe 19?) males. Of those:

  • 5 have mustaches
  • 4 have brown skin
  • 3 are wearing hats
  • 3 are wearing glasses
  • 2 have blue eyes
    …and so on.

If I can only ask about single traits, I can ask about blue eyes, and potentially narrow it down to 2 (but risk only eliminating 2), or I can ask about mustaches, and guarantee that I will eliminate at least 5.

But if I can ask multiple traits, I could say “Does he have a hat OR glasses OR is he bald on top?” and eliminate exactly half with either answer.

That basically seems like cheating to me. I may be wrong; it may be that over time, the greater risks and rewards of single-attribute guesses average out to 50%, but I couldn’t begin to know how to calculate that.

But either way, it just seems like it’s defeating the spirit of the game. It would be like playing a variation on a board game where you can either roll the dice, or just move five spaces every turn. There’s hardly any point to playing.

ETA: Or, what RitterSport said. I agree, though - the girl’s a smart cookie. Keep an eye on her.

7

Ah. I wasn’t considering an OR set. I was considering only ANDs, because that’s the only thing we ever did. ANDs will always be riskier, as someone who has two traits is always a smaller set. ORs, on the other hand, will not. They will always be less risky, as they give you a larger set. It doesn’t matter where you are in the game (EDIT: unless you are silly enough to ask an OR question that covers everyone)

I was only considering questions created like the OP’s first example. Come to think of it, though, the OP’s example isn’t really an AND, either. All the people with facial hair are male. So, as HoD says, it’s really an OR question. And I agree that those make the game easier, and probably should be discouraged.

8

I guess I’m not seeing this. If I asked this question and the person answered yes, it would narrow the possibilities down to men with facial hair - I could start guessing Tom Selleck and Jason Lee and Evil Spock. But if the answer is no, then the possibilities that remain are all women and all clean-shaven men - I’ve only eliminated maybe five percent of the possibilities.

9

This is what Wikipedia says:

“One may have to consider less obvious questions in order to divide the population more evenly. One way to do this is to combine two characteristics into one question. For example, by asking “Is your person a man without facial hair?”, because none of the women have facial hair, one is effectively grouping together all 5 women and all 8 men with facial hair into one group. With this question, one divides the group into 13 and 11.”

It looks like I asked it wrong in the OP, though – it should have been a man without facial hair. I knew it seemed wrong when I was writing it originally.

10

No, the same logic applies. The value of a yes answer is inverse to the value of a no answer.

An evenly weighed question is one in which half the possibilities will produce a yes and half will produce a no. So each question reduces the pool of possibilities by fifty percent.

An unevenly weighed question is one in which, for example, ten percent of the possibilities produce a yes and ninety percent of the possibilities produce a no. So a yes answer will reduce the pool of possibilities by ninety percent while a no answer will reduce the pool of possibilities by only ten percent. A yes answer is more valuable than a no answer.

But a yes answer is also generally rarer than a no answer in an unevenly weighed question. Assuming the pool of possibilities is random, you’ll have a ten percent chance of getting a yes answer and a ninety percent chance of getting a no answer.

So a strategy of combining characteristics into a single question is counter-productive. The broadness of the likely answer reduces the value of the likely answer.

11

Think about it this way, though – if you can always cut the pool in half with properly phrased dual-attribute questions, then you’re guaranteed to get down to 3 choices in 3 questions (given 24 to start with). However, if you go with one attribute questions, it may take more than three questions, if you’re unlucky each time and ask the smaller-population question.

12

I think we’re arguing the same point. My argument isn’t against multi-attribute questions in general. It’s against uneven questions, which multi-attribute questions tend to be. An evenly balanced multi-attribute question is fine.

13

I’d say go for it. The sooner your kids figure out the optimality of a binary search the better.

14

I don’t even see the first question in the OP as being a multi-attribute question. It’s just “does your person have dark hair?”, which is asking about a single attribute, hair color.

As for the question in general, the optimal strategy is to try to divide the set as close to 50-50 as possible. If doing so requires compounded questions, then it’d be absurd not to ask compounded questions.

15

I agree that it’s a better strategy, but my question really is, is it allowed? It doesn’t seem to be disallowed in the rules, so maybe the poll is more, “when you play, do you allow it/think it should be allowed?”

16

I said it before, but I’ll say it again: I don’t think it should be allowed, and this is why:

There’s a wide enough variety and distribution of various traits that I’m pretty sure if you’re allowed multi-attribute questions, you can always cut the pool exactly in half, one way or another. And if both players adopt this strategy, you wind up with a really lame game, where each turn is guaranteed to be optimally successful, right up to the end:

Player 1: eliminates 12 faces
Player 2: eliminates 12 faces
Player 1: eliminates 6 faces
Player 2: eliminates 6 faces
Player 1: eliminates 3 faces
Player 2: eliminates 3 faces

And each turn is going to be really long and boring while each player counts out attributes that will eliminate half. It’s only at the very end that there’s any risk or variability in the game at all, because each player only has a 1/3 chance of choosing correctly, and if they don’t, then a 1/2 chance after that. You might as well skip the other turns and give each player 3 faces to start.