Balderdash

Dec. 10th, 2007 02:31 pm
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[personal profile] jack
I assume it goes without saying that I'm not very good at Balderdash :) However, I was wondering about the rules.

The basic idea (varied slightly in different incarnations) is that one player picks a random word (or film title, or acronym[1]), either by drawing the next card in the pile from the published game, or by flopping a dictionary open in the freestyle version.

She announces it, and then each other player invents a definition, handed to her on a bit of paper. Then she reads them all out, and each player guesses which is correct. You get one point for guessing the correct definition, and one point for each person who guesses yours.

This has the implicit assumption that no-one will know the definition already. Typically, if you know the right definition beforehand, you get N points (where N is 1 or larger), but don't participate in the rest of the round. (One set of rules says the rest of the round is cancelled if several players do.)[2]

The question is, what's the fairest way of doing it? Should players be rewarded for knowing? It's actually barely related to the real point of the game. Giving them a bonus and moving on seems most sensible.

Another option would be that you don't get anything extra; you make up a definition anyway, and just get one extra point for voting for the right one.

Another would be that your definition is entered, and everyone who votes for an equivalent answer to the real one gets a point, but you get a point for anyone who votes for yours instead of the real one.

The things to avoid are: it being an advantage to *not* know the answer, which really seems unfair, and putting too much judgement on the caller. After all, if she doesn't know wha

[1] You know what I mean.

[2] Did someone in fact get it right?

Words are ok, you generally know or not.

Complete the silly law is ok for the opposite reason. They're all made up, so (unless by an immense stroke of luck, you actually really know the answer), you don't get any points for saying something else it's illegal to do on Tuesdays in Cardiff -- after all, there's lots of things -- you have to guess what's on the card.

But we had difficulty with people. Do you have to guess whatever's on the card, however weird? The correct answer for "John Dee" was "invented the crystal ball" and for "Christian Huygens" was "invented the pendulum clock"[3]. Do you get points for saying "British court magician/philosopher" and "Dutch physicist and astronomer"[4]?

Those are possibly less specific, but a whole lot more accurate. They (when we went over to the internet) basically the first sentences of the wikipedia entries.

But if so, how is the caller supposed to know if they're accurate or not? I guessed that John Dee supposedly invented the crystal ball, but I wouldn't done if I didn't know who he was.

[3] Leaving aside the inaccuracy of that.

[4] I wasn't *sure* of either. I knew the scientists I was thinking of existed and had similar names, but I could equally well have been confused with "Jack Dee" and "Hayden Christensen"

Date: 2007-12-11 12:50 am (UTC)
From: [identity profile] cartesiandaemon.livejournal.com
OK, sober reanalysis. I'm probably slightly off the mark, I think I need some things cleared up.

* Skipping the round if anyone knows the word is probably very sensible. You *could* do it without, but you'd have to decide a fair reward, and does create procedural difficulties. If only one person did, giving them a slight bonus would probably be reasonable. Although personally I like knowing whether its a game of bluff or not, more than which it is, so prefer your method.

* And conveniently, that makes the maths easier.

* If you don't care about rewarding the dealer for no-one guessing right, but want the score to be fair if you stop half way through, you could just give the dealer an average of the scores got by the other players that round.

* Alternatively, you could give the dealer a constant score, based on the expected average total score per round. This is easy to calculate: each round scores one point per guess, plus one point for every correct guess. If you assume everyone guess right 1/Nth of the time, that's a total score per round of N (for N people) + N*1/N (N people each having a 1/N chance of guessing right.) = N+1. Divide by N to get the average per player, =1+1/N. You could call that 1, have fractional scores, roll a die and give the player a 1 in N chance of one extra point, or something like that, if you cared.

* If you don't care about the score being exactly fair if you stop half way through, you could just give the dealer one point. That's nearly right, but the dealer falls slightly behind whenever anyone guesses the right answer (one person per round, on average).

* If you want both, you must give the dealer no points when someone guesses right, and more points when no-one does, having an average equal to the average score in a round. Ie. if everyone is wrong every 5 rounds, give the dealer 5 times (the average we worked out in bullet point 2).

Except what is 5 really? If you assume the guesses are random, the chance of person failing to guess correctly is N-1 out of N. The chance of N people *each* failing, is that to the power N. [(N-1)/N]^N

This is the number that I said was approximately 1/3, ie every three rounds. Mysteriously, because we're doing maths, if N is large you get an exact answer -- once every e (=2.718...) rounds.