Friday, 2nd October 2020 ◆ Is this journey with myself working? (8)

I’ve created a simple ‘game’ on Kangaroo which can be used to host quizzing events which do not need a quizmaster. In Quizzie, each participant gets the opportunity to write a round of questions.

Well done if you said Accra

The only alternatives I found online were for events in which there is a quizmaster who prepares all the questions in advance. If this is of any interest to you, it's live now, so grab some friends and give it a go!

How it works:

  1. Between 2 and 20 people can participate
  2. Each person gets the opportunity to host a round of 5 questions
  3. Each correct answer scores 1 point
  4. After their round, the host scores points based on how good their round was
  5. After all rounds a winner is declared

I want to elaborate on the fourth point here. How to score points is an interesting problem for two reasons:

  • I don’t want to encourage metagaming
  • I want hosting a round of questions to be optional (and not engender a big disadvantage)

If we treat this naïvely, during someone’s question round, that player will award 0-5 points to each other player and gain no points for themselves. This has a dire consequence:

  • The optimal play is to pose impossible questions, ensuring that all players get 0 points (and none will earn more than the round’s host)

Although it’s unlikely for a group of friends to game the system on purpose, it does mean the person who happens to write the hardest round will have an advantage. And if people are gaming the system, we end up with a degenerate game where everyone scores 0 and there is no winner.

Furthermore, I want writing questions to be optional, as not everyone will have the time or inclination to do so in such an event. However, if someone does not host a round of questions, they will give out 0 points, and therefore the optimal play is, again, to skip your round of questions.

My first inclination was for the host to earn points equal to the average number of points they give out. However, again, the game degenerates. You will want to ensure you get the maximum points, and so making the questions super easy ensures all players get 5 points and we end up with another tie.

So, I took inspiration from the Dixit school of thought. I decided that the optimum result is for each round’s host to give out 3 to 4 out of 5 points, on average. This is the sweet spot: not too hard, and not too easy. If this is achieved, that round’s host will score 5 points. If they hit either side of the target, the points are reduced.

I came up with the following table:

Average points given away Points earned
0 - 1 0
1 - 1.5 1
1.5 - 2 2
2 - 2.5 3
2.5 - 3 4
3 - 4 5
4 - 4.5 4
4.5 - 5 3

A graph is perhaps better suited:

I always complained about Dixit being too complicated, and I do and make something worse.

Note that all but the last range are top-end exclusive.

The orange line is along \(y = x\), anything above it means you've gained more than you've given out (on average). This shows you're better off veering towards too difficult than too easy, and the highest above the line you can reach is at 3/5 points given away.

That looks like the desired result to me!

This does mean you do get a slight advantage for writing a good round, but it’s not huge - and I think that’s fair. The quiz requires at least a couple of people write rounds, so we ought to encourage it. And, you did have to put in a little extra effort for those juicy points!


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