A conversation about mathematics inspired by a pile of matchsticks. Presented by Katie Steckles and Peter Rowlett.

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A conversation about mathematics inspired by a pile of matchsticks. Presented by Katie Steckles and Peter Rowlett.

Podcast: Play in new window | Download

Subscribe: Android | Google Podcasts | RSS

MATHS FANS! A rare treat for you. Tomorrow night, BBC4 will show The Joy of Winning – an hour long proper proper maths doc packed to the brim with glorious game theory. I think it might just be my favourite thing I've ever done for telly. pic.twitter.com/Xx09Wowwzz

— Hannah Fry (@FryRsquared) August 27, 2018

Hannah Fry presents a new one-off BBC4 documentary about game theory (reading the description, it sounds more classic than combinatorial), which the BBC4 website describes as a “gleefully nerdy adventure”. Should be fun!

This is tomorrow, 28th August 2018 at 9pm on BBC4 and on iPlayer after.

Update: iPlayer link to The Joy Of Winning.

The Upshot is a column in the New York Times based around analytics, data and graphics. (It was conceived around the time when Nate Silver left to work for ESPN). Earlier this week, managing editor David Leonhardt and data journalist Kevin Quealy posted an interesting puzzle, entitled ‘Are You Smarter Than 49,485 other New York Times Readers?’

The puzzle consists of a simple question – you need to pick a number between 0 and 100, and all 49,485 of the responses will be collated (assuming that every single one of the Times’ readership actually enters a number) and averaged. If your guess turns out to be the closest whole number to two-thirds of the average guess, you are clever and you win.

I was invited to contribute to a special issue of *The Mathematics Enthusiast* on ‘Risk – Mathematical or Otherwise‘, guest edited by Egan J Chernoff. I wrote about the Maths Arcade and programming strategies for a game we play there called Quarto. Really, I was sketching an outline of an idea to encourage student project work.

My title is ‘Developing Strategic and Mathematical Thinking via Game Play: Programming to Investigate a Risky Strategy for Quarto‘ and the abstract is below.

For the benefit of overseas readers, or British readers in full-time employment, I should briefly explain the concept of daytime TV quiz phenomenon Pointless. The pinnacle of British public service broadcasting, it’s shown at 5.15pm every weekday on BBC One and is hosted by Alexander Armstrong of comedy double-act Armstrong & Miller, and Richard Osman of comedy double-act Armstrong & Osman. We shall investigate how we can use maths to analyse the show, improve our chances of winning it, and ultimately perhaps improve the show itself.

The aim of the game is in each round to give the most obscure correct answer to a given question. Each question ($Q$) has a large set of valid answers $A_Q$, questions perhaps asking contestants to name “Films starring Bruce Willis” or “Countries without an O in their name”. All the questions have been asked to 100 members of the public prior to the quiz (call this set $P$), and they each have 100 seconds to name as many examples as they can (giving rise to a set $A_p\subseteq A_Q$ for each $p\in P$. The contestant gets a point for every one of the 100 people who named their answer $a$:

\[ \mbox{score}(a) = \begin{cases}

| \{p\in P : a\in A_p \} | & \mbox{if}\ a\in A_Q \\

100 & \mbox{if}\ a\not\in A_Q.

\end{cases} \]

So an obvious answer like Die Hard or France will score a lot of points, and an obscure answer like Striking Distance or Central African Republic will score fewer points. Points are bad (hence the title) so it’s better to dredge up an obscure answer than stick with something safe. However an incorrect answer like Avatar or Mexico scores the maximum 100 points. At the end of the round the contestant with the most points is eliminated.

A piece on the New York Times Economix blog casts a story from Inside Higher Ed as a piece of applied game theory. Professor Peter Fröhlich of Johns Hopkins University has a grading system in which

each class’s highest grade on the final counts as an A, with all other scores adjusted accordingly. So if a midterm is worth 40 points, and the highest actual score is 36 points, “that person gets 100 percent and everybody else gets a percentage relative to it,” said Fröhlich.

Can you spot the problem? The Economix posts points out that this allows “at least two Bayesian Nash equilibria”:

Equilibrium #1 is that no one takes the test, and equilibrium #2 is that everyone takes the test. Both equilibria depend on what all the students believe their peers will do.

In equilibrium #1, everyone scores the same mark – zero – and the calibrated marking scheme maps this onto 100%. The students, realising this, arranged a complete boycott and were all awarded grade A.

Alas, this was not a game theory class! Prof Fröhlich has since changed his grading scheme.

**Further information**:

Dangerous Curves (Inside Higher Ed) has some detail of how the boycott was arranged (had just one taken the test, all would have been forced to follow suit).

Gaming the System (Economix) discusses the related game theory and economics concepts.

Author Robin Sloan offered a simple competition:

give me a prime number of your choosing. I’ll send books to the five people who choose the lowest unique prime numbers. So, if you pick 2 but seven other people pick 2, no book for you. If you pick 3 and no one else picks 3, you get a book.

Which number would you pick?

The primes people chose, including the five winners, and more background information are given in a blog post The Penumbra primes.