Games, Goats and Gold – with Colin Beveridge

Maths Scholars Celebratory Event - 22 September 2018

By Matthew Male, AMIMA

Colin Beveridge, the man behind Flying Colours Maths and author of no fewer than three official “Maths for Dummies” books, gave the Maths Scholars a wonderful talk on the maths of TV game shows. Looking very much the “host with the most” in his smart black suit, complete with waistcoat and, somewhat improbable, Sheriff badge, Colin whirled us through five decades of prime time telly and revealed the surprising mathematical ideas hidden in our popular culture.

First up was Deal or No Deal, in which Noel Edmonds would open boxes with offers of money for contestants – who have to choose between the sums yet to be revealed and those of a dubious “banker” (supposedly a voice on the end of Noel’s telephone). Colin focused on one scenario – a chance of £250,000 or possibly a single penny – versus a sum offered by the banker – and asked us at what level of guaranteed offer we would be prepared to take the risk? Perhaps indicating the low-paid nature of teaching work, colleagues on my table were only prepared to take a risk at sums much lower than the expected outcome of the boxes. As well as teaching the mathematical concept of expectation, this exercise really showed that willingness to take chances with money is hugely dependent on an individual’s economic circumstances and appetite for risk.

colinNext Colin talked us through Play Your Cards Right, which for those of us old enough to remember (and I was the only Scholar on my table in that category!) was where Bruce Forsyth would turn over a sequence of giant-sized playing cards, and ask contestants to guess if the next one would be higher or lower. (And yes, those of us watching at home with our families really did shout out “higher!” and “lower!” at our TV screens.)

It had never occurred to me that this presents a perfect opportunity for some detailed probability calculation – you can see some of it on the flip chart in the photo. We managed to calculate the probability of guessing each turn correctly, and from there derived the chances of completing an overall run of four cards successfully.

The talk ended with a discussion of Let’s Make a Deal, sometimes referred to as The Monty Hall or “car and goats” problem. Colin explained that this seemingly simple problem, based on a real game show, had caused a huge controversy around twenty years ago, with experienced mathematicians and statisticians getting irate and simply not believing the correct solution. If you are interested in the mechanics, have a look at the Wikipedia article. It really is a counter-intuitive result and provoked a great discussion between the Scholars; it was wonderful to see such a thought-provoking and respectful conversation spontaneously take place across the room.

Colin covered much more material, and many other TV shows, in his talk; but you’ll have to go and see him live to find out more. I found it all fascinating and came away with some great ideas for teaching probability to my students, in a fun, meaningful way – anything involving games and money being guaranteed to grab the interest of a teenager!