Over the last four blog posts we’ve been slowly creating an optimal set of strategies for playing the version of Shut The Box that we introduced in the first blog.

This is the fourth in a series of posts that investigates the creation of an optimal strategy for the game Shut the Box, and I’d recommend you read the first three blogs before continuing, starting with Part 1.

This is the third in a series of posts that investigates the creation of an optimal strategy for the game Shut the Box, and I’d recommend you read the first two blogs before continuing, starting with Part 1.

This is the second in a series of posts that investigates the creation of an optimal strategy for the game Shut the Box, the first of which I’d recommend you read before continuing.

I’ve long been fascinated about how computers can be used to determine optimal - or even just good - strategies for playing games with well-defined rules, and in this blog I’ll be working through the creation of such a strategy for a game sometimes known as Shut The Box.

Today we’ll be analysing the latest player-by-player data from the fabulous OneQuestionShootout website, and investigating a single issue: how well can we predict a contestant’s chances of getting back to the desk based solely on the Cash Builder amount that he or she recorded?

There are two fundamentally different ways of simulating the remainder of a sporting competition, which are loosely referred to as ‘cold’ and ‘hot’ simulations. The difference between them comes down to the assumptions made about the dynamics of the abilities of the teams involved. In cold simulations, teams’ assumed abilities are unrelated to the simulated results of earlier games, while in hot simulations they are related to earlier results.

(I’ve found surprisingly scant writing about this topic in academic journals or elsewhere. Please let me know if you come across anything.)

In an earlier blog, we built models to predict the Low and High Offers made to contestants in The Chase UK and found that we were able to explain roughly half the variability in the Offers made - a little more in the case of models built for the Low Offers by Seat, and generally a little less in the case of models build for the High Offers by Seat.

Since that blog was posted, I’ve had some excellent suggestions for things to try that might improve the models’ fit, and I’ve also had some thoughts of my own.

After you’ve watched The Chase for a while, you become familiar with the patterns of the contest and feel as though you can make reasonable guesses about the Low and High Offers that will be made to a contestant at the start of his or her head-to-head, based on how well they did in their Cash Builder, which seat they came from, and the overall state of the contest.

Darragh Ennis became the sixth UK Chaser when he appeared in an episode that aired on the 19th of November 2020 where he won chasing a target of 16 against a team of two finalists, offering five pushbacks and answering the last question with 7 seconds still on the clock.

That started a remarkable run of 14 consecutive wins, which was the best start of any UK Chaser to date.

In late 2021, I wrote a piece describing a series of models designed to estimate the progressive chances of a team’s success on an episode of The Chase Australia as that episodes unfolds.

For today’s blog we’re returning to analyse this Google document from James Spencer, which covers the entire history of Andrew O’Keefe’s reign as host from late 2015 to mid-2021, with the intention of understanding what, if anything the name gender composition of a team tells us about their likely performance.

For today’s blog, we’re going to move away from analysing contestant data and instead analyse Chaser data using:

• For Australia: this Google document from James Spencer, which covers the entire history of Andrew O’Keefe’s reign as host from late 2015 to mid-2021.

• For the UK: data from this website, which covers the entire history of up until 26 November 2021.

In the last blog we build models for The Chase game show to estimate a team’s chances of winning at various points during an episode. We did that using data from this Google document from James Spencer, which covers the entire history of Andrew O’Keefe’s reign as host from late 2015 to mid-2021.

Those models suggested that there was something special about Seat 1 in that the fate of the contestant in that Seat seemed to have particular significance for the team’s eventual fortune. Put succinctly, teams that included the contestant from Seat 1 in the final won money more often than otherwise equivalent teams without the contestant from Seat 1.

After analysing the performance data for Seat 1 contestants and finding little evidence that they were, on average, notably stronger contestants in terms of Cash Builder, Contribution, and FInal Target statistics, I hypothesised that, perhaps

• The presence of Seat 1 in the Final Chase is enough to slightly put off the Chaser (or is a signal that he or she is not quite on his or her game in that episode)

• Contestants in Seat 1 are, on average, better at taking advantage of pushback opportunities

Today we’ll use the Pushback data to explore these hypotheses.

In the last few blogs we’ve built models and created tables to explore various aspects of The Chase game show using data from this Google document from James Spencer, which covers the entire history of Andrew O’Keefe’s reign as host from late 2015 to mid-2021.

Today I want to look at a new aspect: how best to estimate the chances of a team ultimately winning whilst an episode is in progress. In particular, I want to estimate it at five specific points in the contest:

In the last blog we looked at how precisely we could forecast the High and Low Chaser offers using data from this Google document from James Spencer, which covers the entire history of Andrew O’Keefe’s reign as host from late 2015 to mid-2021.

There are other interesting questions that we can investigate using this data, and today we’ll analyse how a contestant’s estimated probability of getting home depends on how well he or she did in the Cash Builder, which offer he or she chose, and other features of the episode.

Previously, we’ve investigated the relative performance of the Chasers on the Australian and UK versions of the show using data from this Google document from James Spencer for the Australian data, and from this website for the UK data.

James, to celebrate the 1,000th episode of The Chase Australia, has recently added contestant-by-contestant data to his Google document, which allows us to investigate another topic I’ve long been interested in: how predictable are the Chasers’ high and low offers?

The introduction of technology into sport to allow those officiating to review crucial events has not been met with the universal approval of fans. There are some who feel it slows the play, some who feel it destroys the spontaneity and emotion around spectacular events that are eventually reviewed, some who believe it undermines the authority of those who are officiating on the field, some who feel it takes away one quintessential element of randomness (the umpire’s decision), and some who believe that, in any case, officiating errors will somehow magically eventually “even themselves out in the long run”. If you’re not a fan of technology in sport, you’ll probably have yet more reasons to dislike it.

The Chase remains a relatively popular gameshow in both Australia and the UK (see here and here) where it is played using identical rules but different currencies.

One particularly interesting feature is the fact that three of the UK Chasers - Anne Hegerty, Mark Labbett, and Shaun Wallace - have also appeared as Chasers in the Australian version, although the latter has appeared in relatively few Australian episodes and all three have been absent of late due to COVID restrictions.

The other day I was reviewing the forecasts of the modellers on Squiggle, a website that aggregates the opinions of a dozen or so people - including me - who attempt to predict, among other things, the final margins in games of men’s AFL.