mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

Euro 2016 stickers

 2016-05-04 
Back in 2014, I calculated the expected cost of filling Panini world cup sticker album. I found that you should expect to buy 4505 stickers, or 1285 if you order the last 100 from the Panini website (this includes the last 100). This would cost £413.24 or £133.99 respectively.
Euro 16 is getting close, so it's sticker time again. For the Euro 16 album there are 680 stickers to collect, 40 more than 2014's 640 stickers. Using the same calculation method as before, to fill the Euro 16 album, you should expect to buy 4828 stickers (£442.72), or 1400 (£134.32) if you order the last 100.
This, however, does not tell the whole story. Anyone who has collected stickers as a child or an adult will know that half the fun comes from swapping your doubles with friends. Getting stickers this way is not taken into account in the above numbers.

Simulating a sticker collection

Including swaps makes the situation more complicated: too complicated to easily calculate the expected cost of a full album. Instead, a different method is needed. The cost of filling an album can be estimated by simulating the collection lots of times and taking the average of the cost of filling the album in each simulation. With enough simulations, this estimate will be very close the the expected cost.
To get an accurate estimation, simulations are run, calculating the running average as they go, until the running averages after recent simulations are close together. (In the examples, I look for the four most recent running averages to be within 0.01.) The plot below shows how the running average changes as more simulations are performed.
The simulations estimate the number of stickers needed as 4500. This is very close to the 4505 I calculated last year.
Now that the simulations are set up, they can be used to see what happens if you have friends to swap with.

What should I do?

The plots below shows how the number of stickers you need to buy each changes based on how many friends you have.
Stickers needed if you and your friends order no stickers.
Stickers needed if you and your friends all order the last 100 stickers. The last 100 are not counted.
In both these cases, having friends reduces the number of stickers you need to buy significantly, with your first few friends making the most difference.
Ordering the last 100 stickers looks to be a better idea than ordering no stickers. But how many stickers should you order to minimise the cost? When you order stickers, you are guaranteed to get those that you need, but they cost more: ordered stickers cost 14p each, while stickers in 6 pack multipacks come out at just 9.2p each. The next plot shows how the cost changes based on how many you order.
The expected cost of filling an album based on number of people in group and number of stickers ordered.
Each of the coloured curves represents a group of a different size. For each group, ordering no stickers works out the most expensive—this is expected as so many stickers must be bought to find the last few stickers—and ordering all the stickers also works out as not the best option. The best number to order is somewhere in the middle, where the curve reaches its lowest point. The minimum points on each of these curves are summarised in the next plots:
How the number you should order changes with the number of people in the group.
How the cost changes with the number of people in the group.
Again, having friends to swap with dramatically reduces the cost of filling an album. In fact, it will almost definitely pay off in future swaps if you go out right now and buy starter packs for all your friends...
                        
(Click on one of these icons to react to this blog post)

You might also enjoy...

Comments

Comments in green were written by me. Comments in blue were not written by me.
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li> <logo>
To prove you are not a spam bot, please type "v" then "e" then "c" then "t" then "o" then "r" in the box below (case sensitive):

Archive

Show me a random blog post
 2024 

Feb 2024

Zines, pt. 2

Jan 2024

Christmas (2023) is over
 2023 
▼ show ▼
 2022 
▼ show ▼
 2021 
▼ show ▼
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

24 hour maths edinburgh bubble bobble correlation sobolev spaces datasaurus dozen data finite group accuracy computational complexity football news london underground mathsteroids ucl latex books world cup geogebra determinants a gamut of games turtles javascript tmip weak imposition electromagnetic field pascal's triangle speed mean chebyshev advent calendar matrix of minors inverse matrices final fantasy map projections reuleaux polygons harriss spiral approximation european cup stirling numbers manchester science festival anscombe's quartet signorini conditions craft binary noughts and crosses youtube platonic solids gerry anderson golden spiral squares frobel light fonts programming chess ternary runge's phenomenon cambridge gather town puzzles propositional calculus interpolation sound boundary element methods cross stitch draughts folding paper polynomials logs databet talking maths in public london christmas card numerical analysis asteroids martin gardner weather station reddit machine learning raspberry pi pythagoras gaussian elimination matrix of cofactors crossnumber misleading statistics game show probability bempp the aperiodical guest posts exponential growth simultaneous equations rugby dataset games inline code pi convergence hannah fry matrix multiplication php realhats live stream coins wool royal baby recursion pac-man royal institution errors matt parker countdown hats zines trigonometry golden ratio plastic ratio bodmas national lottery go pizza cutting christmas palindromes arithmetic fence posts video games stickers braiding sport logic folding tube maps manchester probability dragon curves nine men's morris fractals data visualisation people maths graph theory logo wave scattering crochet curvature numbers captain scarlet sorting quadrilaterals graphs mathslogicbot dates phd menace geometry radio 4 statistics hyperbolic surfaces flexagons dinosaurs hexapawn triangles matrices mathsjam python estimation newcastle standard deviation rhombicuboctahedron preconditioning big internet math-off oeis pi approximation day finite element method error bars game of life chalkdust magazine tennis

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2024