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...

Similar posts

World Cup stickers 2018, pt. 3
World Cup stickers 2018, pt. 2
World Cup stickers 2018
World Cup stickers

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>
To prove you are not a spam bot, please type "b" then "i" then "s" then "e" then "c" then "t" in the box below (case sensitive):

Archive

Show me a random blog post
 2020 

Jul 2020

Happy τ+e-8 Approximation Day!

May 2020

A surprising fact about quadrilaterals
Interesting tautologies

Mar 2020

Log-scaled axes

Feb 2020

PhD thesis, chapter ∞
PhD thesis, chapter 5
PhD thesis, chapter 4
PhD thesis, chapter 3
Inverting a matrix
PhD thesis, chapter 2

Jan 2020

PhD thesis, chapter 1
Gaussian elimination
Matrix multiplication
Christmas (2019) is over
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

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

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2020