# Blog

## Archive

Show me a random blog post**2019**

### Jun 2019

Proving a conjecture### Apr 2019

Harriss and other spirals### Mar 2019

realhats### Jan 2019

Christmas (2018) is over**2018**

**2017**

**2016**

**2015**

**2014**

**2013**

**2012**

## Tags

news light electromagnetic field error bars chebyshev game of life craft hats graph theory mathsjam captain scarlet national lottery misleading statistics platonic solids ternary a gamut of games realhats countdown sorting programming dataset chalkdust magazine accuracy map projections matt parker chess binary bodmas dates sound london london underground propositional calculus palindromes menace raspberry pi royal baby folding paper reddit christmas card trigonometry python inline code weather station estimation puzzles games manchester triangles sport flexagons people maths gerry anderson tennis geometry video games curvature twitter mathsteroids game show probability golden ratio php manchester science festival braiding pac-man mathslogicbot cross stitch approximation probability christmas wool machine learning draughts radio 4 data folding tube maps frobel the aperiodical rhombicuboctahedron plastic ratio bubble bobble arithmetic european cup books reuleaux polygons football speed hexapawn coins fractals asteroids aperiodical big internet math-off rugby go harriss spiral latex logic martin gardner stickers pythagoras javascript statistics oeis pizza cutting noughts and crosses nine men's morris interpolation dragon curves final fantasy world cup golden spiral polynomials## World Cup stickers 2018, pt. 2

**2018-06-16**

This year, like every World Cup year, I've been collecting stickers to fill the official Panini World Cup sticker album.
Back in March, I calculated that I should expect it to cost £268.99 to fill this year's album (if I order the last 50 stickers).
As of 6pm yesterday, I need 47 stickers to complete the album (and have placed an order on the Panini website for these).

### So... How much did it cost?

In total, I have bought 1781 stickers (including the 47 I ordered) at a cost of £275.93. The plot below shows
the money spent against the number of stickers stuck in, compared with the what I predicted in March.

To create this plot, I've been keeping track of exactly which stickers were in each pack I bought. Using this data, we can
look for a few more things. If you want to play with the data yourself, there's a link at the bottom to download it.

### Swaps

The bar chart below shows the number of copies of each sticker I got (excluding the 47 that I ordered). Unsurprisingly, it looks a lot like
random noise.

The sticker I got most copies of was sticker 545, showing Panana player Armando Cooper.

I got swaps of 513 different stickers, meaning I'm only 169 stickers short of filling a second album.

### First pack of all swaps

Everyone who has every done a sticker book will remember the awful feeling you get when you first get a pack of all swaps.
For me, the first time this happened was the 50th pack. The plot below shows when the first pack of all swaps occurred in 500,000 simulations.

Looks like I was really quite unlucky to get a pack of all swaps so soon.

### Duplicates in a pack

In all the 345 packs that I bought, there wasn't a single pack that contained two copies of the same sticker.
In fact, I don't remember

*ever*getting two of the same sticker in a pack. For a while I've been wondering if this is because Panini ensure that packs don't contain duplicates, or if it's simply very unlikely that they do.If it was down to unlikeliness, the probability of having no duplicates in one pack would be:

\begin{align}
\mathbb{P}(\text{no duplicates in a pack}) &= 1 \times\frac{681}{682}\times\frac{680}{682}\times\frac{679}{682}\times\frac{678}{682}\\
&= 0.985
\end{align}
and the probability of none of my 345 containing a duplicate would be:

\begin{align}
\mathbb{P}(\text{no duplicates in 345 packs})
&= 0.985^{345}\\
&= 0.00628
\end{align}
This is very very small, so it's safe to conclude that Panini do indeed ensure that packs do not contain duplicates.

### The data

If you'd like to have a play with the data yourself, you can download it here. Let me know if
you do anything with it...

### Similar posts

World Cup stickers 2018, pt. 3 | World Cup stickers 2018 | World Cup stickers | Euro 2016 stickers |

### Comments

Comments in green were written by me. Comments in blue were not written by me.

Add a Comment