Sequencing Depth and World Cup Paninis

The World Cup is underway and I am back to the blog!  I was recently inspired by the World Cup Paninis to write a post about sequencing depth.  In sequencing, the problem we are often faced with is whether or not enough sequences have been generated to be representative of a population.  Tools we often use to determine whether we have sampled enough are rarefaction curves and the Chao estimate but how many sequences would we need to generate in order to capture a 16S from every organism present in an environment?

This leads me back to the World Cup Paninis — a fun collecting game akin to baseball cards or US state quarters.  Every World Cup a sticker book is published that contains information about all players, teams, and stadiums in the World Cup.  To fill the Panini, one needs to collect 639 unique stickers that are sold in small yellow packets of 7 (notably all stickers are printed with equal frequency).  This year, Afonso and I have set out to fill our very own sticker book and we decided to ask: How many packs of stickers do we need to buy in order to fill our Panini?

This is a classic example of a problem known as the “coupon collector’s problem” where the first few packs of stickers will almost always contain new stickers to place in the Panini album but as one continues to buy more packs of stickers the frequency repeats increases making the expected number of sticker packs needed to complete the album much greater than 639/7.

Afonso and I thought it would be fun to calculate how much money one has to spend to obtain a complete collection of stickers and simulate each scenario.  Check out Afonso’s post for some fun calculations!

The first scenario I simulated was if a person bought a Panini album ($2) and packs of stickers ($1 per pack of 7 stickers) until the sticker collection was complete — with 1,000 runs of this simulation the average amount spent was $632 — almost $1 per sticker and leaving a person with nearly 4,000 repeats!  Now, Panini offers an option in which you can order up to 40 stickers for $0.25 a sticker.  So the next simulation I ran was to buy new packs of stickers until I only needed 40 more stickers from which I proceeded to spend $10 to collect the remaining 40 stickers.  Under this strategy, I only needed to purchase 250 sticker packs making my total of money spent $262  — still a lot of money for stickers!  Perhaps this is why some go to such great lengths like hijacking the panini van for over 300,000 stickers!



One thought on “Sequencing Depth and World Cup Paninis

  1. Pingback: World Cup and coupon… Panini stickers collecting | Relax and Conquer

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