Everyone remembers Euro ’96 for different reasons; Baddiel and Skinner, missed penalties, a major international final at Wembley Stadium. But for me, Euro ’96 was all about collecting the football stickers. It was the first international football tournament that I can properly remember and what I remember the most clearly is buying 1 packet of stickers a week and the subsequent frustration and elation of putting those stickers in their rightful place carefully between the lines.
Now my 8 year old self learnt a lot from that experience. I learnt patience. I learnt to cooperate and negotiate through swapping stickers in the playground. I learnt the name of the Bulgarian goalkeeper (Borislav Mikhailov – he played for Reading). I also learnt that it would take considerably more time and money that I had access to in order to complete my sticker album.
Fast forward 18 years and those lessons have not been forgotten. I like to think I’m patient and I can cooperate. I’ve proved I still know the name of the Bulgarian goalkeeper. I also know it would be a considerable drain on my time and money to collect football stickers again. Oh wait.
Enter one of my old school friends – let’s call him Luke. He thought it would be a good idea to start collecting stickers again for the upcoming World Cup, probably to remind him of a more innocent and carefree age. I thought it would be fun to join him.
So exactly how much is this likely to cost me?
Well there are 640 unique stickers, you get 5 stickers in a packet, and each packet costs 50p. So that’s 128 packets at a cost of £64. Easy. Except – unless you are a very lucky person – most of those stickers will be doubles. Or triples. Or worse. To put this into context, I currently have 5 Javier Mascheranos.
So how many packets do I actually need to buy to get all 640 unique stickers?
Assume that for the first sticker you acquire there is a 100% probability (P) that you don’t have it. Then for the second sticker you acquire there is a probability of 639/640 (99.84%) you don’t have it. The third sticker will have a probability of 638/640 (99.69%). This goes on for quite a while. In the end there is a 0.16% chance that you get the final sticker when you have the other 639.
To work out how many stickers we will need to buy (N) is then quite simple. To get any particular sticker the total number of stickers you need to buy is equal to:
For the first sticker you need just one sticker (1/1 =1). For the second sticker on average you will need to buy 1.002 stickers (1/0.9984 = 1.002). For the third sticker on average you will need to buy 1.003 stickers (1/0.9969 = 1.003). And so on. Finally, once you have 639 stickers, you will on average need to buy 640 (1/0.0016=640) more stickers to get that last one into your collection.
If we add these all up, on average the total amount of stickers that must be bought to complete a collection is 4,505. That’s 901 packets. At a cost of £451.
It’s not all that bad though – remember what I said about cooperating?
If there are 2 of you collecting, then you can swap. In fact, if you take out 640 stickers from the total of 4,505 for one completed album then on average you just need to buy a further 640 combined with the remaining 3,865 to complete a second album. This means you can complete 2 albums at a cost of £258 each.
Following this pattern, if you are lucky enough to have a third friend to swap with then you can complete 3 albums for £193 each. Unfortunately the benefit drops each time you add another friend into the mix. If you want to get the cost under £70 for each person you will need 64 friends actively swapping stickers, but this does highlight the importance of sticking together to get the most out of your World Cup album.
On these odds, my 8 year old self was never going to have much luck completing the album. At 1 packet a week it would take me over 17 years to complete an album of 640 stickers. Would I still have collected the stickers if I had known this at the time? Absolutely I would have – even if just for the memories 18 years on.
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