Hold On – Do Not Buy Those McDonald's Monopoly Stickers

Search "Park Lane" on Twitter, eBay or Facebook marketplace, and aside from the odd luxury property scam, every result is to do with McDonald's.

It's the thirteenth year that the fast food chain has run its Monopoly promotion in the UK, dishing out peel-off stickers with burgers and fries. This year's edition is called "Monopoly Wiiiin!", so named because the idea is that you win stuff, from a free apple pie to £100,000.

Some of the stickers are "instant wins", some are property stickers, and if you collect all the stickers from a certain segment of properties you win a prize. For that top prize, you need to collect both a Park Lane and a Mayfair sticker – the two dark blue properties. While there are only four Mayfair stickers in the entire country, there are many more Park Lanes. This, explained Dr Luke Clark, Director of University British Columbia's Centre for Gambling Research, is meant to fuck with you.

"The differing numbers of tickets in the Monopoly game would create frequent 'near miss' experiences similar to scratch cards, where the player thinks they are close to a jackpot combination – for example, getting their second Park Lane sticker instead of a Mayfair sticker," he said.

Yet, regardless of this fairly obvious ploy, and the Park Lane stickers' abundance, people are trying to cash in by selling them online, in three different ways. The first: flogging them for a fixed price; the stickers have already been sold for everything from a tenner to £45,000. Forty-five thousand pounds. Enough to rent an actual one-bed flat on actual Park Lane for a whole year. The second: people offering to pair up with a Mayfair sticker holder and split the winnings. Third: people on eBay offering a kind of lucky dip, where they say they have a dark blue property and you have to bid and win to find out which one (no prizes, literally, for guessing which one they all have).

So: we know that buying a Park Lane sticker in any shape or form is idiotic. But exactly how idiotic? To find out, I scanned through a load of McDonald's small print and spoke to Professor Charles M Grinstead, Emeritus Professor of Mathematics at Swarthmore College, Philadelphia and author of Introduction to Probability.

McDonald's UK don't divulge how many stickers they print, just that they have "produced a total volume of Game Pieces Labels across all types of qualifying menu items which it considers reasonably likely to satisfy estimated demand for Game Pieces Labels during the Promotion."

To make a rough estimate, let's use the fact that 3.8 million customers a day are served in UK McDonald's. Since the promotion runs for 41 days (21st of March to the 1st of May) that means there will be around 155,800,000 transactions. Each product contains either two or three stickers – so let's call it 2.5 – and assuming every transaction will contain at least one item, there have to be at least 394,080,520 stickers, which we'll round up to 400 million.

The only information McDonald's UK gives us is that the combined total of the nine rarest properties is just over 1.55 million (including Mayfair, of course). Old Kent Road is the ninth rarest sticker, at 1.5 million. That means there are 398.5 million "common" stickers, which represent 17 different properties (including Park Lane). Based on the USA game, of which 76.1 percent of the total stickers are property stickers, this means there should be 302.86 million property stickers. Let's call this 300 million property stickers out of the 400 million total.

This is where it starts getting too complicated for me, so I took my query to Professor Grinstead, who said:

"This average will be highest if the Park Lane sticker is the least common among the common stickers (you imply that this is probably not the case, but let's assume it for now). Then there are at least 1,500,000 Park Lane stickers, since they are more common than the Old Kent Road stickers. This means that every sticker a patron gets has a probability of at least 1,500,000/400,000,000 = 0.00375 of being a Park Lane sticker.

"If the probability of an event is p, then the average number of trials needed for the event to happen is 1/p. So in this case, the average number of stickers a patron needs to obtain to get a Park Lane sticker is no greater than 1/0.00375 = 266.67. If the average order contains 2.5 stickers, then one must buy 266.67/2.5 = 106.7 orders, on average, to obtain a Park Lane sticker."

So if we imagine that Park Lane is the rarest "common sticker", it would still only take you about 100 packs of £1 fries to get one, which would make it "worth" £100, not £45,000.

Of course, for anyone who has ended up with a ton of Park Lanes, it's clear there are far more than 1.5 million of them. If we look at the USA game, we know that all nine "common" stickers have a pretty much equal probability of either 1 in 10 or 1 in 11. Park Place, the US equivalent of Park Lane, has a 1 in 11 chance. So if we split the 300 million "common" property stickers (the rest are instant wins or online codes) by their amount (17), we get an average estimate of each "common" property having 17.6 million copies, meaning:

There is a 1 in 22 chance of a sticker being a Park Lane, compared to a 1 in 100 million chance of a sticker being Mayfair.

This means you'd probably get one Park Lane sticker if you bought nine promotional items. Ultimately, this means Park Lane stickers are not worth very much at all.

My advice: don't buy McDonald's Monopoly Park Lane stickers.

@kylemmusic