McDonald's Monopoly ended up in the United Kingdom in May, but now it started at its fast food restaurants throughout Australia.

The popular contest, available at participating McDonald's restaurants around the world, offers customers the opportunity to collect stickers and win special prizes.

The main prizes include everything from videogame consoles to brand new cars.

However, in an article for The Conversation, Sarah Belet, a graduate student at Monash University, and Jennifer Flegg, professor of Applied Mathematics at the University of Melbourne, analyzed the numbers to find out what possibilities McDonald's diners had. It's about winning.

They discovered that the possibility of someone winning a top prize is only 1 in 136 million, which is as unlikely as winning the EuroMillions jackpot.

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The scientists discovered that the possibility of someone winning the first prize is only 1 in 136 million, which is as unlikely as winning in the accumulated Euromillions well.

The McDonald & # 39; s Monopoly competition returns this month and offers the opportunity to win expensive prizes, all for the price of a Big Mac.

Considering that you could become thousands of dollars richer simply by going to the race of a Macca, the games McDonald's Monopoly have been in the past subject to cheating and a multi-million dollar scandal.

But for those who prefer to play fair, what are their chances of really catching a prize?

To participate you need to buy certain McDonald's foods that include removable Monopoly tickets. Each ticket has three different possible outcomes: an & # 39; Instant Gain & # 39 ;, a & # 39; Probability Card & # 39; or & # 39; Collect to win & # 39;

Instant prizes are a McDonald's food item such as a hamburger or non-food award, such as a movie ticket or a cash gift card, redeemed by entering the 12-digit code on the ticket at a phone application.

One ticket & # 39; Chance card & # 39; it also provides a 12-digit code that, when entered into an application, provides another opportunity to obtain an instant prize or a digital ticket from & # 39; Collect to win & # 39 ;.

The tickets of & # 39; Collect to win & # 39; they are the real meat of the game and they give the main prizes: sometimes a car or large amounts of money.

To win one of these prizes, you must collect all the "Collect to win" tickets of the same color, as you would with the traditional Monopoly game.

For obvious reasons, McDonald's does not tell us much about how these tickets are distributed throughout Australia.

But what it does tell us is the maximum amount of prizes that can be awarded for each type of prize.

Using some pretty basic crunchy numbers, we can get a better idea of our chances of winning a shiny new car by simply buying a Big Mac meal.

What the numbers reveal

This year, McDonald's says that 136,634,083 tickets will be distributed through the restaurants of the fast food giant, and the maximum amount of prizes available is listed.

While we have no way of determining if this maximum is reached, we can still have a general idea of our chances of winning a prize using these values.

McDonald's says there is a one in five chance of winning an instant prize, which could be a food award or a non-food award.

To participate you need to buy certain McDonald's foods that include removable Monopoly tickets. Each ticket has three different possible outcomes: an & # 39; Instant Gain & # 39 ;, a & # 39; Probability Card & # 39; or & # 39; Collect to win & # 39; In the photo is the Australian board

Of course, 13.2 percent plus 8.7 percent gives a 21.9 percent chance of winning an instant win, on average, which roughly matches one in five that McDonald's claims.

The fallacy of the player

It is important not to fall into the fallacy of the player when it comes to collecting tickets to win instantly. Collecting five tickets does not mean that one of them will always be an instant winning ticket.

McDonald's simply promises an average rate of an instant win, due to the fact that about 20 percent of physical tickets include a prize of some kind.

There are 3,415,852 tickets & # 39; Chance & # 39; available, so you have approximately a 2.5 percent chance of getting a ticket & # 39; Chance & # 39; with your purchase.

McDonald's says that one in five, or 20 percent, of Chance's tickets will result in an instant victory. Working the numbers means that you have a 0.5% chance of getting a Chance ticket that will also give you a prize, so it is not a strategy you should have.

The biggest prize tickets

While we know how many entries of & # 39; Instant win & # 39; and & # 39; Chance & # 39; there are, the details around the part & # 39; Collect to win & # 39; of the game McDonald's Monopoly are more closely protected.

Following the previous observations, it seems that for each ticket color "Collect to win", all but one of each set will probably be distributed very frequently. The last, not so common.

The McDonald & # 39; s Monopoly competition returned to Australia this month offering the opportunity to win expensive prizes, all for the price of a Big Mac

In this year's game there are two free one-year fuel prizes available for picking up the three red tickets: The Strand, Fleet Street and Trafalgar Square.

Therefore, it is quite possible that the probability of finding that final red ticket in the set is as low as 2 in 136 million.

If you are planning to win one of the main "Collect to win" prizes, these are the odds that we think you should expect, even if you have collected all but one, depending on the number of prizes available. :

1 in 136 million (one prize each)

– One year rental rental

– One room change bonus of $ 10,000 (US $ 7,200 / £ 5,500)

1 in 68 million (two prizes each)

– One $ 5,000 travel gift card (US $ 3,600 / £ 2,700)

– One year of free fuel

– A new car

1 in 45 million (three prizes each)

– Definitive games package

– Theater at home

1 in 34 million (four prizes)

– BBQ set

1 in 17 million (eight prizes)

– A purchase bonus of $ 1,000 (US $ 700 / £ 550)

Since each ticket has a 12-digit code, you can enter the application to see if you've won a prize, a bold idea could be to enter random codes to see if you can guess a winning number.

There are several reasons why this is a waste of time (no less important is the fact that you need to present a physical copy of a ticket to collect a prize), but also get a mathematical perspective.

Each ticket code consists of a combination of letters and numbers. There are 9 possible numbers (1-9, ignoring 0 not to be confused with the letter O) and 26 possible letters (A-Z, capital letters only) that can appear in a ticket code

Each ticket code consists of a combination of letters and numbers. There are 9 possible numbers (1-9, ignoring 0 not to be confused with the letter O) and 26 possible letters (A-Z, capital letters only) that can appear in a ticket code.

This means that there are 35 possibilities for each of the 12 alphanumeric characters in a code. So, how many possible codes of 12 characters are there? We can calculate that with:

= 35 × 35 × 35 × 35 × 35 × 35 × 35 × 35 × 35 × 35 × 35 × 35

= 3512

= 3,379,220,508,056,640,625

But there is only a maximum of 136,634,083 entries in the game.

Therefore, the probability of entering a 12-digit random code in the application and recognizing it as a valid ticket code is given by:

= 136,634,083 / (3512)

= 0.00000000004

In other words, a 0.000000004 percent chance that you have chosen a valid ticket code at random.

Such a small number is hard to imagine, so let's think differently. If you would like to increase your probability of randomly choosing a valid ticket code to approximately 4 percent (it is still a very small possibility!), You should be prepared to first choose 1011 or 100 billion random codes of 12 characters.

If we assume that choosing, entering and verifying a code in the application only took a second, then entering one hundred billion codes would take approximately 3,180 years. The competition ends next month.

By the way, this is one of the reasons why websites and email services encourage you to choose passwords that have at least eight characters, with a combination of numbers, letters and special characters. People with nefarious intentions take a long time to guess their password if it is as long as the code of a McDonald's Coupon, even if they get a computer to help them.

What is the best way to play?

If you remember that McDonald's Monopoly is very similar to a normal lottery, you'll be better since you can relax and know that there's almost no chance you'll win a big prize.

The aspect of winning instantly is a good advantage if you are already planning a meal at McDonald's, since it is not very unlikely that you can finish with a little fries or a drink.

This article was written by Sarah Belet, a graduate student at Monash University and Jennifer Flegg, a professor of Applied Mathematics at the University of Melbourne.

The article was originally published in The Conversation.

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