Oriental Avenue (line 2) does a lot better and is up there with the best-earning sets until about 25 rolls. The slope of Mediterranean Avenue (line 1) is very shallow, meaning it takes a long time before it will start making money - and even when it does, you won’t make much. Of the properties you can build on, those from the brown and light blue sets start closest to the dotted line because they are so cheap to buy and build on. Each property starts off with a negative value, as you have to invest in them to begin with as soon as a property crosses the dotted line at zero the amount it’s earned in rent exceeds the amount it cost you. With a hotel on each, your earnings are shown up the vertical (y) axis and the total number of your competitors’ rolls along the horizontal (x) axis. The below graph shows a selection of properties from each set. To make a well-informed decision about which are the best properties to buy, you want to know how quickly you’ll make your money back and how quickly you’ll earn the big bucks once you do. So, to find the best strategy, we need to take into account how much you can expect each property, fully loaded with hotels, to earn for every roll of the dice and how much investment is required to get you there. Knowing which sets are likely to give you better returns is your ticket to board-game glory, ensuring it’s you with the smug, satisfied smile on your face while your family members weep into their ice cream bowls over their devastating defeat. This is where mathematics steps in to help. The key to success in Monopoly is noticing that not all properties are created equal. But if you are going to be involved in a vicious fight with your family, you might as well emerge the victor. Monopoly, whose sole objective is to have you force your friends and family into poverty, seems to have the ability to turn even the most angelic of us into a monster. In reality, it ends when your sister accuses one or all of you of cheating, flips the board across the room, and storms off in a shower of miniature plastic houses. Officially, Monopoly ends when all players but one go bankrupt. To our minds, there is nothing more magical than a full-blown family argument caused by a good old-fashioned game of Monopoly.

Forget utilities - these are the properties you really should be investing in.

IStock Mathematicians Hannah Fry and Thomas Oléron Evans have crunched the numbers.

Monopoly strategy