Game theory? It’s a piece of cake! Author reveals how a branch of mathematics used by Wall Street can help the average person get their fair share in life

•  The book describes a solution for three people sharing a cake 

Ordering one dessert and two forks is always a risk.

But that feeling of resentment towards the person across the table taking more than their fair share could have an elegantly simple solution… Game theory.

The branch of applied mathematics – more often used by Wall Street brokers trying to figure out when to sell stock – can also be applied to a slice of cheesecake or chocolate cake, according to a recent book.

To prevent one person in a couple, or a greedy friend, from taking the lion’s share, one of them should move a knife from left to right across the slice, with either person shouting ‘stop’ when they think it has reached the halfway point.

The person who says stop gets the left-hand piece, which they are content with because they believe it is half the dessert.

The book, Numbers: Ten Things You Should Know, by Colin Stuart, suggests people should forget everything they know about how to cut a cake

Meanwhile the person who stayed quiet gets the right-hand piece and is more than happy – believing they have more than half, as otherwise they would have yelled stop previously.

This ‘envy-free’ solution means neither person is annoyed about the other’s portion.

The theory, which has been around for several decades but is little known outside of maths circles, is included in a new book explaining mathematical theory and its applications in real life, by Colin Stuart, a fellow of the Royal Astronomical Society.

He said: ‘The moving-knife solution means everyone is happy, even if the cake is not actually shared 50/50, because neither person feels they have lost out.

‘It is a good way of showing how mathematicians and scientists can be strangely quite whimsical – several of them have set their minds to the puzzle of how best to divide a cake.’

The book, Numbers: Ten Things You Should Know, by Colin Stuart, suggests people should forget everything they know about how to cut a cake.

Slicing triangle-shaped pieces out of it is not the best method if you want to keep the cake moist and prevent it drying out.

Instead, you should cut a long, thin wedge from the exact centre of the cake, and ‘squidge’ the remaining two pieces together to keep the inside away from exposure to the air.

The method, explained in the book, is the invention of scientist Francis Galton, the half-cousin of Charles Darwin.

It suggests people should go back to the cake with the vertical wedge removed and take their next slice by cutting a horizontal wedge across the middle.

The remaining cake pieces can again be pushed together to keep the inside moist – with the help of a rubber band, according to Galton, who published a letter on the subject in prestigious science journal Nature in 1906.

The book also describes a solution for three people sharing a cake where different parts of it are more delicious – for example if some areas of the cake have more buttercream or chocolate sprinkles.

If three people called Tom, Dan and Sarah are quarrelling over their share, Tom can cut the cake into three pieces – any of which he would be happy to receive.

Dan and Sarah can choose their piece, and if they choose different ones, everyone is content, according to the theory devised in the 1960s.

The theory, which has been around for several decades but is little known outside of maths circles, is included in a new book explaining mathematical theory and its applications in real life, by Colin Stuart, a fellow of the Royal Astronomical Society

But if they choose the same one, Sarah should cut a sliver off her favourite piece until she thinks it has the same amount of sprinkles or buttercream as her second favourite, and then Dan should choose one of these two slices.

Whichever he chooses, Sarah won’t mind, as she thinks both are equal in value, and she will take the other.

And Tom will be happy with the third piece which hasn’t changed since he cut it.

All that remains is for the sliver cut off the cake to be shared out, which starts the process again, but with the person who got the trimmed slice getting to cut the sliver up first.

There is even, as of seven years ago, an algorithm for how to share a cake between four people, but the book concludes it might be simpler to just ‘get a cake for everyone’.

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