The fairest simple way for two people to split something is "I cut, you choose": one person cuts it into two pieces they would be happy with either way, and the other person picks first, so neither can end up with less than they think is half.
Mathematicians have studied this for eighty years. Here is the useful part.
Splitting something fairly sounds like a kitchen problem. It is also a real branch of mathematics, usually called the cake-cutting problem, and some of its answers work perfectly well at a dinner table.
One person cuts, the other picks. The cutter has every reason to make the two pieces equal, because they will get whichever one is left. The chooser can always take the piece they think is bigger.
For food that can be weighed, a kitchen scale ends the argument. Cut, weigh both pieces, trim a sliver from the heavier one and move it across. This is exactly what Halfsies scores: lighter half over heavier half.
For a round pizza, a square brownie or a rectangular cake, any straight cut through the exact centre splits it in half. Finding the centre is the only hard part. On a rectangle, it is where the two diagonals cross.
Someone slowly moves a knife across the cake. Anyone can shout "stop" when they think the piece behind the knife is a fair share. They take it and leave the game. Repeat with whoever is left. Everybody gets at least what they consider their share.
The first person cuts a piece they think is fair. Each person in turn may trim it if they think it is too big. The last person to trim it takes it. It works for any number of people and suits things that can be shaved down, like a slab of cheese.
A rule of thumb for groups: whoever cuts the pizza picks their slice last. It is the same idea as I cut, you choose, scaled up, and it quietly makes everyone cut more carefully.
Not everything is cake. For a bill, an even split is only fair if everyone ordered about the same. Otherwise each person pays for their own items and the shared dishes are split evenly.
| Situation | Best method |
|---|---|
| Two people, one dessert | I cut, you choose |
| Round or square food | Cut through the centre |
| Three or more people | Moving knife or last diminisher |
| Food you can weigh | Scale it and trim |
| Group with a pizza | The cutter picks last |
It is the mathematical question of how to divide something between people who may value its parts differently, so that each person feels they got a fair share.
For two people, yes. The cutter can always make two pieces they like equally, and the chooser can always take the one they prefer, so neither gets less than half by their own judgment.
The moving knife method works: move a knife slowly across the cake and let anyone call stop when the piece behind it is a fair third. They take it, and the remaining two finish with I cut, you choose.
Usually a few percent off, and much worse on odd shapes with long thin parts. Halfsies is a free daily game built entirely around that skill.