Stealing is never worse than splitting. So why does it lose?
In one round of split or steal, stealing always pays at least as well as splitting, whatever the other player does. That's true. It stops being good advice the moment the game is played more than once.
One true fact, two very different results
One round: $100 on the table
| They split | They steal | |
|---|---|---|
| You split | You $50, them $50 | You $0, them $100 |
| You steal | You $100, them $0 | You $0, them $0 |
Whatever they do, stealing gets you the same or more. If they split, $100 beats $50. If they steal, you get $0 either way.
Eight rounds against The Mirror
The Mirror splits in round 1, then copies whatever you did the round before.
The best move for one round can be the worst habit over many. Stealing wins a single round, but against The Mirror the first steal turns a partner who splits into one who steals back. After that you both get $0, round after round. Splitting gives up a one-time $50 and keeps $50 coming every round.
The same trap shows up anywhere people deal with each other more than once: a business overcharging a regular customer, a coworker taking credit for shared work, a country breaking a trade deal. The move that wins today can cost everything after. Before trusting "this is always the best move," ask whether the game ends after one round.
Where in your life does a choice that wins once cost you in every round that follows?
Other ways to play against The Mirror
| Your plan | What happens | You get | The Mirror gets |
|---|---|---|---|
| Always steal | One $100 grab, then $0 forever | $100 | $0 |
| Steal once in round 1, then split | $100, then The Mirror steals once and you get $0, then $50 a round | $400 | $400 |
| Always split | $50 every round | $400 | $400 |
| Split, then steal in round 8 | $50 a round, then a $100 grab The Mirror can't answer | $450 | $350 |
A steal in the very last round pays, because there's no next round for The Mirror to copy it. That only works if you know exactly when the game ends and your partner doesn't react to it. When both players know the last round, each has a reason to steal in it, then in the round before, and so on, and the cooperation can unravel. That's one reason long-running relationships, with no fixed end, tend to stay more cooperative.
Where The Mirror comes from
The Mirror plays a strategy called tit for tat. Around 1980, political scientist Robert Axelrod ran computer tournaments where strategies played a repeated version of this kind of game against each other. Tit for tat, one of the simplest entries, won both tournaments. The split-or-steal setup is also the final round of the British game show Golden Balls, where it was played only once, the situation in which stealing's logic is hardest to beat.
Braess's paradox shows the same pattern on the road: each driver picking the route that's best for them can leave everyone stuck in slower traffic.
Related exhibits
Sources: Payoffs and results calculated from the rules shown; Robert Axelrod, The Evolution of Cooperation (1984), for the tit-for-tat tournaments; the split-or-steal format from ITV's Golden Balls.