A pot of coins starts small and doubles every time someone passes. You and an AI opponent take turns. Take the pot now for a guaranteed (if smaller) prize, or pass and hope your opponent keeps growing it instead of grabbing it all.
Chance the AI passes instead of taking on its turn. Higher = more trusting (and more tempting for you to wait too).
Your turn — pot is 2 coins. Take or pass?
No moves yet. Take or pass! 👆
Pure logic says: since the last player to move should always take, the second-to-last player should take earlier to avoid being taken from, and so on — all the way back to the very first move! This is called backward induction. Yet in real life (and in your game!), people usually pass more than logic predicts, because trust has real value too.
The Centipede Game is named for its shape when drawn as a diagram of moves — a long row of branching points that looks like a centipede's many legs. Two players alternate turns, and on each turn the current player chooses to "take" a shared pot of money (ending the game immediately) or "pass" (letting the pot grow bigger, but handing control to the other player). The pot keeps growing every round, so total wealth is highest if both players keep passing all the way to the end — but each individual player has a personal incentive to grab the pot before their opponent does.
Game theorists solve this puzzle using a technique called backward induction: start at the very last possible move and work backward. At the final step, the player whose turn it is should always take, since there's no more growth to gain by passing. Knowing this, the player just before them should also take, since passing would only let the other player grab everything next. Following this logic all the way back to the first move implies that a perfectly rational player should take immediately, even though this leads to a tiny payoff compared to what patient cooperation could have produced.
What makes the Centipede Game famous is that real humans almost never behave this way. Experiments show most people pass several times before taking, earning more than pure game theory predicts. This reveals an important truth: people care about trust, fairness, and reputation — not just cold calculation — and sometimes that makes everyone better off.
Use a small pile of coins or candy. Start with 2 pieces and take turns choosing to "take" (end the game, keep most of the pile) or "pass" (double the pile and give the other person the choice). Play several rounds with different partners and compare how far people let the pile grow before someone takes it — then discuss why nobody takes it immediately, even though pure logic says they should!
What is the Centipede Game?
It's a sequential game where two players take turns choosing to "take" a growing pot for themselves, or "pass" to let it grow bigger, risking the other player taking it all next.
What does game theory predict will happen?
Using backward induction, a perfectly logical player should take the pot on the very first move. Yet real players usually pass several times before taking.
Why do real people pass more than theory predicts?
People often trust their partner, care about fairness, or enjoy growing the shared pot together, so cooperation lasts longer than the purely logical prediction.
What is backward induction?
It's a way of solving a game by reasoning from the final move backward to the first, figuring out what the last player would do, then working backward step by step.