The Growing Pot

How it works

Four pounds sits on the table, 3 on Ann's side. She can take her 3 and end it, or pass - each pass doubles the pot and hands the choice across to Ben. Six rounds, reaching 256 if everyone passes, and whoever takes gets the larger share. Both see the whole ladder up front. The story asks how far the pot actually gets. You lock in a guess, then step through the answer and breakdown.

How scoring works

No grading - your guess is displayed back beside the answer. The story teasers share one lifetime unlock for free users.

The key insight

Start at the last move: the final mover takes, since there is no future to protect. The player before, knowing that, takes first - and the logic chains all the way back, so Ann takes the 3 on move one and the pot never grows. The collapse depends on common knowledge of rationality running the full six levels deep; in experiments even a little doubt keeps people passing well into the middle of the ladder.

The full step-by-step solution lives at /brain-teasers/centipede/solution.

A worked example

Round 6: Ben takes the larger share rather than let the game end paying him less. Round 5: Ann knows this, so passing hands Ben the take - she takes first. Each earlier node collapses identically, landing on Ann taking 3 at move one with 253 pounds of potential surplus never created.

Common mistakes

• Guessing 'they pass a few times then take' as the theoretical answer - that is the empirical result, not the equilibrium.

• Reasoning forward from move one instead of backward from the last node.

• Confusing this with the prisoner's dilemma - here nothing dominates; the unravelling comes from the known endpoint.

Why interviews test this

Interviewers want the unravelling argument stated confidently, then the acknowledgment that observed play differs and why - a test of treating models as tools. The written solution is at /brain-teasers/centipede/solution.