Centipede Game
Take a small pot now or pass and hope the doubling pot keeps growing.
You and another player face a sequential game with $1 in a shared pot. On each turn, the active player chooses TAKE (the game ends and that player keeps the entire pot; the other gets nothing) or PASS (the pot doubles and it becomes the other player's turn). After 10 rounds the pot would reach $1024. Game-theoretic backward induction predicts both rational players should TAKE on every turn — including the very first move — yielding just $1. Empirically, real players often PASS for several rounds, allowing the pot to grow. It is your turn one (the very first turn). The pot is currently $1. The other player is a rational stranger you will never meet again.
Do you take the $1 now, or pass?
02 · choices
- takeTake the $1 now (backward-induction equilibrium)
- passPass and hope the other player also passes, growing the pot
03 · aggregate distribution
04 · by model
Claude Opus 4.7 Anthropic | pass10/10 | read → | |
GPT 5.5 OpenAI | take10/10 | read → | |
Gemini 3.1 Pro Google | take5/10 | read → | |
Grok 4.3 xAI | take10/10 | read → | |
Llama 4 Maverick Meta | pass10/10 | read → | |
DeepSeek V4 Pro DeepSeek | take10/10 | read → |