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Comment by lossolo

5 days ago

> it’s also more efficient [than o1 or o3] with its thinking.

"So under his saturate response, he never loses. For her to win, must make him unable at some even -> would need Q_{even-1}>even, i.e. some a_j> sqrt2. but we just showed always a_j<=c< sqrt2. So she can never cause his loss. So against this fixed response of his, she never wins (outcomes: may be infinite or she may lose by sum if she picks badly; but no win). So she does NOT have winning strategy at λ=c. So at equality, neither player has winning strategy."[1]

Why use lot word when few word do trick?

1. https://github.com/aw31/openai-imo-2025-proofs/blob/main/pro...