expression
extremely difficult; a one-in-a-thousand chance
Rare idiomatic expression emphasizing that success is so unlikely it is almost impossible. Used to describe a situation where the odds are overwhelmingly against you.
この難問は千番に一番の兼ね合いだ。
This difficult problem is a one-in-a-thousand chance.
彼が試験に合格するのは千番に一番の兼ね合いだろう。
The odds of him passing the exam are extremely slim.
A similar expression meaning 'one in a thousand', but less emphatic than 千番に一番の兼ね合い.
The expression literally means 'a balance of one in a thousand attempts', combining 千番 (a thousand times) and 一番 (one time) with 兼ね合い (balance, likelihood). The exact origin is uncertain, but it likely developed as a figurative way to express extreme improbability.