ためしがない says something has never once happened, however many chances it has had. It follows a verb in the た-form and is a complaint: the speaker has watched it fail again and again and expects nothing better. means "precedent, instance" and is almost always written in kana; its kanji, rarely seen, is .
。
He has never once come on time.
。
This plan has never once worked out.
。
What that person says has never once been right.
ためしがない or たことがない
reports a gap in experience, with no feeling attached. ためしがない is about something that comes up again and again and always goes the same way, so it suits a habit or a repeated letdown, not a single thing you've never tried.
。
I have never eaten natto.
。
He has never once kept a promise.
- × 納豆を食べたためしがない → 納豆を食べたことがない
Usage notes
These go beyond complaining about other people.
About yourself
The subject is usually someone else, or a thing. Used about yourself, it is rueful: you never manage it.
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I have never once managed to stick with my New Year's resolutions to the end.
ためしはない
With in place of が, the denial is stronger.
。
There has never been a time when she was pleased with a gift I gave her.
Lingaku