What does "Ani k'dai" mean in Hebrew?

It doesn't make sense as posted. (If a Hebrew speaker today was going to say something like that, he might say in slang: Ani sha - veh.) "Kdai" isn't used like that.

Is it possible that the site said: Aino kdai? That means "not worth it". Post a link if you like.

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Nice question! Hardly anyone asks about a phrase from the Talmud here. The discussion took place during the later years of Roman persecution of the Jews. (As I suspected above, the roughly transliterated "ani" does not mean "I", but rather "I am not". I would have transliterated it: Eini.) The phrase "Eini kdai" means: "I'm unworthy".

In your context , it's part of the statement that a sincere convert might make upon being told by the rabbis of the trials and tribulations to which the nation of Israel is subjected in this world. The convert could be exposed to the same suffering upon joining the nation or s/he could turn back. If the potential convert responded: "I know and I am unworthy", the rabbis were to accept her/him immediately.

Here's an article that discusses conversion sources and divergent procedural approaches within Torah Judaism.

http://www.lookstein.org/articles/conversion.htm

A translation and basic discussion of the Talmud passage from which your quoted phrase is taken: http://myjewishlearning.com/lifecycle/Conversion/I... (Don't worry if terms like "braita" seem unfamiliar at this point. It refers to teachings from the time of the Mishna unpublished in that early body of work, but included later when the writers of the Gemara quoted the mishnaic sources.)

Related food for thought: http://www.torahmitzion.org/eng/resources/show.asp...

Ani=me or I

K'dai=Worth it

Could be loosely translated "I am worth it"