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When it comes to watching an anime, I tend to get my choices from three locations:
1) From the new released season - therefore I always have something that is currently being aired
2) Those series which I've heard about and as such should get around to watching (like Ah! My Goddess and Death Note).
3) I read the entry of the anime and the synposis and decide from there.
So, how has this served me over the years...well out of the 254 different anime which I've watched some of, I've dropped a total of 11, which isn't too bad really. But of those 11 most I dropped within the first episode and only a few I watched for more.
It therefore is quite the interesting question as to know when I will finish watching an anime or not. Elementhunters I knew I wouldn't like it after seeing the introduction and the first 5 minutes of the show....mainly because I knew that the animation style would really annoy me. Its funny in someways that I stop watching a series because of the animation, but its not the first time I've done that. Sci-fi Harry was one I stopped watching for the same reason.
However, if you look at some series there are those which i've watched about 5 episodes before dropping and that was simply because I couldn't make my mind up with them. Azumanga Diaoh was such a series and the reason why I dropped it was because...well...I just never found it worth the time to watch.
On the whole however, once I start a series, I finish watching it. Mainly because I hope and really do hope, that at some point it will get better. In conclusion then:
Anywhere between 5 minutes and 5 episodes...