>>80601712>>806028581st episode is usually a pilot, and it's usually not great. If it is great, that's a good sign.
2nd episode is either a direct continuation of the first or the first random character/world development episode. The writers are feeling things out.
3rd episode is when the show should start hitting the feel of what it's going to be (at least as it finds its footing) and usually gives you a good idea of what things are going to be like.
Here's the thing. The first three episodes don't have to be good in and of themselves, they just have to show promise. I can't think of a single good show I watched where, by the end of the first three episodes, I didn't think: "Well, this seems like it could/should shape up to be a fun ride, I'll keep going and see where it ends up."
I have had some shows pass the three episode test and then nosedive before the first season was over. I've had some shows start "not amazing, but good enough to watch in the background", and end up amazing by the end. I've seen others that were pretty good straight from the start. I have never had a show have three straight terrible/boring episodes with no hope or redeeming qualities and become good. Not once.
Everyone's got a different tolerance, but three episodes is more than enough to sell me that you know how to write a show. The exception is shows with short episodes, where two episodes can often count as "one" larger one. But shows that have 20 or 40 minute episodes? If someone can't pull out anything good in 80 to 110 minutes, that's a very bad sign.