Please note, however, that if you clear your cookies several times in a row, they end up identifying your machine in some other way (I think IP based? But that wouldn't work for very busy IPs, e.g. busy workplace with many employees, so maybe it's IP and amount of traffic over time?).
Disclaimer: I am a paying subscriber since 2010 and have tried the above just out of curiosity.
Edit: I suppose the simple answer is "3 articles", but that just seems like a rather low limit to me, hence my question. I'm wondering if maybe their detection is simply bad (e.g. maybe my browser reloaded an article and it counts that as an additional read?)
Re paywalls, HN's rule is that they're ok as long as there's a standard workaround. This is in the FAQ: https://news.ycombinator.com/newsfaq.html.
You could also try the Facebook linkout method:
http://facebook.com/l.php?u=<URL> (or just otherwise spoof your referrer to facebook.com)
Yet to find a paywall willing to deny social media traffic. They'll die without it and they know it.