[tonyb]

It works because the route to 1.2.3.4 is relatively stable. The routes would only change and end up at data center #2 if data center #1 stopped announcing the routes. In that case the connection would just re-negotiate to data center #2.

[xg15]

Ah, ok, that makes sense. So for a given point of origin, anycast generally routes to the same server?

[majke]

Correct. From a single place, you're likely to BGP-reach one Cloudflare location, and it doesn't change often.