Shrouds do two things: 1) they improve the efficiency by reducing tip vortex losses; 2) they increase the effective diameter of the turbine, so Betz' law is circumvented to SOME degree.

I worked for a time on shrouded propellers for ship propulsion and studied ducted propellers for aircraft. These are more efficient than unshrouded propellers - but in each case the difference is under 10% - this is combined gain from reduced losses and larger apparent diameter. With turbines, things are a bit more complex, because with a well designed duct you achieve an effective diameter actually larger than the duct itself, and capture the additional wind energy from that extra area. Taking things to absurdity, I am fairly sure (without doing the math...) that you could have a relatively small turbine inside an enormous duct, and achieve 3x the power of an unshrouded turbine of that diameter. But this is a poor solution, because the large duct will surely cost a lot more than a larger conventional wind turbine.

I think this is what you meant to quote.

http://en.wikipedia.org/wiki/Betz%27_law

Are current turbines already within a factor of 3 of Betz' law, or at least within a factor of 3 of a practical limit?

Yes, they are within 20% of the Betz' limit. But you must understand that the Betz' law refers to "available power", and the "available power" is higher for a shrouded turbine due to its larger apparent diameter.

Most informative, thank you.