In the beginning of the doubling cube discussion, Chris Bray says there have been two really bad and two really good books written about the doubling cube. So.. what books is he referring to?

Don't know about bad cube books, but two good ones could be:

Walter Trice: Backgammon Boot Camp
Kit Woolsey: The Backgammon Encyclopedia (Volume 1: Cube Reference Positions)

Certainly the Woolsey book must be one of the good ones.

The other good one may be an oldie that was first rate in its time. Often accurate in its approach, but limited by today's standards (because the author only rolled out 100 games for each position), Jeff Ward's book gave us the Ward racing formula among other things.

The Doubling Cube in Backgammon by Jeff Ward
http://www.bkgm.com/books/Ward-Doubl...ackgammon.html

Backgammon Galore! also lists a couple of others that use the word "Double" or "Doubling" in their titles:

Backgammon: Winning With The Doubling Cube by Peter Bell
http://www.bkgm.com/books/Bell-Winni...blingCube.html

Double ... now? An Authentic Cube Remedy by James Lortz
http://www.bkgm.com/books/Lortz-DoubleNow.html

Judging by the reader comments, Bell's book is probably one of the criticized texts. Ironically, Bray is quoted as having praised the work in one of his early columns.

Trice deserves mention because his text presents the Trice62 rule for racing doubles. It is one of the best.

Nack Ballard and Neil Kazaross have recently combined to improve on it. The Nack58 formula states that from the leader's pipcount you subtract 32, double the result, and find the nearest sqrt (square root). When added to the leader's pip count, the result gives the highest pip count where the trailer can take. When the trailer's pip count is one less than this maximum, the leader has a redouble. When the trailer's pip count is two less than the maximum, the leader has an initial double.

When the leader's pip count is less than 58, use the original Trice62 rule (subtract 5 from the leader's pip count, divide by 7, round down) to establish the same doubling window.

See the original discussions of Nack58 at:
http://www.bgonline.org/forums/webbb....pl?read=87795
http://www.bgonline.org/forums/webbb...mes;read=59714

Seems kind of an absurd statement to make, if that is all he writes. What is the reader supposed to do with this bit of information then?

There was another book entirely devoted to cube strategy: Dynamic Cube Strategy by Gaby Horowitz and Bruce Roman (1978 or so). It's an awful book, even for its time. I suspect this and the Lortz book are what Bray was referring to as the bad books.

The Bell book is a cube book for complete beginners, and it covers the basics of cube handling slowly and in detail. I think it's very good for its intended audience. Most of the mediocre reviews are from people who buy the book expecting it to be something other than a beginner book, and are then disappointed.

The Bell book and the Woolsey book are probably the "good" books that Bray was referring to. The Ward book is hard to classify because it was intended to be the first of a three book series, and the others were never written. It only covers bearoffs and races, but it does a very good job there. In particular, it introduces the "Ward count", which according to Trice's computer analysis is slightly more accurate than the Thorpe Count.

hope Bill Robertie will provide clarification?

Yes, that's all Bray wrote. There is a Further Reading section in the back, but there is no allusion to his earlier statement there.