I do not know of any online source where you can examine the problems in Robertie’s
501 Essential Backgammon Problems. I can, however, point you to an excellent resource for those who do have Robertie’s book. It is the web site by Timothy Chow where he posts many GNU rollouts of problems in the book. Chow deliberately withholds any board diagrams, so that unless you have the book, the rollout data are essentially meaningless.
Here is an excerpt from Chow’s introduction:
The rollouts below (performed by GNU Backgammon) are the ones that in my opinion are the most interesting. This list includes all positions where GNU Backgammon significantly disagrees with Robertie; these are highlighted using BOLDFACE ITALIC. The other positions have been included for a variety of reasons. For example, in some cases, GNU disagrees with Robertie, but (in my opinion) only slightly; in other cases, Robertie and GNU agree, but GNU thinks there is another move that is almost as good as Robertie’s recommendation; in still other cases, GNU thinks that the doubling cube is not in the most logical position.
By Timothy Chow
http://math.mit.edu/~tchow/robertie/robertie501.html