The 4th edition of Baumanns' Collecting Antique Marbles included new chapters on carpet bowls. That's why the edition was recommended to me when it came out and I got it right away. I should study it more! I wrote to the author of the carpet bowl sections, Roger Matile, and he gave me some info to share, all his words from here:
Full sets of ceramic carpet bowls varied a bit, but in general they included four to six pairs of matched bowls and a white jack that might or might not have a logo on it. Logos were generally those of the companies selling the sets, not necessarily the logos of the potteries that manufactured the bowls themselves.
I'm attaching a photo of my own full set for comparison to the one on your web site, which appears to be half a full set of bowls that has seen fairly extensive use. Interestingly enough, the bowl patterns provided by your reader are a close match to the ones in my full set, which came from the auction of the contents of a Canadian fishing lodge.
Sets were generally divided equally between pairs of sponge-printed and lined bowls. The bowls your reader shows are crosslined and crown patterned.
For a full rundown on carpet bowls, including the game itself and bowling carpets, see the four chapters I wrote for the fourth edition of my friend Paul Baumann's "Collecting Antique Marbles," published in 2004. Here's a link to it on Amazon: https://www.amazon.com/dp/B0056JSKWA/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1