Click on this link for a list of all the Ebay categories (it's a big 388K page):

http://listings.ebay.com/aw/listings/overview.html

It shows all the categories, arranged hierarchically, with the # of current items listed in ( ).

However, on my Netscape browser, I can roll over each category and preview the URL in the window at bottom of the screen. It contains the category # as part of each URL (for example, the first listing for Antiques & Art: General is category # 12).

If you want / need ALL the category #'s, it's probably easiest to print out the page, then preview each category # and write it down on the print-out.

For the casino categories, go to Collectibles (1st column toward bottom), then Casino...
FYI, the 4 casino categories are:
General #573
Chips #899
Strikes #3443
Tokens #3512