To venture a good guess.
The 'Provisional Patent Number' may be hard to search for but the '/32'. Could be for 1932.
J.G 7 could also be a company initial. Or the operators initials with a unit number.
(Bump)

Well, I don't know anything about the game type/era beyond what you've probably already found out, but if you'd like to go the patent search route, I can tell you that the number likely corresponds to a patent application beginning with GB19320036055, based on what I've seen of items with similar labeling and the "current" form application numbers that they correspond to. GB being country code for Great Britain and 1932 being the year of filing.

Unfortunately, neither Google Patent search or Espacenet turns up a direct match for that application number. That could either mean that it was an application that never issued as a patent, the old application hasn't been loaded online, or some other issue with the updated application number or search system.

Depending on how much time you want to dedicate, you could go here:

http://worldwide.espacenet.com/advancedSearch

and search for application numbers beginning with "GB1932" and a publication date range of "1932:1934" (most applications of this era were published within 2 years of filing). That nets a TON of results, but you can try limiting it to patents in English and play around with key words in the title to narrow things down somewhat. Things like: game, machine, amusement, etc.

Hope that helps.

I couldnt find a match in 1931 or 1932 in ipdb

working thru 33 but it seems earlier than that

--Jeff