I imagine that Professor Hoffmann’s card-game rule-booklet entitled Five Hundred is one of the scarcer booklets by Hoffmann. The Bodleian Library gives the year 1908 for that title, so that year presumably appeared on the title page, and it seems likely that 1908 was the date of the first edition. Independent of that, I have a copy of Hoffmann’s Patience With the Joker dated July 1st, 1907, on the title page. Five Hundred is not listed on the inside front-cover, which supports the idea that Five Hundred appeared after that.
I have never seen or heard of a copy dated 1908, apart from the one in the Bodleian Library.
Below is a scan of one of my two copies of the booklet. Since the first edition apparently was published in 1908, and since Goodall did not have a branch in Birmingham after 1912, this edition likely appeared during one of these years: 1908, 1909, 1910, 1911, or 1912.
I also have another copy of Five Hundred, which omits the title-page reference to Birmingham, and which shows Hoffmann’s real name and pen name on the title page. In an advertisement on the inside front-cover, it lists Rover Bridge and Outlaw Bridge, which I believe first appeared in or around 1917. Based on this information, and not on exhaustive analysis, it appears that my later copy dates from 1917 or somewhat later.