Bill Mullins wrote:
The Magicpedia article quotes a version of this tale from Oct 1776. It also appeared in the Edinburgh Advertiser
of Aug 6 1776 (from Newspaperarchive.com) as well as The Universal Magazine
of Aug 1776.
But it may go as far back as 1763.
In those books published in 1770s, there is a sentence saying that the soldier then continued as follows: when I count the number of dots in a pack of cards, there are 365; so many days are there in a year.
This suggests that the joker was already introduced by that time because a 52-playing-card deck has 364 dots, and the joker must have counted for an additional dot.
However, according to the Oxford Dictionary of Card Games, David Parlett, pg. 104 and A History of Playing Cards and a Bibliography of Cards and Gaming, Catherine Perry Hargrave, pg. 345, the joker was originally introduced in about 1860 and 1870s respectively, although a 52 card pack was certainly introduced far before 1700s.
So, I wonder how the author of the Soldiers Prayer Book counted for the additional dot without the joker.