I've been searching for the answer of the origin/ history of pub games in British pubs. However, this is what I've encountered in some different sources ( including Wikipedia):
In his book, Beer and Skittles, Richard Boston claims that the first regulation concerning national control of pubs was about pub games; Henry VII's statute of 1495 restricted the playing of "indoor games which were distracting Tudor pubmen from archery.
That being said, the time the first pub games were played isn't mentioned anywhere, so I wonder when and where were pub games first played? Why are games an integral part in pub culture in Britain historically? (besides some reason like games are for fun).