Though backgammon is not European, the game's popularization and general ruling owe greatly to this part of the world - strategies included. Here is a summary of western influences on backgammon plays or strategies.
Backgammon is said to be a melting pot of several ancient European games squeezed into one. There's the Tric-trac, Ludus, Nard, and other rarely heard of games in the modern world. Hence, influences on backgammon plays date back from the ancient world to the present. The Greeks of old were fond of playing Ludus Duodecim Scriptorum which made use of lines that amounted to 12 in all. At a glance the game resembled backgammon in several respects.
In 1693 the royal princes of France were said to play a backgammon-looking game called Tric-trac. Nard was earlier introduced in history in Sicily by Arabs and is said to date back 902 AD. All these ancient games had similarities with how backgammon looks today and also have influences on backgammon plays. But nothing beats the contribution of the Roman Empire in the popularization of the game in all of Europe and other parts of the world where the empire's influence was enormous.
Backgammon those times became a household word, no matter the status of the family. It was enjoyed by the rich and poor, famous and infamous. Hence, the influences on backgammon plays broadened to include all sectors of society in the known world. Old English terminologies in the game could be traced back in to the infamous Crusades. Due to its prevalence the Church that time banned it through France's Louis IX. The Crusades and probably even the church all had influences on backgammon plays, especially in the conquering concepts of the game.
In 1526, however, numerous board games were burned. This was on the order of Cardinal Wolsay. At this point many influences on backgammon plays had probably been reduced to mere ideas. Nevertheless, some form or traces of the former strategies employed in the game had been restored. Being forced underground majority of the rules and strategies that had governed it could have been partially recovered.
When Queen Elizabeth came into the picture backgammon was revived out in the open. The rules and strategies had been restructured and formalized into standards and new influences on backgammon plays once more emerged. This became prevalent in England and France.
Today's backgammon is a result of those erstwhile influences on backgammon plays that prevailed through the centuries. It is a historical treasure.