Backgammon is a game consists of a box, chips and dice where players will move in the bays of the box according to the number they get when rolling the dice.
In Islam, the default assumption about games and amusements is that they are permissible. This is the case for any game or amusement, as long as it does not distract a Muslim from religious obligations, worldly duties and the remembrance of Allah, and as long as there is no specific textual evidence prohibiting it.
With respect to the textual evidence, a Muslim is supposed to obey Allah and His Messenger (peace be upon him) even if doing so might go against that Muslim's personal desires and even when he or she might not understand the wisdom behind the particular command or prohibition.
Therefore, we have two principles which we can approach the question of backgammon. In light of these principles, we need to consider that the Prophet (peace be upon him) said: "Those who play backgammon, it is as if they have immersed their hands in the flesh and blood of swine." [Sahîh Muslim (1770)]
Also, it is related from Abû Mûsâ al-Ash`arî that he heard the Prophet (peace be upon him) say: "Whoever plays backgammon has disobeyed Allah and his Messenger." [al-Muwatta' (2/958), Sunan Abî Dâwûd (4938), and Sunan Ibn Mâjah (3726)]
Though this second hadîth does not reach us with a strong chain of transmission, some scholars, including al-Albânî, have deemed it to be a good (hasan) narration in consideration of how various lines of transmission support one another.
On the basis of these two hadîth, the majority of scholars have concluded that playing Backgammon is unlawful in Islam. There have even been a few scholars who claimed this to be a matter of juristic consensus (ijmâ`).
Abû Hanîfah and his colleagues deemed the game to be forbidden. So did Mâlik and his main students. This was also the view of Ahmad b. Hanbal.
As for al-Shâfi`î, the established narration from him is that playing backgammon is disliked. His students differed as to whether he meant that it was disliked in Islam to the point of sinfulness or simply frowned upon. [Refer to al-Mâwardî, al-Hâwî al-Kabîr (17/187)]
There were a number of scholars who saw nothing wrong with playing backgammon in and of itself. They also acknowledged the above-mentioned hadîth. However, they understood the Prophet (peace be upon him) to be referring to playing backgammon for money. It was the prevalent practice during the Prophet's time to gamble with backgammon. It was almost never played merely for amusement.
These scholars are applying the principle of specifying the general wording of a text in accordance to the dictates of the general circumstances in order to get at the intended meaning. This view of backgammon was held by many eminent Successors, including Sa`îd b. al-Musayyib, al-Hasan al-Basrî, `Abd Allah b. al-Mughfal, al-Sha`bî, and `Ikrimah. [al-Istidhkâr (8/461]
In my opinion, the textual evidence is strong and its apparent meaning is that playing backgammon is forbidden. At the same time, it is a strong argument that this prohibition is qualified to refer to the practice of gambling with backgammon, especially since the Successors who held this view were known for their piety and asceticism. This view is also in conformity with the general ruling on games and pastimes that they are lawful, while still acting upon the texts.
At the same time, a believer should give unqualified wording of the texts the respect it deserves. Leaving off this particular game is certainly the more cautious option, especially when there are so many other games available. It is possible that there is a particular quality of backgammon that makes it objectionable from an Islamic perspective.
For instance, some Muslim jurists have speculated that the game might have its origins in Zoroastrian religious beliefs, with the alternating black and white zones on the board representing the dualism of good and evil, with the number of trqacks representing the general constellations and the overall shape symbolizing the concept of divine compulsion.
And Allah knows best.