Praise be to Allah.
It is not permissible to play backgammon because it involves the use of dice which are haraam and emphatically forbidden, because of the report narrated by Muslim (2260) from Buraydah (may Allaah be pleased with him), according to which the Prophet (peace and blessings of Allaah be upon him) said: “Whoever plays with dice, it is as if he dipped his hand in the flesh and blood of a pig.”
Dice are the small cubes on which numbers are written and they are played with.
Al-Nawawi said in his commentary on Muslim: … This hadeeth is quoted as evidence by al-Shaafa’i and the majority of scholars for the prohibition on playing with dice. What is meant by “dipping his hand in the flesh and blood of a pig” is if he were to eat them, so this prohibition (on dice) is likened to the prohibition on eating (the flesh and blood of a pig). End quote.
Abu Dawood (4938) and Ibn Maajah (3762) narrated from Abu Moosa al-Ash’ari that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Whoever plays with dice has disobeyed Allaah and His Messenger.” Classed as hasan by al-Albaani in Saheeh Abi Dawood.
It was also narrated by Ahmad (19519) in the words: “Whoever plays with cubes (dice) has disobeyed Allaah and His Messenger.” Classed as hasan by al-Arna’oot in Tahqeeq al-Musnad.
These ahaadeeth indicate that it is haraam to play with dice, so every game which involves playing with dice is also haraam, and that does not apply only to backgammon.
Ibn Qudaamah (may Allaah be pleased with him) said in al-Mughni (10/171): Chapter on games: Every game which involves gambling is haraam, no matter what game it is. It is the gambling which Allaah has commanded us to avoid, and the one who does that on a regular basis, his testimony is to be rejected. That which is free of gambling is the game in which there is no payment by both sides or either side. Some of these games are haraam and some are permissible. That which is haraam is games with dice. This is the view of Abu Haneefah and most of the companions of al-Shaafa’i. End quote.
Al-Zayla’i narrated that there was consensus that it is haraam to play with dice. Tabyeen al-Haqaa’iq (6/32).
It says in Fataawa al-Lajnah al-Daa’imah (15/210): It is not permissible to play with dice even if that does not involve prizes, especially if it distracts one from praying on time. So it is essential to refrain from doing that, because it is the kind of entertainment that is haraam. End quote.
This is the ruling on playing backgammon in general. If in addition it involves betting, false oaths or distracting people from prayer, then it is even more haraam.
And Allaah knows best.