Peace be upon you.
Grand Ayatollah Sayyid Sistani (may Allah protect him):
Playing with gambling instruments such as chess, backgammon, and dice is prohibited when there is a stake involved, and taking a stake is also forbidden. The winner does not own the stake.
As for playing without a stake, it is prohibited for dice and chess.
Grand Ayatollah Sayyid Khamenei (may Allah protect him):
It is not permissible to play backgammon, which is considered a gambling instrument, even without a stake.
May you be successful in all good.