Giving Sadaghah (alms-giving) is a Mustahab (recommended) act in Islam and according to the traditions it has so thawab (reward).
For instance, look at the following hadith from the Prophet (pbuh) regarding Alms.
The apostle of Allah (pbuh) said:
The alms(al-Sadaghah) will remove the plagues (Aafaat) from its owner and removes the torture of the day judgment.
Bahar al-Anwar, Vol.96, Pg.129.
Or likewise there are so many other traditions which point out the rewards of almsgiving.
But I was wondering if it is permissible to give alms to the addicts? And likewise if Allah will give us all of its thawabs which mentioned in many traditions in the case that we give it to the addicts as poor people?
(I inquired this question because we can guess (not sure) that addict people will waste their money to buy narcotic substances..)