Agathodemons take the form of winged serpents. [1, 2]
Some Agathodemons guard the physical home and those that live there.  In such an abode, those that reside in the home would provide an offering of wine for the guardian.  Many of the later accounts of Agathodemons consider them as spirits instead of physical entities. 
Depending on the account Agathos Daimon translates to "Good Demon"  or "Good Divinity." The latter translation is likely due to another Greek entity referred to variously as Agathadeamon, Agathodiamon, and Agathos Diamon. This is the deity of health, good fortune, and life and husband to Tyche Agathe.  Many of his attributes likely color those of the Agathos Diamon.
The possible inheritance from Agathodiamon, married to Tyche Agathe, connects to the Oracle of Trophonius.  Anyone that desired to speak with the Oracle of Trophonius had to stay in a house consecrated to Agathos Daimon and Agatha Tyche (Good Demon and Good Luck) for several days while observing the rules of purification. 
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