In fact he did once hurl a stick to demonstrate the principles of immortality to a king, with rather disastrous results as the stick rebounded and killed the king. This is all neither here nor there as he was not a God and it is his connections with ZEUS that merit him a mention.
One of AMPHITRYON’s ongoing adventures was to rid the Theban countryside of a child-eating fox which could never be caught or killed. ZEUS, with ulterior motives, lent him a hound called Laelaps, which could catch and kill any animal it chased. You can see the unresolved equation here can’t you?
After much amusement at AMPHITRYON’s dilemma, ZEUS resolved the matter by turning both animals into stone. This then freed up AMPHITRYON to chase up some stolen cattle and fight an immortal thief who had one vulnerable hair on his head, which involved some plucking involving the thief’s daughter.
Whilst all this was going on, ZEUS homed in on Mrs Amph, who was called ALCMENA, his Tryon outfit duplicating AMPHITRYON to perfection so he could have his willful way. Did any God have more willful ways than ZEUS?
The resultant proof of ZEUS’s fertility was the birth of HERACLES. When AMPHITRYON put in an appearance as ZEUS was leaving by the back door, ALCMENA was very surprised that he wanted to do it again so soon, but luckily made no comment. When she gave birth she had twins and HERACLES brother was named IPHICLES.