In the original story, Loki was despised by a lot of Gods and Goddesses for his behavior and trickery. His mind games were no match for anyone even for Ra's third eye because Loki never lied, he only messed with people's minds with his words.
Loki's slyness was the reason why he was one of the Major Arcana, The Fool. Although there was no strongest or weakest amongst the Major Arcana except for The World, The Fool was limitless since the number that represent The Fool was zero. With that being said, The Fool had no worries because there was nothing to lose in the first place.
Ra would accept Hera's offer after Loki managed to anger him and made him act rashly during the meeting as Loki reported. The offer that Hera proposed wasn't half bad, it was even a good deal if Ra thought about it because even if he lost, his reputation would rise for helping them.