Commentary for Avodah Zarah 50:19

The Mishnah states that a Jewish woman should not be left alone with a non-Jewish man. The question is—how does this differ from the rule with regard to being left alone with Israelites? The Mishnah in Kiddushin rules that a woman should not be isolated with a Jewish man. Therefore, the prohibition here must refer even to three idolaters. While she can be alone with three Jews, she cannot be alone with three idolaters. [Rashi explains that the Talmud says “three” and not two because a woman is always allowed to be isolated with three Jewish men. Sometimes, she may not be isolated with two. For instance, if they are on the road. If one needed to go to the bathroom, she would be isolated with one].

It is prohibited for Jewish women to be isolated with loose Israelites, those who would not be ashamed to have sex with her in front of other men. This is true no matter how many there are. Thus again we are faced with the question—how does the rule for isolation with non-Jews differ from the rule concerning isolation with Jews?

There is a leniency in the laws of seclusion—if a man’s wife is with him, another woman may be isolated with him and his wife. The idea is that the man will have some sense of shame in front of his wife and will not come to have sex with another woman. This, according to this sugya, is true for Israelites but does not apply to non-Jews. They will have sex with another woman even in the presence of their wives.

The Talmud asks why we fear that the idolater might have sex with her but do not seem to be concerned that he will kill her.
R. Yirmiyah limits the rule in the mishnah to a woman who is important. In such a case they should not be isolated lest they have sex. But we do not need to fear that he will murder her because he would be afraid to do so.
R. Idi says that women have a way of defending themselves from murder. According to Rashi, this refers to her ability to seduce him. Once he is seduced he will not want to murder her.

This line of the Talmud is very difficult to explain and there are many opinions among rishonim as well as many different readings of the text itself. I will explain according to a dominant opinion which reads the Talmud slightly differently—“ a woman who is considered important among women but not among women.” To R. Yirmiyah, since she is not important among men, meaning she does not have strong ties to the government, she might be murdered. But to R. Idi, all women have their own protection, so we do not need to worry about murder.
Rashi has an entirely different explanation, but since he is universally rejected by later commentaries, I have not explained according to him.

The key phrase here is “even though she is in a state of peace.” This implies that even though she will not be murdered, she still should not be alone with them for fear of fornication.

All of these are precautions that an Israelite should take around a non-Jew so that the non-Jew will not be able to act violently against him.
If the idolater has a sword, and is right-handed, then the sword will be on the non-Jew’s left, and the Jew’s right. The Israelite will thus be able to prevent the non-Jew from drawing. But if he is holding a stick, then it will simply be in the non-Jew’s hand. Better to keep him to the left, so that he could feel if the non-Jew makes his move.
The Israelite should always be on the higher ground, where it is safer to defend oneself.

If the idolater asks the Jew where he is going, he should tell him he is going further than he actually is. This way the idolater will think he has more time to kill him, and the Jew will be able to make a quick getaway. This is what Jacob did when travelling with Jacob—he told him he was going to Seir, but he got off the road at Succoth, which was earlier.

In this story, the students of Rabbi Akiva fulfill their teacher’s instructions and lie to the bandits who meet them on the road.

This story involves the thieves of Babylonia. In the story, the thieves pay a price when Rav Menashe puts them under the dreaded ban.
In the end, the Bavli notes how much greater the generally violent robbers in the land of Israel are than the mere thieves in Babylonia. The robbers praised R. Akiva for his sound advice, whereas the thieves cursed R. Judah.