1) AGADAH: QUEEN ESTHER, AND A NIDAH WHO WALKS BETWEEN TWO MEN
The Gemara says that if a woman walks between two men while she is a Nidah, a tragedy will result. If she has just begun her state of Nidah, one of the men will be killed. If she is near the end of her flow, a quarrel will arise between the two men.
The VILNA GA'ON (Kol Eliyahu 142) uses this Gemara to explain why Queen Esther invited Haman to join her and the king at the first dinner she made in the king's honor, as part of her plan to persuade him to rescind the decree against the Jews. Since she had no intention to reveal her identity as a Jew or to beseech the king to save her people from the evil plot of Haman until the second meal, why did she invite Haman to the first? The Gemara in Megilah (15b) provides many possible explanations for Esther's conduct.
The Vilna Ga'on writes that "had I been there, I would have added another reason why she invited him." The Gemara in Megilah (15a) says that when Esther heard the news of Haman's plot against the Jews, it shocked her so much that she became a Nidah. Three days later, she made the first dinner party for Achashverosh and Haman. Her motivation was to invite the two of them and to situate herself, a Nidah, between them. If she was at the beginning of her state of Nidah, then one of them would die, and the decree would be annulled. (The Gemara in Ta'anis (29a) says that when the senate issued a decree, if one person in the senate would die, then it would be taken as an omen that the decree must be annulled. However, it is not clear that this rule actually applied in the case of Haman, because it is evident from the Megilah that his death did not cause the decree to be rescinded, since the decree was signed with the king's signet and it was necessary for the king himself to repeal it.)
If she was at the end of her state of Nidah, then a quarrel would arise between Achashverosh and Haman, and again Achashverosh would rescind the decree. Either way, the decree would be revoked as a result of Esther's strategy. (In the end, her strategy was successful in both ways. A quarrel erupted between Haman and Achashverosh, and Haman was killed.)