Which means that it starts after sundown, on Saturday.
Which means that the 13th of Adar is Shabbat. Which means that the Fast of Esther is pushed back to the 12th of Adar. Which means that the 13th is Yom Nicanor.
I hate Yom Nicanor. I much prefer the Fast of Esther.
(Quick recap: Alexander the Great dies. His empire falls into bits. Each of those bits is still "Greek" in culture, but is its own little thingy. One of the Greek-Flavor Mini-Empires was the Selucid Empire, based in Syria, and the dynasty that was in charge of that chunk at the time of our story were a bunch of guys named Antiochus. Antiochus IV had, for a number of reasons that seemed like a good idea at the time, invaded Israel/Judea to find their weapons of mass destruction and depose their dictator. They didn't have weapons of mass destruction, OR a dictator, so they decided it was high time they made both, and they did. The Syrian army marched in and captured Jerusalem, where they were greeted as liberators. And then a fundamentalist cleric from one of the rural villages became the leader of an insurgency. His sons act as warlords, but, of course, they can't stand up to the Syrians in combat, largely because, back in Antioch, most of the people are driving around in their giant carts with yellow ribbons saying "SUPPORT OUR TROOPS" on them. That, however, doesn't keep the insurgency from killing the Syrians piecemeal. However, the insurgents DO manage to win one battlefield engagement, on the 13th of Adar, against the Selucid general "Nicanor". And then the fundamentalist clerics declare that Adar 13 will be known as "Yom Nicanor" forevermore, to remind people of when they kicked Selucid butt. After the Selucids left, the fundamentalist cleric's family became the new dictators, since they didn't have dictators before, and they did the kind of good, careful, and just management of the country that you expect from religious fundamentalist dictators. This, of course, made Yom Nicanor deeply embarrassing to the non-fundamentalist religious leaders who came later, and who instituted a fast day on Adar 13, to wipe out the embarrassment of Yom Nicanor. Of course, about one in every seven years, that fast day lands on the Sabbath, and you can't have minor fast days on the Sabbath, so the fast day moves -- and once it moves, BANG! there's Yom Nicanor.)