Born between 11pm and midnight: which day is yours?
A BaZi chart’s day pillar is the day you were born, and its stem is your day master, the part of the chart that stands for you. For a birth between 23:00 and midnight, schools disagree about which day that is, so they can give two different day masters.
What decides it is the sun, not the clock. In Kuala Lumpur the sun runs about an hour behind the clock: a birth at 00:30 on 15 June 2000 was, by the sun, 14 June 2000, 23:16, the late Rat hour of the day before. The site’s default gives it the day pillar Water Rabbit (Gui Mao, 癸卯); the other school gives Wood Dragon (Jia Chen, 甲辰).
What the two schools say
The Rat hour runs from 23:00 to 01:00. The late Rat hour school (Wan Zi Shi, 晚子时): the day changes at midnight. From 23:00 to midnight is still the day you were born, but the hour’s stem is counted from the next day, so the hour pillar is already the next day’s first. This site uses that school by default.
The day starts with its Rat hour (Zi Chu Huan Ri, 子初换日), at 23:00: a day begins with its Rat hour, so at 23:00 it is already the next day, and the day pillar is the next day’s.
Both give the same hour pillar. They differ only in the day pillar, and the day pillar’s stem is the day master, which the whole reading is built around.
What the classics fix
None of the classical works this site reads says in so many words which day 23:00 to midnight belongs to. What they do fix is how each hour’s stem is counted from the day’s stem, with the Rat hour first:
遁时如甲子日子时生人即甲己，还加甲，便知子时乃甲子，丑时乃乙丑，顺行十二时。
For the hours: someone born in the Rat hour of a Jia Zi day — Jia and Ji days “start again from Jia” — the Rat hour is Jia Zi and the Ox hour Yi Chou, and so on in order through the twelve.
San Ming Tong Hui (三命通會), volume 2, On Counting the Months and Hours (论遁月时)
If the Rat hour is the first hour of a day, the day begins at 23:00, which is the second school’s answer. Under this site’s default, the 23:00 hour carries the next day’s stem, so that day-and-hour pair is not one of the 120 the same work reads hour by hour; a chart in that hour is told so rather than given someone else’s passage. Both schools are in use, so this page gives both answers.