When Rosh Hasana is on a Thursday then Asara b’teives will usealy be on a Thursday too, however if Cheshvan and Kisleiv are both 30 days like this year then Asaras B’teives will be on a friday. This is correct with Assoro b’Teves coming out on Friday Erev vaYechi; But this also transpires when Rosh haShono is on a Shabbos and both Cheshvon & Kisslev are 29 days, then Assoro b’Teves will also be on a Friday, but Friday Erev vaYigash.
Hence Assoro b’Teves comes out on a Friday approximately 20% of years.
In 10 & 11 years time {5784 & 5785}, will be 1st time in 51 years, that Assoro b’Teves is 2 years running on a Friday. That last happened 51 years before this upcoming occurrence, and will again happen 47 years after that.
What is also pretty rare (like this year) is saying “v’sayn bracha” on Chanukah….That happens every leap year.
on 1st nite of Chanukah and even then, not all Hebrew leap years. But by 7th nite of Chanukah, much rarer. But what is even rarer and in fact the rarest of all Amidas, is what happened on 7th nite of Chanukah 1994, having Atto Chonantonu, veSen Berocho, Yaaleh veYovo & Al haNissim all combined in the same Amidah, something which often only transpires once every 95 years, so even rarer than Birkas haChamo or Assoro b’Teves 2 years running on a Friday.
In the UK, not only the fast ends early, it starts around 6.15am However in Paris which has Savings time in winter & double savings time in summer as do all European countries except UK & Ireland, Assoro b’Teves commences just before 7AM.