Does the English idiom “Heads or tails” when flipping a coin (to randomly determine between two options, when such a need arises) exist in other languages? Do Spanish speakers call “cabezas o colas”? Germans “kopf oder schwanz”? Etc. etc. etc.
NOTE: I got the German from Google translate, so if I’m wrong, blame Google. 
I believe it’s cara ou coroa in Portuguese: “Face or Crown”
The French expression is “pile ou face”. The “face” refers to heads. I’m not sure where “pile” comes from. Curse you for making me wonder.
In Québécois slang there’s also the less-PC “tête ou b*tch”. The literal translation of “head” is “tête”.
It’s “Kopf oder Zahl” (Head or Number) in German. The German word Schwanz means both tail of an animal or slang for penis, so you might want to avoid using wrong translations like Google. (And I am blaming Google for not knowing established phrases. Dumb thing.)
Why is it tails in English, anyway? Head of the King or Queen on one side, number of value on the other side - makes sense. Later, it’s a picture on one side, number smaller. But why tails?
In dutch its “Kop of Munt” translate into heads or coin
In Thai, one side is หัว (Head) and the other ก้อย (Little finger, little). Google translates ก้อย to “reverse side”, but my informants (two Eurasian teenagers raised in Thailand by Mrs. Septimus and myself) are unaware of any “reverse side” usage except with coins.
It probably relates more to the local currency than the language. And maybe not even the current local currency. When I was growing up in Mexico, it was Eagle or Sun. All Mexican coins had an eagle on one side, but I don’t recall any that had a Sun on the other.
tête ou b*tch
I don’t understand this.
If tête is referring to the Queen, then who’s the bitch? Or, conversely, if the Bitch is the Queen, then why is the reverse side being called tête?
In Hebrew, it is (or was) “Crowns or feathers” based on the obverse and reverse of the coins.
Mexico: “Aguila o sol?” That is, “the eagle or the sun?” Because, well, traditionally there was one on one side of a coin, and the other on the other.
Generally what is being flipped is a quarter. Until the state quarters started it was George Washington on the front and an eagle on the reverse. Why ‘heads or tails’ rather than ‘heads or eagle’? WAG: they’re the same number of syllables, and tails sounds like a good reverse of heads, being on the opposite end of a critter.
Are you sure it’s an AE expression, and not a general English one? Because otherwise, you need an explanation before US quarters.
After all, the German Mark didn’t usually show heads, either. The expression has been around some time, so it’s based on old coins.
You are correct. “Tails” in the sense of the non-head side of a coin, has been around since around 1680, according to etymonline.com:
That said, “tails” sounds like one logical opposite of “head” to me, so it being used for the backside of a coin doesn’t sound odd to me at all.
It exists in at least 5 indian ( Asian) regional languages I know.
It is an old phrase in English.
Here’s a math book printed in 1776 that uses tails to refer to the back side of a coin when talking about the possible outcomes of tossing 11 halfpence.
Here’s a play, “The Atheist” by Thomas Otway, originally written in 1684 (the linked copy printed in 1726) that also uses the phrase:
So for origins of the English phrase I think it has to go back to England and their coins.
That sounds like it comes from “tête-bêche”, sometimes used in English to refer to a pair of stamps printed upside down relative to each other.
That makes two of us. But “tête” is the queen’s side, I’m pretty sure.
ETA: I like Giles’ hypothesis.
And just because old cites by famous people are liked: Alexander Pope used it in 1727 in “Peri Bathous, or the Art of Sinking in Poetry,” the essay which introduced the word bathos.
But “head or penis?” would make flipping a coin so much more interesting. 
In Hebrew (in Israel) it’s “Etz o Pali” - “Tree or Pali”, with “Pali” being short for “Palestine”. My guess is that it refers to a specific coin that was in circulation sometime between 1918 and 1948.
Anyway, the Tree is the picture, and the Pali is the number.