Follow-up: a quick Googling gave me this.
But you don’t know if the coins used at that time showed any tails?
I’m afraid I can’t see the logic in calling a backside tails. Humans don’t have tails, they have a butt, so it would either be “head or butt” or “Head or feet” if you want logically. Usually it seems to be what’s on the other side of the coin, though - “Heads or number” or “Head or [whatever]”.
shrug To me, it doesn’t seem odd at all. “Tail” is, indeed, used for “butt” in English sometimes. “Tail” as an opposite to “head” is common in English. The “head” of a line vs the “tail” of a line. A passage from Deuteronomy 28:13 “And the LORD shall make thee the head, and not the tail; and thou shalt be above only, and thou shalt not be beneath.” " I had never actually thought of “head” and “tail” as literally meaning a head and tail, but rather meaning “front” and “back.”
Besides, the more interesting question for me is why is it always in the plural?
Ffynes-Clinton’s Welsh Vocabulary of the Bangor District gives “cing ta brits.” Cing is the English word “king” (the Welsh for “king” is brenin and he defines brits as “‘the figure of Britannia on the reverse side of copper coins’; only used in phrases connected with tossing coins” but since it is pronounced bridge I wonder if it’s “king or bridge” — anyone know if there was a British coin with a bridge on the back in the Victorian era? I know there was a Britannia, but that seems far-fetched. Otherwise, it seems to be “tu blaen neu tu chwith,” literally “front side or back side.” Chwith is “left” and by extension both “back” and “wrong, strange” (cf. sinister).
It has a Mayan calendar shaped like the Sun on the reverse side. There’s a Cantinflas movie called Águila o sol (1938, one of his earliest films), so I guess it’s a fairly common expression.
In Norwegian it’s kron eller mynt, i.e. crown or mint. The defining part being mint, the side the value is marked on. But some people don’t know this and use the expression wrong when the coin has a crown or crowns on the same side as the value.
In Japanese it’s omete (front) or ura back.
People don’t have heads at one end and tails at the other, but lots of common farmyard and domestic animals do. Coins don’t represent people but they do represent property, and farm animals were an important form of property, so it makes more sense to personify a coin as an animal than as, well, a person.
The monarch’s head on one side of a British coin is a pretty ancient and unvarying practice. The other side, however, could have a variety of designs and inscriptions; there was little or no commonality about what these might be. Hence it was easier to specify the obverse of a coin as “not the head” or “opposite the head” than by reference to what was on it, and “tails” worked for that purpose.
There is a fair amount of variation in Latin American countries, besides the “aguila o sol,” which is unique to Mexico. The generic one is “cara o cruz” (face or cross).
Heads is always face, but Wikipedia lists a bunch of variations for the tails:
escudo (coat of arms), corona (crown), sello (seal), numero, letra (words), ceca (mint).
Tail, as a general antonym for ‘head’ is faily general though - ‘top to tail’ is a less common variant of “top to toe”, likewise “head over tail” and “head over heels” - ‘tail’, as well as meaing tail, also just means the trailing end of something, or the opposite end from the head.
In a modern context, there is a pair of *nix commands called head and tail, which return the first or last few lines respectively, of a file.
In the context of coinage, some British coins do/did have tails on the reverse side, for example:
The modern decimal 10p piece has lions on it (each coin in the set has a segment of the Royal Shield - the 10p has the top left part, and shows a pair of lions passant). Previous versions all the way back to decimal day had a single lion.
Sovreigns and Silver Crowns had a horse and rider (the horse with conspicuous tail)
Half Crowns had a depiction of the Royal Shield, with a total of 7 lions on it.
Shillings had a lion, Some Farthings (albeit later ones) had a wren Guineas had several different shields or crests, all with lions, and so on.
It’s not a question of language – as many of the above replies illustrate, it often depends upon what’s on the coin, or local slang. So the reply in Mexico might be different from that in Spain, from that in some country in South America.
In one of C.S. Foresyer’s Hornblower novels, set in the British navy in the Napoleonic era, one officer asks another to call “Ace or Spade” before flipping a coin.
Well, the answer for Spain is the same one Erdosain mentions as the generic one: cara o cruz.
While there are dialectal variations, I don’t think it’s any more wrong to say that “in English, it’s ‘head or tails’; in Spanish, it’s ‘cara o cruz’” than it is to say “in English it’s ‘thank you’, in Spanish it’s ‘gracias’”.
If we insist that humans do not have tails and the rear end of a human can’t be called a tail, then the expression “chasing tail” has frightening new meanings.
Schvantz I win Stucke you win.
Voof.
Yes, because language and expressions have to be logical, the way calling the part of the body where we have a tail bone the tail isn’t, and calling the floppy part opposite the butt a Schwanz is.
I know that languages aren’t logical. I just had a problem with it being presented as “Completly logical of course”.
If tails as opposite to head even for humans has indeed a long history in the English language, but other examples have fallen out of use, that’s an explanation that makes more sense to me.
And calling the penis a Schwanz= tail: well you can waggle it much better than the vestigial tailbone humans have. 
“One logical opposite” is how I personally phrased it, and it is, indeed, a logical opposite of “head” in English, not just in literal usage, but in figurative usage.