What the idiom dictionaries say
There appears to be a clear split in preference between British English usage and U.S. English usage on this idiom. Christine Ammer, The American Heritage Dictionary of Idiom (1996) offers this discussion:
in the cards Likely or certain to happen, as in I don't think Jim will win—it's just not in the cards. This term, originally put as on the cards, alludes to the cards used in fortune telling. {Early 1800s}
John Ayto, Oxford Dictionary of English Idioms, third edition (2009) agrees with Ammer that "in the cards" is simply a later variant of "on the cards":
on the cards possible or likely.
This phrase, a North American variant of which is in the cards, probably refers to the practice of using playing cards or tarot cards to foretell the future.
Cambridge International Dictionary of Idioms (1998) seems a bit less sure about the distribution of usage of the two terms than Ammer and Ayto are:
be on the cards British, American & Australian
be in the cards American & Australian
to be likely to happen[.] Tarot cards are a special set of cards with pictures on them, which some people believe can be used to find out what is going to happen in the future. - 'Do you think there'll be an election next year?' 'I think it's on the cards.' - (often + for) There are some big changes in the cards for next year.
But it agrees that in UK "on the cards" is primary form used. Perhaps in North America "on the cards" was influenced by "in the stars" (which seems to mean something similar when used as in Cassius's speech in Julius Caear, "The fault, dear Brutus, is not in our stars/But in ourselves, that we are underlings") to become "in the cards."
Early Google Books matches
I ran Google Books searches from 1700 forward for "on the cards," "in the cards," "not on the cards," and "not in the cards." One very early match for "[not] in the cards" appears in Charles Churchill, "Independence," in The Gentleman's and London Magazine (September 1764):
Had fortune on our getting chanc'd to shine/Their birthright honours had been your's or mine./'Twas a mere random stroke, and should the Throne/Eye thee with favour, proud and lordly grown,/Thou, tho' a Bard, might'st be their fellow yet,/But FELIX never can be made a Wit./No, in good faith—that's one of those few things/Which Fate hath placed beyond the reach of Kings./Bards may be Lords, but 'tis not in the cards,/Play how we will, to turn Lords into Bards[.]
This sense of "in the cards" seems to be the the one that remains current today—namely, "destined to become reality"—but oddly enough, it uses in, not on, despite being a British instance. The first instance of "[not] in the cards" appears a generation later. From "New Parliament," in The London Magazine (April 1784):
But whatever may be the prospects of either party, the restoration of our affairs is equally doubtful. It has long been the familiar saying of one of our oldest and wisest statesmen "that it is not on the cards to save us." The plan lately adopted of fortifying our coasts against invasion ts an ominous circumstance. We are surprised it should so long have escaped the notice of declaimers of the times.
Here, it seems to me, the meaning is somewhat different: "on the cards" seems to mean "the responsibility of fortune," although the precise meaning isn't easy to deduce. In any case, both eighteenth-century examples seem to be referring to the practice of using playing cards to foretell the future.
The first instance I found of "on the cards" in the sense of "possible" is from "Chess without the Chess-board," in Fraser's Magazine (March 1840):
Book-players can solve a checkmate in eight or ten moves, perhaps, without touching the pieces ; but then they are told beforehand that the thing can be done,—that it is "on the cards."
A final point of possible interest arises in connection with a discussion of the game Minchiate in Samuel Singer, Researches Into the History of Playing Cards (1816):
"There is no game on the cards, of which I have any knowledge (says Mr. Smith,) that requires closer attention, or a more ready talent for figures, or greater exercise of the memory, than this of Minchiate.
The odd thing here is that the phrase "game on the cards" seems to be synonymous with "game of cards" or "card game." In fact Singer uses the wording "game on the cards" three times in his book, and "game of Cards" five times (only once with a lowercase c). I don't know what the significance of the difference in capitalization is, but in the instances of "game on the cards," the c is never capitalized. An earlier example of "game on the cards" appears in 1782, in the context of a description of a game called Lottery Tickets.
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Digression: What do British lords make of the expression 'on the cards'?
As Ammer suggests, in the cards is the overwhelming favorite among U.S. English speakers. I remember the first time I encountered "on the cards" because it arose in a legal opinion I was reading for a first-year Contracts class in law school. In Victoria Laundry v. Newman Industries (1949), Lord Justice Asquith permitted himself to use the phrase in order (he thought) to clarify the level of certainty he had in mind as a standard for cases of breach of contract:
It is indeed enough ... if the loss (or some factor without which it would not have occurred) is a 'serious possibility' or a 'real danger'. For short, we have used the word 'liable' to result. Possibly the colloquialism 'on the cards' indicates the shade of meaning with some approach of accuracy.
Or perhaps not. In Koufos v. Czarnikow (1967) the House of Lords took up the question of what Lord Asquith meant by "on the cards" and struggled a bit with the phrase's pungent odor of informality. Lord Reid made these points:
It has never been held to be sufficient in contract that the loss was foreseeable as "a serious possibility" or "a real danger" or as being "on the cards". It is on the cards that one can win £100,000 or more for a stake of a few pence—several people have done that; and anyone who backs a hundred to one chance regards a win as a serious possibility—many people have won on such a chance, ... It appears to me that in the ordinary use of language there is a wide gulf between saying that something is not unlikely or quite likely to happen and saying merely that it is a serious possibility, a real danger, or on the cards.
Lord Morris of Borth-y-Gest contributed this:
They ["Certain illustrative phrases"] are valuable by way of exposition, but for my part I doubt whether the phrase "on the cards" has a sufficiently clear meaning as to qualify it to take its place with the various other phrases which line up as expositions of the rule [governing breach of contract].
And Lord Pearce weighed in with this comment:
I do not however accept the colloquialism "on the cards" as being a useful test, because I am not sure just what nuance it has either in my own personal vocabulary or in that of others. I suspect that it owes its attraction, like many other colloquialisms, to the fact that one may utter it without having the trouble of really thinking out with precision what one means oneself or what others will understand by it a spurious attraction which in general makes colloquialism unsuitable for definition, though it i often useful as shorthand for a collection of definable ideas.
Moral of story: Don't anticipate smooth sailing for your legal reasoning if you've couched it in a colloquialism and if the reviewing board consists of a bunch of Peers.
Best Answer
to fire in the sense of being fired: Etymonline.com
and from the OED