This seems to be a BrE/AmE distinction – is it?
And do Americans use the phrase with more of a mystical Tarot card slant, compared to its British English meaning of simply 'likely to happen'?
Learn English – In the cards or on the cards
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Best Answer
The Cambridge Dictionary of American Idioms says both forms (in and on) are used, and that the origin is in Tarot:
But, despite the mystical origins, in both the US and UK, the idiom simply means "very likely to happen":
Note the the very American bent to the first example (not to mention this is the "Cambridge Dictionary of American Idioms").
On a personal note, I've never heard "on the cards" used here (East Coast of the US), and somehow it sounds illogical to me; I understand "in the cards" to mean "in the reading of the cards", or "in the forecast of the cards", that is, the cards somehow contain the prediction in a metaphorical, abstract sense. A commentor (Jon Jay Obermark) also mentioned that in the American Midwest, the phrase is understood as relating to playing cards (in particular poker), and "in the cards" means "[inevitably] due to the arrangement of the deck prior to it being dealt", which also calls for the "in" (because the deck already contains the outcome).
By contrast, "on the cards" strikes my ear as firmly locative (the only thing I would expect to be on the cards is a stack of poker chips holding them down, or maybe some mustard).