Those 'set' operations ...

Please note that the term "set" is used very loosely in this post. :)

... a suit like "AKQxxx" is valid but one like "AAKxxx" is not. (There is only one Ace of spades ....)

This seems like a two-phase problem. Once you verify that a string is in a standard format with, say, no character occuring twice, it may be very easy to count characters unambiguously.

Within reasonable limits, a single regex could be very handy for verifying that a string:

• has min to max characters from a given set of characters;
• that the characters in the string are only from the set;
• that each character from the set occurs only once in the string; and
• that the characters in the string are in a required order.

It may be enough just to verify that no character occurs more than once in a string. For that,
    length $string == uniq split '', $string
or
    $string !~ m{ (.) (?= .*? \1) }xms
does the trick.

And there are many other conceivable approaches, all depending on your precise requirements.

Update: Added another simple no-repeat test.

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