It would be best to begin with a definition:
able-whackets. A popular sea-game with cards, wherein the loser is beaten over the palms of the hands with a handkerchief tightly twisted like a rope. Very popular with horny-fisted salts.
The Sailor’s Word-Book, by William Henry Smyth, 1867.
There were many such rough and spirited games to while away time on board ship, including High Cockalorum, Sling the Monkey and Baste the Bear, of the last of which one observer commented that it was “a recreation of which nobody tired except the unfortunate actor who was cast for the bear.”
This is a more detailed contemporary description:
And here I may relate our game of Able Whackets. The cards called “good books”; the hand, “flipper”; a handkerchief tightly braided up, “good money.” At the loss of the game he that was the winner would say, “I demand the good money,” and to the loser, “Hold out your flipper: this is for the loss of the good game called Able Whackets, and a precious hard thump”; another would say, “This is for the same,” and so on all round.
Recollections of My Sea Life from 1808 to 1830, by Captain John Harvey Boteler, published by The Navy Records Society in 1942.
It was a particularly suitable game with which to tease a gullible greenhorn, such as a young midshipman. One ploy was to insist that the correct names were used for everything associated with the game. As well as those Captain Boteler listed, the board of green cloth was the card table and to stand able meant you claimed a winning hand. A miscall of one of these terms resulted in every other player around the board of green cloth beating the offender’s flipper with the good money.
None of the many descriptions explain the card game itself. Though it was clearly of secondary importance in the gulling of the unwary, it must have had some rules, but we’re never told what they were. This tells of the end of another game:
The victim was called to receive punishment. Murray having demanded the “good money,” desired him to hold out his flipper, and he began, “This is for the loss of the good game called Able Whackets, this is for the same, and this is for my standing Able and your losing the game;” and at each time fell a stroke which nearly cut his hand off. At the expiration of this, Weazel withdrew his hand to offer it to the next. “Avaust there!” said Murray; “hold out your flipper again!” and he received three more most powerful cuts for Weazel’s having stood Able and having lost the game.
The Arethusa: A Naval Story, by Frederick Chamier, 1837.
We may presume that standing able provided the first part of the name, perhaps with a nod to the rank of able seaman in the Royal Navy. The second part must surely be from whack or thwack.