The phrase ‘not playing with a full deck of cards’ or ‘one card short of a full deck is a familiar one which I’m sure needs no explanation of meaning, however, there is a bit of a debate on where these phrases actually come from. Some say the idioms came out of the 1950s, yet they fail to explain how that came to be just that some of the first recorded usages were around that time. There is another story circulating though about these phrases which, if true, would explain that.
The standard playing card deck is a deck of 52 cards called the Anglo-American pack which stemmed from an earlier pack, the English pack. These decks of cards were so popular that a tax was levied against them as an extra source of income for the Crown. Queen Anne was the first to implement this tax in 1588 (which was later revised in 1628, 1711 until eventually being abolished in 1960 as being too much trouble to collect) and, as proof that the tax had been paid on the deck, the first card of the deck would receive a hand stamp. The first card being the Ace of Spades which is also why that card is the most ornate in the deck. Eventually, the hand stamp was abandoned and replaced with officially printed versions. However, this tax gave rise to the story that some would try and buy decks of 51 cards instead of 52 in order to avoid the tax and thus ‘were not playing with a full deck.’
Regardless of if the phrase originates from the 1950s or from a 16th century tax, the meaning of the phrase is still the same.