There is some confusion as to how to tell the age of certain double decks of cards made by Kem. (Kem was the original 100% plastic playing card.) This is usually because sellers don't know that there is a dating code on the Ace of Spades.
Most often the cards will be listed as "vintage 1935" or something similar. This is because the design on the Ace of Spades was copyrighted in 1935 when Kem cards were first being produced. This does not mean, however, that the particular deck you are looking at was printed in 1935.
Sometimes also the deck will be listed as "vintage 1947" or "vintage 1940", which again are mistakes caused by the fact that certain printed material--replacement order card, bridge scoring card, brochure, etc.--is copyrighted 1947 or 1940 when that particular piece of literature was created or first included with the decks.. This does not mean, however that the particular deck you are looking at was printed in 1947 or 1940 or whenever.
The simple way to determine when a particular Kem deck was printed is a number which can be found below and to the left of the face on the Ace of Spades. This number is either 3 or 4 digits long, for example "258" or "1070"
The first digit or two digits indicates the month the deck was printed, while the last two digits indicate the year the deck was printed. In the first example above, the deck was printed in February (month 2) of 1958; in the second example, the deck was printed in October (month 10) of 1970.
It is not unusual for the two decks in a set to have been printed at different times. I have one double deck where one was printed September of 1959 while the other was printed May of 1960.
Some older decks have the number below and to the right of the face, while some very old decks will have a letter and number combination. Also in some of the older decks, the year was indicated by a single digit; for example, "C108" indicates that the deck was printed in October of 1948; "C102" (common on WWII decks) were printed in October, 1942. Needless to say, these are few and far between.
If the age of the deck is important to you, be sure to examine the Ace of Spades for this number and don't assume that the cards date from 1935 or 1947 just because there's a copyright for that year somewhere amongst the paperwork.
NOTE: The above only applies to standard index decks, the ones with small pips and numbers in the corners. In jumbo index decks, which have large numbers and letters in the corners and are commonly used in poker, the date code is often omitted, probably for space reasons.
UPDATE: It has been brought to my attention that, since US Playing Card Co. purchased Kem (2004) the date codes have changed slightly. Some of the decks printed used a letter + number to indicate the year printed: A=1998, B=1999, C=2000, and D=2001. For example, if the deck has "A12", that deck was printed in December of 1998. Subsequent years use the same month/date code as the older, pre-USPC decks: "202"= February, 2002, etc.
UPDATE: I have been asked lately about Kem decks which are slightly smaller (known as 'cadet' size) than a normal bridge size card, sometimes in a leather pouch case. They have a profile of an eagle on the back with a line of stars; the background is either blue or red. They usually have a code mark of "C102". These decks were printed in 1942, specifically intended for use by the US Armed Forces during WWII. They are smaller than a normal deck so as to more easily fit in a breast pocket, and they were popular with the troops in the field because water and mud wouldn't ruin them. A true piece of American history.