There was a time when scholars erroneously believed that tarot cards came to us from Egypt, but now we know that the source was much farther east.
Although often a scholar's impulse is to attempt to reduce cultural phenomena to linear evolutionary patterns that can be easily codified and outlined, it is probable that cards were invented or reinvented many times throughout history.
Playing cards or gaming sticks in some form or another appear in Korea and China first. Some intriguing card-like gaming objects have been found on the other side of the land bridge, in Alaska and on into North America. In most cases the Asian cards are long and narrow, suited, and numbered. North American gaming sticks are more informal, but still tend to be numbered and divided into four sets. Both Korean cards and North American gaming sticks are based on the concept of divinatory arrows.
The fact that the number of suits across continents is normally based on multiples of four probably relates to the fact that many traditional games are based on the four cardinal directions.
What we can deduce from this is that some form of gaming object with this basic shape and organization has probably existed in human culture for a very long time, but it did not begin to closely resemble modern playing cards until later.
It is not possible now to say whether Chinese money cards or Korean fighting arrow cards were the first to be created, but it is quite likely to have been one of these two. They do not appear to be extremely related to one another, at least not to a degree that would indicate true cultural diffusion. However, most other types of cards around the world appear related to one or the other (or both) of these ancient forms of playing cards. In any case, Chinese money cards were probably invented about 1100 CE.
Mongols conquered China, ostensibly aqcuiring some playing cards at the same time. We know for sure that Kublai Khan had heard of playing cards, since his words on the subject are recorded by one of the members of his court. (Essentially, he directed them to treat gambling with cards just like gambling without cards.)
I have not been able to determine what Mongolian playing cards may have looked like, if they did exist, but I do know that playing cards feature in Mongolian folk stories and riddles. I assume they must have introduced their own adaptations as they integrated playing cards into their folklore, because when playing cards appeared next it was in a significantly modified form.
These modified cards originated in Persia under the name ganjifeh, and are first mentioned in the 16th century when a Persian Moghul ruler sends cards to his friend in India. It is partially because the Moghuls originated in Mongolia that I believe playing cards must have been transmitted via Mongolia.
Another persuasive detail is that printing appears to have come with Mongolians at around the same time. It would be easy for me to say too much on the subject, but Mongolian playing cards may have travelled, like the printing press, into Southwestern Asia far earlier than they appeared in Europe.
The earliest anyone could expect to see cards in Southwestern Asia would be about the 12th or 13th century, for this is when local ganjifah artisans claim India possessed playing cards in or near their present form.
Persian ganjifeh playing cards have many similarities to Chinese money cards, indicating that the early Persian cards were probably a reinterpretation or misinterpretation of the existing Chinese custom. It is also possible that the suits of Korean fighting arrow cards played a role in the development of ganjifeh.
Once these cards got to Moghul India, they became quite popular and spread widely. Indian ganjifah are brightly colored, round, and hard. A proud tradition of hand-painting these round ganjifah cards exists still today in India and Persia.
Although there is no strong historical relationship between Indian ganjifah and tarot cards, they do provide a good link between the imagery on Persian ganjifeh and the suit marks on Mamluk playing cards.
Only one deck and one card fragment in the Mamluk format have been found to date, so it would be quite easy to draw too much information from this single data point.
Still, the discovery of the Mamluk playing card deck in 1942 raised some very important questions about where European cards came from. They provide a crucial link between ganjifeh and the cards of the West.