Chess
Chess diviation was done in China, as far I remember.
Chess in context with Tarot?
autorbis in his complicated world keeps it as a strong possibility, that the Cary-Yale, done rather early (perhaps 1428, perhaps 1441) for Filippo Maria Visconti, was influenced in its original form by Chess and the same notorious Chess-player Filippo Visconti (had an own chess-club at his court in 1427, and there was a visit of a master-player in 1429) in that way, that it had originally 64 pip and court cards and 16 trumps. 64 cause the 64 fields of a chess-board and 16 trump cards cause the 16 figures used by one player. This is only a suggestion by autorbis, he himself sees also other possibilites, but according to his analyses this is most likely.
http://geocities.com/autorbis/VMnew.html
Further he mentioned in personal talk, that the Goldchmidt and Guildhall cards have strange figures and the presence of a bishop there + the chequered ground (also in another deck, I forgot the name) point in the same direction: Chess took an influence. autorbis sees it as an early version, that was overcome by the later development, autorbis assumes, that the 5x14-deck (not related to chess) were much more farspread than any 5x16-version in the early phase (which happened before the idea to a deck with 22 special cards was born). See his opinion at:
http://geocities.com/autorbis/pbm14new.html
Pratesi, who is known for his studies and explorations about the Michelino-deck and the card sitution in Florence made also suggestions in direction to chess (Pratesi is a general game-researcher, not fixed upon Tarot, who also made some worthful explorations in the field of Chess, Checkers and Go), although based on other considerations, the backgrounds are not totally clear to me.
An excessive visit to
http://games.rengeekcentral.com/
(please detect the Appendix) might show you, that the interest in Chess and other games was very high and full of experiments, they didn't play only in one way with a game and explored also variants. This spirit should also assumed for the development of playing card decks. Although this book is of Spain and of King Alfonso and of 13th century, it might well tell something about Filippo Visconti's habits and ways to experiment with games.