Poker

 was a card game.

When the First Doctor summoned several of his future selves for help in facing some knights, the Second Doctor, Third Doctor, Fifth Doctor and Sixth Doctor played a hand, ostensibly for a gold bow in the First Doctor's possession, but actually to decide who would have to help the First Doctor. The Fifth Doctor lost the hand, leaving him to face the knights, while the Third Doctor won with a full house. (PROSE: Five Card Draw)

The Doctor won a planet in a game of poker on 25th century Earth against a Draconian. (PROSE: Lonely Days)