Capara and Little Timmy decided to play Cheat for prizes. Each time someone won, the loser had to give the winner a candy rock. After an hour of playing, Capara and Little Timmy decided to give the games a rest. At the end of the game, Capara had won three games, while Little Timmy had won three new pieces of candy rocks.
How many individual games did Capara and Little Timmy play in one hour?
Please provide the answer in numerical form.