Solitaire

Solitaire was a card game which involved laying cards atop each other, alternating colour. For example, red seven on black eight, black three on red four, etc.

The Second Doctor plays solitaire. (TV: The War Games)

You may be looking for the audio story.

The First Doctor set such a complicated password on the Soul Pirate's console that it couldn't do anything other than play solitaire. (PROSE: A Big Hand for the Doctor)

The Second Doctor played solitaire while waiting on Gallifrey for Jamie and Zoe. (TV: The War Games) The Celestial Toymaker played solitaire just before Charlotte Pollard entered the Toy Shop. (AUDIO: Solitaire)