The first one was Tabletop Conquest by Brent Newhall, a free solo strategy game where you must try to reach the capital of a foreign kingdom and not run out of troops from the conflicts on the way. Winning will depend on luck somewhat but there is strategy in figuring your odds for each battle, based on the enemy and on the surrounding terrain. Overall, a simple, nice game to spend some free time.
The other game I played was Dungeons by Shane Garvey, author of other solo games such as Chronicles of Arax and Battle Quest. In my opinion, Dungeons is a more elegant, streamlined iteration of the author's efforts in creating a solo adventure/dungeon delving game.
Each game of Dungeons is a random sequence of combat encounters and non-combat events tied together by a quest. The core book has six quests and the first expansion brings another six. To play, you select one of a roster of characters, which are defined in terms of combat stats. The rules are easy to grasp and the game moves quickly. My first game took me around 10 minutes and ended in defeat against a zombie, after a few unfortunate encounters. It was not as detailed as a paragraph-based game but it did not feel bland or overly generic.
Both of these solo games are played without any preparation, requiring only a few dice and a sheet of paper. I found both to be satisfiying for a quick break or to finish a busy week, as it was the case.