Higashi no Eden, Sword Art Online Recommendations
Both of these anime revolve around a young man trying to escape from a seemingly unavoidable death, in which they meet allies, enemies, and eventually a lover along the way. A main plot point in both is a "game of death". They both have a lot of action, but it's balanced well with the character interaction and emotional scenes.
In both of these anime there is the protagonist who got in a ''game'' kind of without his permission(or without knowing the master's real purpose).
In addition, in both of these anime the protagonist wants to find the truth about the situations they are in and want to eliminate the one responsible for it!