Gamesmanship is a kind of strategy when playing a game. It means you do things that might not be allowed but are tricky enough that the other person doesn't realize it. It is like trying to win the game without following all the rules. For example, if you were playing a game of tag, you could pretend to trip and fall down, even though you weren't really tripped by someone else, so that you are given more time to run and get away.