This is a fascinating topic, yet one that may be too complicated to answer fully. The Hunger Games series' use of violence isn't one-dimensional. There are multiple layers to how violence affects politics, individual behavior and social psychology.
I base this strategy on someone like me. I wouldn't be a Career, nor would I be very powerful. Strategy depends so much on the individual's strengths and weaknesses. As an all-around mediocre physical being, this is the strategy I'd take.