This work explores methods for proving and disproving security of systems under adaptive adversaries. Adaptive adversaries are ones which make their next move based on the previous observations. Our first contribution is a new game based characterization of security. We show that the game accurately captures security of deterministic and probabilistic systems against adaptive (probabilistic) adversaries. In addition, we build on top of the game characterization and present techniques that expedite proving the existence of attacker and defender strategies, and consequently proving security or vulnerability of systems. The first is what we call attack (and defense) slopes which give simple sufficient criteria for existence of winning strategies (for attacker and defender). The second is reductions of one game to another achieved by mapping a strategy of one to that of the other. We show that such reductions can prove or disprove security by reducing from a game of a secure system or reducing to that of a non-secure system.