The use of card counting in Blackjack has received considerable media attention in the past decade. Basic strategy is simple to understand but the reasoning behind the probabilistic advantage is full of nuance and complications. We will provide a conceptual understanding of the mathematics underlying the advantage of counting cards in Blackjack. Multiple strategies will be discussed with attention to their relative benefits and efficacy of shifting the probability of winning towards the player and away from the casino. We will explain analytical approaches such as the Monte Carlo Method, a simulation method dependent on randomness; and the Kelly Criterion, a popular formula for scaling bet sizes.