Since we know the basic principle of the algorithm, let's concentrate on the search strategy. There are two values: alpha and beta, respectively. The alpha value is the lowest score a player can achieve, thus avoiding considering any move where the opponent has the opportunity to lessen it. Similarly, the beta value is the upper limit, and no matter how tempting the new option is, the algorithm assumes that the opponent won't provide the opportunity to take it.
Given the alternation between each player (minimizing and maximizing), only one value needs to be checked at each step.