This is similar to the "alpha-beta cutoff" that is used say in computer-game play. As soon as you determine that a player would be worse-off than you already know he could be, then you stop searching because you don't care how much worse-off he would be. But I am not sure that this optimization would really apply because "the score of any particular kid" depends entirely upon which other kid you are comparing him to. It is a hamming-distance problem.