Two players, B and R, play the following game on an innite grid of unit squares, all initially colored white. The players take turns starting with B. On B's turn, B selects one white unit square and colors it blue. On R's turn, R selects two white unit squares and colors them red. The players alternate until B decides to end the game. At this point, B gets a score, given by the number of unit squares in the largest (in terms of area) simple polygon containing only blue unit squares. What is the largest score B can guarantee?
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