Consider an infinite board with the following pattern:

Each gray rectangle has dimension \(2\times 3\), and the distance between two neighboring rectangles is 1.A game consists of throwing a circular token, which has a diameter of 1, on the board. If the token is completely inside a gray rectangle, you will receive 150 cents. Otherwise, you will receive 0 cents. What is the expected number of cents that you will receive after a throw?

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