A deck of 2n cards consists of n red and n black cards. The cards are shuffled and then turned over one at a time. Suppose that each time a red card is turned over, we win 1 unit if more red cards than black cards have been turned over by that time. (For instance, if n = 2 and the result is r b r b, then we would win a total of 2 units.) Find the expected amount that we win.
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