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Roughly: 1/2 * 1/2 * 1/2 = 1/8.

To get an exact answer, we'd need to know whether these guesses are completely random, or if the guesser is using a strategy (e.g. if the first was black, is the guesser going to choose red because there are more red than black cards left or not). Using a strategy would make the guesser get them all right slightly more than 1/8th of the time (the exact odds can be calculated). Guessing randomly will, on average, make you right 1/8th of the time.

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