public class HowLongWillMyGameLastSlightlyBetter {
	
	public static double probFinishOnTurnNOrLaterRecursive(int turnStop,
			int specialCards, int normalCards) throws IllegalArgumentException {
		if (turnStop > specialCards + normalCards || turnStop < specialCards) {
			throw new IllegalArgumentException(
					"That's just a silly number to ask for since it's out of range.");
		}
		double tempProbability = (double) (specialCards)
				/ (double) (specialCards + normalCards);
		
		if (turnStop == specialCards + normalCards) {
			return tempProbability;
		}
		return (tempProbability + probFinishOnTurnNOrLaterRecursive(turnStop,
				specialCards, normalCards - 1) * (1.0 - tempProbability));
	}

	public static void main(String[] args) {
		int specialCards = 5;
		int normalCards = 16;
		System.out.println("With " + specialCards + " special cards and "
				+ normalCards
				+ " normal cards in the deck the following is true: ");
		for (int i = specialCards + normalCards; i >= specialCards; i--) {
			double cumulativeProbability = probFinishOnTurnNOrLaterRecursive(i,
					specialCards, normalCards);
			System.out.println("The probability to finish on turn " + i
					+ " or later is "
					+ (((int) (cumulativeProbability * 10000)) / 100.0) + "%");
		}

	}


	
}