/**
 * Context: I'm making a variable length board game. There is a deck of cards
 * that tell the players what to do each turn. 5 of the cards are 'Discard
 * Energy' cards and after drawing all 5 of these cards the players will have no
 * energy left and they lose the game. Depending on the distribution of these
 * cards, the game will last a different number of turns. If all 5 cards are at
 * the top of the deck, the game will be over in 5 turns. If one of the cards
 * finds its way to the bottom of the deck, every turn card will be drawn before
 * the game is over. I'm ok with this, as long as 'most' games last a minimum
 * number of turns. I think 15 turns is a good length of time. So my question is
 * this: how many non-'discard energy' cards should I include in the deck? Is
 * there an equation that will tell me the percentage of games that last at
 * least 15 rounds given the total number of cards? What about an equation that
 * tells me the percentage of games that will be shorter than 10 games?
 * Alternatively, what if I said I wanted 90% of the game to last 15 turns or
 * longer. How many cards would I need? Thanks!
 *
 * http://www.reddit.com/r/CasualMath/comments/16i6eo/
 * probability_question_how_long_will_my_game_last/
 *
 * Goal:
 *
 * Make a program that simulates drawing cards until a target number of special
 * cards are hit and then prints out the the probability and cumumaltive
 * probability of each number of turns
 * */

public class HowLongWillMyGameLast {

	public static void main(String[] args) {
		/*
		 * The use of doubles for integer values is to avoid having to recast to
		 * skip integer division
		 */

		// control variables
		double totalNumberOfCards = 21;
		double numberOfEnergyCards = 5;
		int numberOfTrials = 1_000_000;
		boolean showCumulative = true;

		// data
		/* index represents finishing turn, value how many times finished there */
		double[] numberFinishedOnTurnN = new double[(int) totalNumberOfCards + 1];

		for (int i = 1; i <= numberOfTrials; i++) {
			double deck = totalNumberOfCards;
			double energyCards = numberOfEnergyCards;
			int turn = 0;
			while (energyCards > 0) {
				if (Math.random() >= 1.0 - (energyCards / deck)) {
					energyCards--;
					deck--;
				} else {
					deck--;
				}
				turn++;
				if (deck < 0) { // check for infinite loops
					System.out
							.println("drawing cards from a non-existant deck :-(");
					System.exit(1);
				}
			}
			numberFinishedOnTurnN[turn] += 1;
		} // end of simulations

		// calculate average number of turns
		Double averageNumberOfTurns = 0.0;
		for (int i = 0; i < numberFinishedOnTurnN.length; i++){
			averageNumberOfTurns += i*(numberFinishedOnTurnN[i]/numberOfTrials);
		}

		// printouts


		System.out.println("There were " + (int) totalNumberOfCards + " in the deck, of which " + (int) numberOfEnergyCards + " were energy cards. " + numberOfTrials + " trials were run." );
		System.out.println("On average the games lasted " + averageNumberOfTurns.toString().substring(0,5) + " turns");
		if(showCumulative){
			double cumulativeFinishes = 0;
			for (int i = numberFinishedOnTurnN.length-1; i >= (int) numberOfEnergyCards ; i--){
				cumulativeFinishes += numberFinishedOnTurnN[i];
				System.out.println((int)(cumulativeFinishes/numberOfTrials * 100) + "%" + " of the games finished on turn " + i + " or later");
			}

		} else {
			for (int i = (int) numberOfEnergyCards; i < numberFinishedOnTurnN.length; i++){
				if (numberFinishedOnTurnN[i] > 0.0){
					System.out.println((int)(numberFinishedOnTurnN[i]/numberOfTrials * 100) + "%" + " of the games finished on turn " + i);
				}
			}
		}




	}
}