A quick simulation for how many cards need to be crafted to make a specific Darkmoon Deck.

DarkmoonDeckSim.cpp

#include "pch.h"
#include <chrono>
#include <iostream>
#include <random>
#include <vector>

using std::cin;
using std::cout;
using std::endl;
using std::vector;

int main() {
	cout << "Simulates the number of cards needed to craft a darkmoon deck." << endl;

	unsigned long long seed =
		std::chrono::system_clock::now().time_since_epoch().count();
	std::mt19937 rngesus(seed);
	cout << "seed: " << seed << endl;

	std::uniform_int_distribution<int> dist_deck(0, 3);
	std::uniform_int_distribution<int> dist_card(0, 7);

	struct Card {
		bool isDeck = false;
		int num = -1;
	};

	auto flip = [&] () -> Card {
		Card card;
		if (dist_deck(rngesus) == 0) {
			card.isDeck = true;
		}
		card.num = dist_card(rngesus);
		return card;
	};

	vector<double> attempts;
	int TOTAL_ATTEMPTS = 10000;
	cout << "Enter the number of iterations to run: ";
	cin >> TOTAL_ATTEMPTS;
	for (int i = 0; i < TOTAL_ATTEMPTS; ++i) {
		vector<bool> deck(8, false);
		bool isDeckFinished = false;
		int cards_made = 0;
		while (!isDeckFinished) {
			Card c = flip();
			if (c.isDeck) {
				deck[c.num] = true;
			}

			isDeckFinished = true;
			for (bool hasCard : deck) {
				isDeckFinished = isDeckFinished && hasCard;
			}
			cards_made++;
		}
		attempts.push_back(double(cards_made));
	}

	auto shrink_avg =
		[] (vector<double> set, int chunk_size) -> vector<double> {
		vector<double> out;
		for (int i = 0; i < set.size() / chunk_size; i++) {
			double total_i = 0;
			for (int j = 0; j < chunk_size; j++) {
				int index = i * chunk_size + j;
				if (index < set.size()) {
					total_i += set[index];
				} else {
					break;
				}
			}
			double avg_i = double(total_i) / chunk_size;
			out.push_back(avg_i);
		}
		return out;
	};

	vector<double> shrinker(attempts);
	while (shrinker.size() > 1) {
		shrinker = shrink_avg(shrinker, 10);
	}

	cout << "Average cards needed per deck: " << shrinker[0] << endl;
	cout << "(" << TOTAL_ATTEMPTS << " iterations)" << endl;

	int delay = 0; cin >> delay;
	return 0;
}