packopeningsimulator

format compact
rng('shuffle')
% HEARTHSTONE PACK OPENING SIMULATOR
% Opens packs until every plain card is collected

% Set number of trials to run (increases accuracy and run time)
n = 10000;

% Pick the set to be run (1 = classic
set = 1;                % 2 = goblins vs gnomes
                        % 3 = the grand tournament
                        % 4 = whispers of the old gods
                        % 5 = mean streets of gadgetzan)

% Optional: input the current state of the collection
% From the chosen set:
% Number of commons where one is owned
userC  = 0;
% Number of commons where two are owned
userC2 = 0;
% Number of rares where one is owned
userR  = 0;
% Number of rares where two are owned
userR2 = 0;
% Number of epics where one is owned
userE  = 0;
% Number of epics where two are owned
userE2 = 0;
% Number of legendaries owned
userL  = 1;
% Current dust total
userD  = 0;

% DON'T EDIT ANYTHING BELOW HERE
% Store the size of each set
% Rows are different sets, columns are different rarities
setSize = [94 81 37 33;
           40 37 26 20;
           49 36 27 20;
           50 36 27 21;
           49 36 27 20];

% Store the probability of each rarity occuring for each individual card
% Rows are plain/golden, columns are common/rare/epic/legendary
% Accurate to within ~1% based on HearthSim pack data
rarity = [0.8809558 00.0185221 0.0770890 0.0045338 0.0146196 0.0006866 0.0033284 0.0002646];
% Manipulate the array based on various pity timers
legendaryDist = [0 rarity(7)/sum(rarity(7:8)) 1];
epicDist = [0 rarity(5)/sum(rarity(5:8)) sum(rarity(5:6))/sum(rarity(5:8)) sum(rarity(5:7))/sum(rarity(5:8)) 1];
rareDist = [0 rarity(3)/sum(rarity(3:8))  sum(rarity(3:4))/sum(rarity(3:8))  sum(rarity(3:5))/sum(rarity(3:8))  sum(rarity(3:6))/sum(rarity(3:8))  sum(rarity(3:7))/sum(rarity(3:8))  1];
commonDist = [0 rarity(1) sum(rarity(1:2)) sum(rarity(1:3)) sum(rarity(1:4)) sum(rarity(1:5)) sum(rarity(1:6)) sum(rarity(1:7)) 1];

% Set an array to store how many packs each trial runs
packsOpened = zeros(1,n);

% Run the trial 'n' times
for a = 1:n
    % Generate a collection
    %common = repmat(2,1,setSize(set,1));
    common      = [zeros(1,userC2) ones(1,userC) repmat(2,1,(setSize(set,1)-(userC2+userC)))];
    rare        = [zeros(1,userR2) ones(1,userR) repmat(2,1,(setSize(set,2)-(userR2+userR)))];
    epic        = [zeros(1,userE2) ones(1,userE) repmat(2,1,(setSize(set,3)-(userE2+userE)))];
    legendary   = [zeros(1,userL)  ones(1,setSize(set,4)-userL)];
    % Set the dust count, pack count, and pity timers to zero
    dust = userD;
    pityEpic = 0;
    pityLegendary = 0;

    % Keep opening packs until either the collection is complete OR enough
    % dust is left over to craft the remaining
    while (sum(common)+sum(rare)+sum(epic)+sum(legendary) > 0) && (40*sum(common) + 100*sum(rare) + 400*sum(epic) + 1600*sum(legendary) > dust)
        % Open a pack
        packsOpened(a) = packsOpened(a) + 1;
        % Randomly give each card a 'rarity number', then translate it
        % 1 = Common,   2 = GCommon,    3 = Rare,       4 = GRare
        % 5 = Epic,     6 = GEpic,      7 = Legendary,  8 = GLegendary
        cardRand = rand(1,5);
        cardRarity = zeros(1,5);

        % The 'first' card has adjusted rarity, based on pity timer
        if pityLegendary >= 40
            for b = 1:2
               if cardRand(1) >= legendaryDist(b) && cardRand(1) <= legendaryDist(b+1)
                    cardRarity(1) = b+6;
                end
            end
        elseif pityEpic >= 10
            for b = 1:4
               if cardRand(1) >= epicDist(b) && cardRand(1) <= epicDist(b+1)
                    cardRarity(1) = b+4;
                end
            end
        else
            for b = 1:6
               if cardRand(1) >= rareDist(b) && cardRand(1) <= rareDist(b+1)
                    cardRarity(1) = b+2;
                end
            end
        end

        % Generate the other four cards
        for c = 2:5
            for b = 1:8
               if cardRand(c) >= commonDist(b) && cardRand(c) <= commonDist(b+1)
                    cardRarity(c) = b;
                end
            end
        end

        % Increase pity timers by one if none were opened
        if cardRarity(1) < 5 && cardRarity(2) < 5 && cardRarity(3) < 5 && cardRarity(4) < 5 && cardRarity(5) < 5
            pityEpic = pityEpic + 1;
        else
            pityEpic = 0;
        end
        if cardRarity(1) < 7 && cardRarity(2) < 7 && cardRarity(3) < 7 && cardRarity(4) < 7 && cardRarity(5) < 7
            pityLegendary = pityLegendary + 1;
        else
            pityLegendary = 0;
        end

        % For each card, dust the golden cards, add the plains to the
        % collection if needed, or dust them if already owned
        for c = 1:5
            if cardRarity(c) == 1
                draw = randi(setSize(set,1),1,1);
                if common(draw) > 0
                    common(draw) = common(draw) - 1;
                else
                    dust = dust + 5;
                end
            elseif cardRarity(c) == 2
                dust = dust + 50;
            elseif cardRarity(c) == 3
                draw = randi(setSize(set,2),1,1);
                if rare(draw) > 0
                    rare(draw) = rare(draw) - 1;
                else
                    dust = dust + 20;
                end
            elseif cardRarity(c) == 4
                dust = dust + 100;
            elseif cardRarity(c) == 5
                draw = randi(setSize(set,3),1,1);
                if epic(draw) > 0
                    epic(draw) = epic(draw) - 1;
                else
                    dust = dust + 100;
                end
            elseif cardRarity(c) == 6
                dust = dust + 400;
            elseif cardRarity(c) == 7
                draw = randi(setSize(set,4),1,1);
                if legendary(draw) > 0
                    legendary(draw) = legendary(draw) - 1;
                else
                    dust = dust + 400;
                end
            else
                dust = dust + 1600;
            end
        end
    end
end
maxPacks = max(packsOpened);
avgPacks = ceil(mean(packsOpened));
minPacks = min(packsOpened);
stdPacks = std(packsOpened);
intervallower = ceil(avgPacks - 1.96 * stdPacks / sqrt(n));
intervalupper= ceil(avgPacks + 1.96 * stdPacks / sqrt(n));

minPacks
intervallower
avgPacks
intervalupper
maxPacks