%% Anvil Comparisons
% Edoweiss
% 2018-04-12

% In this script we perform a monte carlo simulations to estimate the cost
% of making a brand new weapon versus attempting over and over on an
% existing weapon using golden anvils

close all; clear all; clc

%% Simulations Targets/Parameters
trials = 10000;
available_potential = 8;
targetLevel_List = [11 12 13 14 15 16];
initial_level = 6; % initial level for the gold anvil case

% costs in millions
remakeCost_List = [8];
goldenCost_List = [2.5 5 7.5 10];

%% Upgrade Costs
cTable = [  52469
            75104
            97739
            120374
            143009
            165643
            188278
            210913
            233548
            256183
            348522
            452179
            567153
            693445
            831054
            979980
            1140224
            1311785
            1494664
            1688860
            1894373];

%% Setup
pTable = [  1
            1
            1
            1
            1
            0.88
            0.78
            0.68
            0.59
            0.51
            0.50
            0.50
            0.50
            0.50
            0.50
            0.50
            0.50
            0.50
            0.50
            0.50
            0.50
            0.50
            0.50
            0.50
            0.50
            0.50 ];

%% Perform Simulations across many different target levels

attempt_Array_1 = [];
attempt_Array_2 = [];
silver_Array_1 = [];
silver_Array_2 = [];

for target_level = targetLevel_List

%% Normal Anvils, Remaking Weapon

attempt_List_1 = []; % number of new weapons made
silver_List_1 = []; % amount of silver expended
for i = 1:trials
    % initiate trial
    pot = available_potential; % potential of the weapon
    lvl = 0; % current enhancement level
    silver = 0;
    attempts = 1; % total attempts using a new weapon
    while lvl < target_level % keep trying until we make the target
        if pot > 0
            check = pTable(lvl+1);
            silver = silver + cTable(lvl+1);
            if rand < check % success
                lvl = lvl + 1; % increase the level
            else % failure
                lvl = lvl - 1;
                pot = pot - 1;
            end
        end
        if pot == 0 % weapon broke
            attempts = attempts + 1; % make a new weapon
            pot = available_potential;
        end
    end
    attempt_List_1 = [attempt_List_1; attempts];
    silver_List_1 = [silver_List_1; silver];
end

%% Gold Anvils, One Weapon

attempt_List_2 = [];
silver_List_2 = [];

for i = 1:trials
    lvl = initial_level; %
    silver = 0;
    attempts = 0;
    while lvl < target_level % keep trying until we make the target
        attempts = attempts + 1;
        check = pTable(lvl+1);
%         silver = silver + cTable(lvl+1);
        if rand < check % success
            lvl = lvl + 1;
        else % failure
            if lvl > 11
                lvl = 10; % forces level to 10 when you fail at > 11
            else
                lvl = lvl - 1;
            end
        end
    end
    attempt_List_2 = [attempt_List_2; attempts];
    silver_List_2 = [silver_List_2; silver];
end

attempt_Array_1 = [attempt_Array_1 attempt_List_1];
attempt_Array_2 = [attempt_Array_2 attempt_List_2];
silver_Array_1 = [silver_Array_1 silver_List_1];
silver_Array_2 = [silver_Array_2 silver_List_2];

end

% convert silver to millions
silver_Array_1 = silver_Array_1/10^6;
silver_Array_2 = silver_Array_2/10^6;

%% Plot Results - attempts and enhancement cost
% remaking weapons
fig1 = figure; hold on
xlabel('target enhancement')

yyaxis left
errorbar(targetLevel_List, mean(attempt_Array_1,1), std(attempt_Array_1,1))
ylabel('weapons made')

yyaxis right
errorbar(targetLevel_List, mean(silver_Array_1,1), std(silver_Array_1,1))
ylabel('cost of enhancements (million silver)')
grid on
hold off
saveas(fig1,'remaking_01.png')

% using golden anvils
fig2 = figure; hold on
xlabel('target enhancement')

yyaxis left
errorbar(targetLevel_List, mean(attempt_Array_2,1), std(attempt_Array_2,1))
ylabel('golden anvils consumed')

yyaxis right
errorbar(targetLevel_List, mean(silver_Array_2,1), std(silver_Array_2,1))
ylabel('cost of enhancements (million silver)')
grid on
grid minor
hold off
saveas(fig2,'goldens_01.png')

%% Plot Results - total costs
% calculate total costs
totalCost_Cell_1 = [];
totalCost_Cell_2 = [];
for i = 1:length(remakeCost_List)
    remakeCost = remakeCost_List(i);
    totalCost_Cell_1{i} = attempt_Array_1*remakeCost + silver_Array_1;
end
for i = 1:length(goldenCost_List)
    goldenCost = goldenCost_List(i);
    totalCost_Cell_2{i} = attempt_Array_2*goldenCost + silver_Array_2;
end

% plot a variety of different costs values
fig3 = figure; hold on
A = [];
B = [];
xlabel('target enhancement')
ylabel('total cost (million silver)')
for i = 1:length(remakeCost_List)
    plotData = totalCost_Cell_1{i};
    A{i} = plot(targetLevel_List, mean(plotData,1),'-',...
        'color',[1,0.5,1-i/length(remakeCost_List)]);
end
for i = 1:length(goldenCost_List)
    plotData = totalCost_Cell_2{i};
    B{i} = plot(targetLevel_List, mean(plotData,1),'--',...
        'color',[0,0.5,i/length(goldenCost_List)]);
end
legend([A{1} B{1}],{'remaking','goldens'},'location','northwest')
set(gca,'XTick',11:16)
grid on
hold off
saveas(fig3,'multi_comparisons.png')

% plotting a particular cost value
fig4 = figure; hold on
xlabel('target enhancement')
ylabel('total cost (million silver)')
ylim([0 1800])
i = 1;
plotData = totalCost_Cell_1{i};
errorbar(targetLevel_List, mean(plotData,1),std(plotData,1),'o-',...
    'color',[1,0.5,1-i/length(remakeCost_List)]);
i = 1;
plotData = totalCost_Cell_2{i};
errorbar(targetLevel_List, mean(plotData,1),std(plotData,1),'o--',...
        'color',[0,0.5,i/length(goldenCost_List)]);
legend('remaking','goldens','location','northwest')
grid on
hold off
saveas(fig4,'my_case.png')