%% 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 17 18 19 20 21];
Level_List = [6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26];
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
            2111204
            2339353
            2578819
            2829602
            3091702
            3365120
            3649856
            3945909
            4253279
            4571967
            4901972
            5243294
            5595934
            5959892
            6335166];

%% 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
            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 = [];
diamond_Array = [];
silver_Array_1 = [];

%% Normal Anvils, Remaking Weapon

for target_level = targetLevel_List
attempt_List_1 = []; % number of new weapons made
silver_List_1 = []; % amount of silver expended
diamond_List = []; % number of diamond anvils expended
for i = 1:trials
    % initiate trial
    pot = available_potential; % potential of the weapon
    lvl = 5; % current enhancement level
    silver = sum(cTable(1:5));
    attempts = 1; % total attempts using a new weapon
    dmd = 0;
    while lvl < target_level % keep trying until we make the target
        if pot > 0
            check = pTable(lvl+1);
            dmd = dmd + 1;
            silver = silver + 3*cTable(lvl+1);
            if rand < check % success
                lvl = lvl + 1; % increase the level
            else % failure
                lvl = lvl;
                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];
    diamond_List = [diamond_List; dmd];
    silver_List_1 = [silver_List_1; silver];
end

diamond_Array = [diamond_Array diamond_List];
attempt_Array_1 = [attempt_Array_1 attempt_List_1];
silver_Array_1 = [silver_Array_1 silver_List_1];

end

%% Diamond Anvils, One Weapon

level_results = [];
attempt_List = []; % number of new weapons made
silver_List = []; % amount of silver expended
for i = 1:trials
    % initiate trial
    pot = available_potential; % potential of the weapon
    lvl = 5; % current enhancement level
    silver = sum(cTable(1:5));
    attempts = 0; % total diamond anvils consumed
    while pot > 0 % keep trying until we make the target
        check = pTable(lvl+1);
        attempts = attempts + 1;
        silver = silver + 3*cTable(lvl+1);
        if rand < check % success
            lvl = lvl + 1; % increase the level
        else % failure
            pot = pot - 1;
        end
        if lvl == 35
            break
        end
    end
    level_results = [level_results; lvl];
    attempt_List = [attempt_List; attempts];
    silver_List = [silver_List; silver];
end

%%

silver_Array_1 = silver_Array_1/10^6;

%% 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_diamond_01.png')

% remaking weapons
fig3 = 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(diamond_Array,1), std(diamond_Array,1))
ylabel('diamond anvils used')
grid on
hold off
saveas(fig3,'remaking_diamond_02.png')


% trying until you run out
fig2 = figure; hold on
xlabel('enhancement level')
ylabel('cumulative probability')

histogram(level_results,'Normalization','cdf')
saveas(fig2,'dia_cdf.png')