%% Anvil Comparisons
% Edoweiss
% 2018-05-25

% 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 = 20000;
available_potential = 8;
initial_level = 5; % initial level for the gold anvil case

d_anvils_init = 30; % number of diamond anvils available
d_price = 50; % price of a diamond anvil
g_price = 4; % price of a golden anvil
g_anvils_init = d_anvils_init*d_price/g_price; % golden anvil equivalent

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

%% Initialize Output Arrays
n_levels = []; % levels from using just normal anvils
g_levels = []; % levels from using just golden anvils
d_levels = []; % levels from using just diamond anvils

%% Normal Anvils
% we keep trying until we run out of available potential
for i = 1:trials;
    pot = available_potential; % potential remaining
    lvl = initial_level; % current enhancement level
    while pot > 0
        if lvl < length(pTable)
            check = pTable(lvl+1);
        else
            check = 0.50;
        end
        if rand < check % success
            lvl = lvl + 1;
        else % failure
            lvl = lvl - 1;
            pot = pot - 1;
        end
    end
    n_levels = [n_levels; lvl];
end

%% Golden Anvils
% we keep trying until we run out of golden anvils
for i = 1:trials;
    lvl = initial_level; % current enhancement level
    g_anvils = g_anvils_init; % number of golden anvils at our disposal
    while g_anvils > 0
        g_anvils = g_anvils - 1;
        if lvl < length(pTable)
            check = pTable(lvl+1);
        else
            check = 0.50;
        end
        if rand < check % success
            lvl = lvl + 1;
        else %failure
            if lvl > 11
                lvl = 10;
            else
                lvl = lvl - 1;
            end
        end
    end
    g_levels = [g_levels; lvl];
end

%% Diamond Anvils
% we keep trying until we run out of golden anvils
for i = 1:trials;
    pot = available_potential; % potential remaining
    lvl = initial_level; % current enhancement level
    d_anvils = d_anvils_init; % number of golden anvils at our disposal
    while pot > 0 && d_anvils > 0
        d_anvils = d_anvils - 1;
        if lvl < length(pTable)
            check = pTable(lvl+1);
        else
            check = 0.50;
        end
        if rand < check % success
            lvl = lvl + 1;
        else %failure
            pot = pot - 1;
        end
    end
    d_levels = [d_levels; lvl];
end

%% Compute histograms
% diamond anvil case
[h_n,e_n] = histcounts(n_levels,'Normalization','pdf');

for i = 1:length(e_n)-1 % get centers of bins
    c_n(i) = (e_n(i)+e_n(i+1))/2;
end

% golden anvils case
[h_g,e_g]  = histcounts(g_levels,'Normalization','pdf');

for i = 1:length(e_g)-1 % get centers of bins
    c_g(i) = (e_g(i)+e_g(i+1))/2;
end

% diamond anvils case
[h_d,e_d]  = histcounts(d_levels,'Normalization','pdf');

for i = 1:length(e_d)-1 % get centers of bins
    c_d(i) = (e_d(i)+e_d(i+1))/2;
end

%% Plot
fig1 = figure; hold on
plot(c_n,h_n,'k')
plot(c_g,h_g,'color',[1 0.7 0])
plot(c_d,h_d,'color',[0 0.5 1])
legend('normal','golden','diamond')
ylabel('Probability Density')
xlabel('enhancement level')

saveas(fig1,'3pdf.png')