using Random
using Plots

mutable struct Bandit
    p::Number #the win rate
    p_estimate::Number #How to estimate the win rate
    N::Number #Number of samples

    Bandit(p) = new(p,5,1)
end

function pull(ban::Bandit)
   return convert(Int,rand() < ban.p) 
end

function update(ban::Bandit, x::Number) #x is a sample number
    ban.N += 1
    ban.p_estimate = ((ban.N - 1) * ban.p_estimate + x) / ban.N
end

num_trials = 10000;
ϵ = 0.1;
bandit_probs = [0.2,0.5,0.75];

bandits = [Bandit(p) for p in bandit_probs];
rewards = zeros(num_trials);
num_times_explored = 0;
num_times_exploited = 0;
num_optimal = 0;
optimal_j = argmax([b.p for b in bandits]);
println("Optimal j: ", optimal_j);
    
for i in 1:num_trials 
    j = argmax([b.p_estimate for b in bandits])
    x = pull(bandits[j])
    rewards[i] = x
    update(bandits[j],x)
end

for b in bandits
    println("Mean estimate: ", b.p_estimate)
end

println("Total reward earned: ", sum(rewards))
println("Overall win rate: ", sum(rewards)/ num_trials)
println("Number of times selected each bandit ", [b.N for b in bandits])

cumulative_rewards = cumsum(rewards)
win_rates = cumulative_rewards ./ Array(1:num_trials)
plot(win_rates) 
plot!(ones(num_trials) .* max(bandit_probs...))