stars_in_rank = [5 5 5 5 5 5 5 5 5 5 ...
                 4 4 4 4 4 ...
                 3 3 3 3 3 ...
                 2 2 2 2 2];

win_rate = 0.50:0.025:1.0;

win_streak_limit = 5;
no_lose_limit = 20;


start_rank = 25;
start_stars = 0;


iters = 5000;
game_recorder = zeros(length(win_rate), iters);
% Loop over the different win rates
wr_iter = 0;

for wr = 1:length(win_rate)

    for i = 1:iters
        win_streak = 0;
        rank = start_rank;
        stars = start_stars;
        games_played = 0;
        while rank > 0

            % Play a game
            games_played = games_played + 1;
            % Win
            if rand() < win_rate(wr)
                win_streak = win_streak + 1;

                % Check win streak
                if win_streak >= 3 && rank > win_streak_limit
                    stars = stars + 2;
                else
                    stars = stars + 1;
                end

                % Check rank up
                if stars > stars_in_rank(rank)
                    stars = stars - stars_in_rank(rank);
                    rank = rank - 1;
                end
                %disp('win')
                %disp(['rank ' num2str(rank) ' stars ' num2str(stars)])
            % Lose
            else
                win_streak = 0;

                % Only lose stars if low enough rank
                if rank < no_lose_limit
                    stars = stars - 1;
                end

                if stars < 0
                    stars = stars_in_rank(rank) - 1;
                    rank = rank + 1;
                end
                %disp('lose')
                %disp(['rank ' num2str(rank) ' stars ' num2str(stars) ' iter ' num2str(i)])
            end
        end
        game_recorder(wr, i) = games_played;
    end
end

plot(win_rate,mean(game_recorder,2),'o-')