Unnamed

win_rate = 0;
for B = 0 : 26
    R = 26 - B;
    prob_distr = nchoosek(26, R) * nchoosek(26, B) / nchoosek(52, 26);
    
    win_R = 0;
    win_B = 0;
    if R >= 2
        win_R = nchoosek(R, 2);
    end
    if B >= 2
        win_B = nchoosek(B, 2);
    end
    prob_win_given_distr = (win_R + win_B) / nchoosek(26, 2);
    contribution = prob_distr * prob_win_given_distr;
    win_rate = win_rate + contribution;
    fprintf('B: %d R: %d distr_winrate: %.03f cum_winrate: %.03f\n', B, R, prob_win_given_distr, win_rate);
end