有两堆硬币，一堆有27个，一堆有26个，分别抛这两堆硬币，哪堆的正面朝上的硬币数量多，哪堆算赢。问，27个硬币的那堆赢的概率有多少？输的概率有多少

coin.m

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 有两堆硬币，一堆有27个，一堆有26个，分别抛这两堆硬币，  %
% 哪堆的正面朝上的硬币数量多，哪堆算赢。问，27个硬币的那  %
% 堆赢的概率有多少？输的概率有多少?                    %
%                                                  %
%                                                  %
%   p_win =  0.5000,        p_lose =  0.3919       %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



a_num = 27;
b_num = 26;

p_a = zeros(1, a_num + 1);
p_b = zeros(1, b_num + 1);

for i=1:(a_num + 1)
    p_a(i) = nchoosek(a_num, i-1) * (1/2)^a_num;
    if(i > (b_num + 1))
        break;
    end
    p_b(i) = nchoosek(b_num, i-1) * (1/2)^b_num;
end

if (sum(p_a) ~=1 || sum(p_b)~=1)
    error('fucked in early stage');
end

p_win = 0;
p_lose = 0;
p_equal = 0;

for i=1:(a_num + 1)
    for j=1:(b_num + 1)
        if (i > j)
            p_win = p_win + p_a(i) * p_b(j);
        end
        if (i < j)
            p_lose = p_lose + p_a(i) * p_b(j);
        end
        if (i == j)
            p_equal = p_equal + p_a(i) * p_b(j);
        end
    end
end

if (abs(p_win + p_lose + p_equal - 1) > 1e-4)
    error('checked failed');
end

p_win
p_lose
p_equal