问题描述:在可以随机选择出场顺序的情况下,如果把比赛规则从三局两胜制改为五局三胜制,齐王胜出的概率是上升了还是下降了?五局三胜的赛制下,大家的马重新分为5个等级。前提条件仍然是齐王每种等级的马都优于田忌同等级的马,且田忌高一等级的马要优于齐王低一等级的马。
matlab代码如下:
clear, clc, close all;
% 定义齐王和田忌的马的等级,分别用数字表示,数字越大等级越高
qwang_horses = [5 4 3 2 1]; % 齐王的马等级
tiji_horses = [4 3 2 1 0]; % 田忌的马等级
% 生成所有可能的出场顺序组合
qwang_orders = perms(qwang_horses);
tiji_orders = perms(tiji_horses);
% 计算三局两胜制下齐王胜出的概率
win_count_qwang_5of3 = 0;
for i = 1:size(qwang_orders, 1)
for j = 1:size(tiji_orders, 1)
qwang_order = qwang_orders(i, :);
tiji_order = tiji_orders(j, :);
win_count_qwang_5of3_round = 0;
for k = 1:length(qwang_order)
if qwang_order(k) > tiji_order(k)
win_count_qwang_5of3_round = win_count_qwang_5of3_round + 1;
end
end
if win_count_qwang_5of3_round >= 3
win_count_qwang_5of3 = win_count_qwang_5of3 + 1;
end
end
end
total_combinations_5of3 = size(qwang_orders, 1) * size(tiji_orders, 1);
probability_qwang_5of3 = win_count_qwang_5of3 / total_combinations_5of3;
disp(['五局三胜制下齐王胜出的概率: ', num2str(probability_qwang_5of3)]);