孩子参加上海围棋升级赛，规则是
1级者7局5胜升至初段
2级者7局5胜升至1级
3级至5级7局4胜升一级
6级至8级6局3胜升一级
9级至10级5局2胜升一级
同时，如果一场比赛中，如果已经胜利了可以升级的场数，就不需要再比了，如果失败了剩余比赛都胜利了也一定升不了级的场数，也不需要再比了。
对于升级的概率比较感兴趣，写了个模拟程序。算出大概的通过率是
1级者7局5胜升至初段 5/7 17%
2级者7局5胜升至1级 5/7 17%
3级至5级7局4胜升一级 4/7 50%
6级至8级6局3胜升一级 3/6 66%
9级至10级5局2胜升一级 2/5 80%
可以看出，一开始通过率很高，到后面升级还是很困难的。
程序如下：
'''
simulate 100 player
how to match: play with adjacent player
each player has 50% rate to win
if play win win_count_to_pass times, it is passed, no need to match
if player failed (total_games-win_count_to_pass+1) times, no need to match
'''
import random
def check_if_passed(list_item, win_count_to_pass):
cnt=0
for i in range(7):
if list_item[i+1] is True:
cnt += 1
if cnt >= win_count_to_pass:
return True
else:
return False
def check_if_kicked(list_item, raced_cnt, total_games, win_count_to_pass):
fail_cnt = total_games-win_count_to_pass+1 # for pass 2/5, fail 4 games will fail, for pass 5/7, fail 3 games will fail
if raced_cnt<fail_cnt: # have not race fail_cnt times
return False
cnt=0
for i in range(raced_cnt):
if list_item[i+1] is False:
cnt += 1
if cnt == fail_cnt:
return True
else:
return False
# first round, 1 vs 2, 2 is already played with 1, so next loop start from 3
def check_if_raced(list_item, which_game):
if list_item[which_game+1] is True:
return True
else:
return False
def getPasRate(total_games, win_count_to_pass):
students_win_list = []
students_raced = []
for i in range(100):
students_win_list.append([i, False, False, False, False, False, False, False, False]) # last bool True indicate pass
students_raced.append([i, False, False, False, False, False, False, False])
for i in range(total_games):
for j in range(0, 100):
if check_if_raced(students_raced[j], i) or check_if_passed(students_win_list[j], win_count_to_pass) \
or check_if_kicked(students_win_list[j], i, total_games, win_count_to_pass):
continue
else:
for k in range(j+1, 100):
if check_if_raced(students_raced[k], i) or check_if_passed(students_win_list[k], win_count_to_pass) \
or check_if_kicked(students_win_list[k], i, total_games, win_count_to_pass):
continue
else:
if random.randint(1,100) % 2 == 0: # j win
students_raced[j][i+1] = True
students_raced[k][i+1] = True
students_win_list[j][i+1] = True
students_win_list[k][i+1] = False
print("Race " + str(i+1) + ", player " + str(j) + " vs " + str(k) + ", player " + str(j) + " wins")
else: # k win
students_raced[j][i+1] = True
students_raced[k][i+1] = True
students_win_list[j][i+1] = False
students_win_list[k][i+1] = True
print("Race " + str(i+1) + ", player " + str(j) + " vs " + str(k) + ", player " + str(k) + " wins")
break # player 1 already played with 2, no need to play with others
win_count = 0
for i in range(100):
if check_if_passed(students_win_list[i], win_count_to_pass):
win_count += 1
students_win_list[i][8] = True
#print("player " + str(i) + ": ")
#print(students_win_list[i])
return win_count
if __name__ == '__main__':
pass_count = getPasRate(5,2)
print(pass_count)
网友评论