命运子弹
Bullets of Fate
题目详情
房间里有 个持枪者。每到钟声响起，所有人同时随机选择另一个人射击。
被射中的人当场死亡，存活者在下一次钟声继续同样过程。
最终要么全死，要么只剩 1 个幸存者。
问：当 时，出现幸存者的概率极限是多少？
备注：原作者也未给出严格证明。
In a room stand armed and angry people. At each chime of a clock, everyone simultaneously spins around and shoots a random other person. The persons who get shot, fall dead and the survivors spin and shoot again at the next chime. Eventually, either everyone is dead or there is a single survivor.
As grows, what is the limiting probability that there will be a survivor?
Warning: I could not solve it. The solution only shows what I tried.
解析
目前更像是一个“数值观察题”。原作者通过模拟/暴力/动态规划实验发现：该概率似乎趋近于 0.5，但未给出严格证明。
中文侧保留这一结论与限制：只有经验现象，没有证明。
Original Explanation
Solution
I have tried the following scripts
Following is the pattern.
It appears to be moving towards 0.5 but I do not have any proof or any intuitive logic as to why.
Also, not sure why these waves appeared, and why the wavelength is expanding.