科学证明十赌九输 完全解释赌徒心理

赌徒其实最大的心理特点就是盲目乐观,他们总是能够乐观地认为,自己可以翻本,甚至可以赚钱。其实输赢就是一种概率,而概率属于自然科学领域,是一种不可战胜的规律,所以我们要了解一个什么叫概率,先了解几个概念。

一、独立事件

你在玩一个极其简单的掷硬币的游戏,前几次掷出的均为正面,那么在下一把时,你总会觉得掷出反面的概率大于50%。但事实上,无论你前面是连续掷出了100个正面,对后面第101次投掷也是没有影响的。这就叫“相互独立事件”。错把独立事件当成相互关联事件,就极容易掉进了“赌徒谬误”(也称蒙地卡罗谬误)的坑里。

当然也有一种逆向的思维,他们认为既然前5次都是正面,那么凭着我的“运气”第6把同样是正面的几率更大,这也被称为热手谬误,属赌徒谬论的另一个版本。

无论是赌徒谬误还是热手谬误,都属于一种会赢的错觉。

二、大数定律

所谓大数定律,指的是随机事件的大量重复出现中,往往呈现出必然的规律。也就是说,在实验条件不变的情况下,重复实验越多,随机事件出现的频率就越近似于它的概率。当随机事件发生的次数足够多时,发生的频率便趋近于预期的概率。所以大家都认为,随机便是均匀,如果过去一段时间内发生的事件不均匀,大家就会以为未来的事情会尽量往“平衡”的方向走。也就是如果连输几把的话,下一把赢面就会更大。但大数定律的工作机制,并不是为了和过去已发生的事情搞平衡与对抗。因为,没有人能够知道,到底要多大的基数,才会使得各个结果得到平衡。

对于该问题,概率论早就给出了答案——无穷大,而大多数赌徒都死在足够大基数的试验当中

三、概率偏向资本积累更多的一方

早在18世纪初,那群热爱赌博的概率论数学家们,就提出了那个让赌徒们闻风丧胆的“赌徒破产定理”。所谓赌徒破产定理,指的是在“公平”的赌博中,任何一个拥有有限赌本的赌徒,只要长期赌下去,必然有一天会输个精光。假设赌徒的初始资金是n,每赌一次或输或赢,资金分别会变为n-1和n+1。输或者赢的概率为 1/2,求一直赌下去。赌徒资金变为0的概率是多少?

假设从资金为n开始一直赌下去,n变为0的概率是P(n)。
那么我们有: p(n) = (p(n + 1) + p(n – 1))/2,对n>0.即数n有一半的机会变成n+1,一半的机会变成n-1。
而当 n = 0 的时候,即使不用赌,赌资也等于全部输光了,所以 p(0) = 1。
由此,p 可以看作一个满足下列递推关系的数列
p(0) = 1
p(n+1) = 2 * p(n) – p(n-1)
设p(1)的值为a, 那么显然0< a<=1。利用p(n+1) = 2 * p(n)-p(n-1),得:
p(1) = a
p(2) = 2a – 1
p(3) = 2(2a-1) – a = 3a – 2
p(4) = 4a – 3

p(n) = na – n + 1.
我们知道p(n) >= 0对于任意的n成立。
在n(a-1)+1这种情况下,a无限接近1,所以我们证明了p(1) 约等于 1. 同样的过程可以得到p(2)约等于 1, …,
一直下去,p(n) 约等于 1,也就是赌徒资金变为0的概率为1。

这样,我们得到了一个违背直觉的结论:无论你多富有,只要你的财富不是无限的,只要你用50%的概率赌下去,必然会在某一次赌博中输个精光。同时我们也理解了,为什么越有钱的人运气越好,会变得越来越有钱。在赌场当中,只要庄家的钱比你多,即使在50%的随机概率下,因为原始资本的不同而变得并不公平。而且,一般的赌场,赌徒每次赢的概率远比50%要小,毕竟赌场要赚钱,就会设计有利于赌场的赌局。

四、错误理解的赌场必胜法则

所谓赌场必胜法则就是,下一把是上一把两倍的赌注,一旦赢一把,就可以将之前所有的输的钱全赢回来,还能够得到100%的利润,具体操作如下:

第一把下注100押大,输了;

第二把下注200押大,输了;

第三把下注400押大,输了;

第四把下注800押大…

这种加倍赌注法随着赌注越来越大似乎增大了赢的概率,但不要忽略你承担的风险也会越来越高,在后面,只要你输一次,就很容易被打入18层地狱永不翻身。很多网络是招揽人赌博的人就是采用这种倍投办法拉你入坑,

但我们可以看出,在绝对公平的情况下,由于所掌握的基数不同,赢的机率会偏向资本偏多的一方

假设每一次赌局中,输赢的概率都是50%,而参与者有10名手持500块的富人和90名手持100块的穷人进行赌局,每人每次都拿出1块钱进行赌局,按绝对公平的概率进行重新分配(我认为公平的赌局就是在没有人坐庄的情况下,财富的随机重新分配,),在经过大约20000次的赌局之后,财富的积累如下图所示:

以上红线代表富人,绿线代表穷人,可以看出最终财富仍然积累到少数富人手上,而穷人可能会更穷,虽然富人中虽然也有败家玩意,但他们仍有很大概率将财富值维持在较高水平。富人和穷人生活在两个世界中,只是偶有交集而已。看来即便是绝对的公平,这个世界也会因为出身的不同而残酷无比,而赌场就是体现这种残酷最典型的地方。

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