关于Stat 110课程中Story Proof的构成与有效性的技术问询

我最近在跟着Stat 110的系列讲座学习，接触到了**Story Proof（故事证明）**这个概念。我在作者的《概率论导论》里读到了这样一段解释：

A story proof is a proof by interpretation. For counting problems, this often means counting the same thing in two different ways, rather than doing tedious algebra. A story proof often avoids messy calculations and goes further than an algebraic proof toward explaining why the result is true. The word “story” has several meanings, some more mathematical than others, but a story proof (in the sense in which we’re using the term) is a fully valid mathematical proof. - Introduction To Probability, page 20.

不过我还是有点困惑：故事证明到底是由什么构成的？

目前我的理解是，故事证明会构建两个现实场景，它们应该是在计数同一个事物，接着把这两种计数方式转化为数学表达，最后让它们相等。

但这里有个疑问：如果不做具体的数学验证，怎么能确保这两个场景真的在计数同一个对象呢？难道到头来还是得去核对数值层面的证明？那这样的话，故事证明不就变得多余了吗？

备注：内容来源于stack exchange，提问作者Connor