I have been recently been going through Blitzstein in an attempt to put my probability on a stronger foundation then it currently is. There is a large emphasis on the use of "story" proofs/definitions in the book
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.
I can understand the appeal since they bypass substantial amounts of algebra in certain cases. However, thinking of the stories is not easy for all problems. And when one has finished the book, I am not sure how useful those skills will be. (For some context, the earlier math/stat courses I had never emphasized the use of story proofs).
In general, how useful are "story" proofs beyond the context of the book I am currently doing (Blitzstein).
I have been going through Blitzstein in a lot more detail. I was initially surprised by his emphasis on story proofs (mostly because my none of earlier courses/professors/books ever emphasized it).
But now that I went through a chapter in detail, I have found that the emphasis works wonders. It is a very different perspective from the one that you get from a mathematical/algebraic focus. Also, the entire book reads like a story (a good one!) where there is a lot of discussion happening.
In conjuction with a book/questions that focus on mathematical derivations, this book will work wonders.