The Chernoff bound is one of the most widely used tools in theoretical computer science. It's rare to find a randomized algorithm that doesn't employ a Chernoff bound in its analysis. The standard proofs of Chernoff bounds are beautiful but in some ways not very intuitive. In this paper, I'll show you a different proof that has four features: (1) the proof offers a strong intuition for why Chernoff bounds look the way that they do; (2) the proof is user-friendly and (almost) algebra-free; (3) the proof comes with matching lower bounds, up to constant factors in the exponent; and (4) the proof extends to establish generalizations of Chernoff bounds in other settings. The ultimate goal is that, once you know this proof (and with a bit of practice), you should be able to confidently reason about Chernoff-style bounds in your head, extending them to other settings, and convincing yourself that the bounds you're obtaining are tight (up to constant factors in the exponent).

翻译：切尔诺夫界是理论计算机科学中最广泛使用的工具之一。在随机算法的分析中，几乎很难找到不应用切尔诺夫界的情况。切尔诺夫界的标准证明虽然优美，但在某些方面并不十分直观。本文展示一种不同的证明方法，该方法具有四个特点：(1) 该证明为切尔诺夫界的形式提供了强烈的直观解释；(2) 该证明易于理解且（几乎）无需代数运算；(3) 该证明同时给出了匹配的下界，直至指数中的常数因子；(4) 该证明可推广至其他场景中切尔诺夫界的泛化形式。最终目标是，一旦掌握此证明（并通过少量练习），读者应能在脑海中自信地推导切尔诺夫式界限，将其推广至其他场景，并确信所获得的界限是紧的（直至指数中的常数因子）。