**An English translation of the paper titled *Endliche Automaten und Zufallsfolgen* ** Here is an [English translation](files/schnorr_Eng.pdf) of a German paper (translated by me + Google Translator) here. The funny thing is, I don't know any German, nor my English writing is excellent. **Title**: Finite Automata and Random Sequence (or Endliche automaten und zufallsfolgen) **Authors**: C. P. Schnorr and H. Stimm. **File**: [the English translation](files/schnorr_Eng.pdf). **Acknowledgment**: Professor Schnorr granted permissions to put the papers above on this page. This paper contains the so-called Schnorr-Stimm dichotomy theorem, which concerns finite-state gamblers that bet on infinite sequences of symbols taken from a finite alphabet. The theorem asserts that, for each such sequence S, the following two things are true. * 1. If S is normal in the sense of Borel (meaning that any two strings of equal length appear with equal asymptotic frequency in S), then every finite-state gambler loses money at an exponential rate betting on S. * 2. If S is not normal, then there is a finite-state gambler that wins money at an exponential rate betting on S. Not a lot of people really read the originally proof, since it is in German. I decided to read it nonetheless. So I used Google Translator to help me along the way. I took notes carefully because I didn't want to retype everything I had typed and asked Google Translator again. I reframed Google Translator's output together with my understanding and generate this document. Their paper also contains a detailed reproof (and extension) of [Agafonov's theorem](files/agafonov.pdf), whose original proof is way too short to be comprehended.