Fundamentals.  @Fundamentals21mBook: https://zeuspay.com/btc-for-institutionsnpub12eml5kmtrjmdt0h8shgg32gye5yqsf2jha6a70jrqt82q9d960sspky99gAverageGarynpub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9Pascal's Trianglehttps://en.wikipedia.org/wiki/Pascal's_triangleIn this episode, we delve into the fascinating world of probability distributions and their relevance to Bitcoin's security and mining processes. We start by discussing the concept of probability distributions, such as binomial and Poisson distributions, and how they help us understand the likelihood of different outcomes in various scenarios. This understanding is crucial for modeling events like coin flips or mining block rewards, where knowing the average payout and the necessary capital to sustain operations over time is essential. We also touch on the importance of randomness and entropy in cryptographic applications, emphasizing the need for truly random variables to ensure security. The conversation then shifts to the adversarial nature of Bitcoin's network, highlighting the importance of understanding potential attack vectors, such as a 51% attack. We explore how the Poisson distribution is used to model the probability of mining success over a given period, and why it's vital for the network to be tested through both simulated and real-world attacks. The episode underscores the necessity of open-source software in creating robust systems that can withstand various threats, and the role of probability in ensuring the resilience and security of Bitcoin's decentralized network.