Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc) - IS CHESS A GAME OF CHANCE? Classical vs Frequentist vs Bayesian Probability

Learn more about probability - and so much more - at http://www.brilliant.org/treforbazett. My thanks to Brilliant for sponsoring today's video. Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor What, exactly, is probability? In this video we will see a few different perspectives on chance, the classical or a priori viewpoint, the frequentist or empirical viewpoint, and finally the Bayesian or subjective viewpoint. We're even going to consider the game of chess, what appears to be overwhelmingly a game of skill, but which the limits of our bounded rationality still results in probabilistic elements. 0:00 Intro to Probability 0:50 Classical Probability 2:09 Frequentist Probability 5:18 Bayesian Probability 7:14 Is Chess a game of chance? 11:05 Underestimate the role of chance 11:47 Brilliant.org/treforbazett Classical Probability: This is when we have a finite set of equally likely possibilities, and thus the probability of an event A is just the number of times A occurs out of all the possibilities. This is great when we know everything about a situation like a normal deck of cards. Frequentist Probability: This is when we do emperical studies and see how frequently event A occurs, particularly in the limit as we do a large number of studies. This is great when we don't know a priori exactly what is going on like some deck with an unknown number of cards removed, but the downside is we need to be able to do a large number of trials. Bayesian Probability: This is when we begin with a prior probability and when we gain new information we update our worldview (often using Bayes' Theorem) to get a posterior probability. This viewpoint is subjective because you and I may get different results given different information and different even if we had the same prior probability. COURSE PLAYLISTS: ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa ►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw ►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 ►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography