Mathematics of Maximizing Profit in Gambling/Investing - Kelly Criterion

In this video, we introduce the Kelly criterion which is the formula that gives optimal risk that maximizes the long term profit, and we will proceed to derive the formula in a nonstandard way. The necessary prerequisite materials like random variables, transformations of random variables, expected value, generalized mean are introduced in the video. Links: Proof that E(B) = np proofwiki.org/wiki/Expectation_of_Binomial_Distrib… Wiki page which has detailed information about the median and the mode of the binomial distribution en.wikipedia.org/wiki/Binomial_distribution geometric mean is the limit of the power mean as the power goes to 0 planetmath.org/derivationofgeometricmeanasthelimit… Chapters: 00:00 Intro 03:18 Problem Statement 04:51 The Kelly Criterion 06:36 What is an Average? 11:53 First Step towards the Model 13:30 Random Variables 16:00 Expected Value 18:05 Transformation of Random Variables 20:20 Random Variable for the Problem 22:26 Median of Random Variables 29:15 Mode of Random Variables 31:18 Geometric Mean of Random Variables Music🎵: Track 1: Make a bet - BGM President    • [브금대통령](도박/긴장/Casino) Make a Bet [무료음...   Track 2: Confusion in my mind - BGM President    • [브금대통령] (방황/혼란/Emotional) Confusion i...   Track 3: Aurora Currents - Asher Fulero    • Aurora Currents - Asher Fulero   Track 4: The Confused Mind - BGM President    • [Royalty Free Music] The Confused Min...   Track 5: YOLO - BGM President    • [Royalty Free Music] 복세편살/YOLO (Comic...   Track 6: Forest_Sage - PeriTune    • 【無料フリーBGM】幻想的なヒーリング「Forest_Sage」   Track 7: Soul Searching - Causmic    • Soul Searching   Corrections: 18:22 Y=1/X should be 1/X if X ≠ 0 and 0 if X = 0 21:59 E(R) = (1+r)^n, not (1+r)^2