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
https://proofwiki.org/wiki/Expectatio...
Wiki page which has detailed information about the median and the mode of the binomial distribution
https://en.wikipedia.org/wiki/Binomia...
geometric mean is the limit of the power mean as the power goes to 0
https://planetmath.org/derivationofge...

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)^20