Martingales and the Benefits of Optional Sampling

I answer the following questions: what are martingales? What is optional sampling? And, how can it help us?

This video takes a brief look through history - what martingales are and how they came to be - before getting into the mathematical ideas and, finally, look at a gambling game between Alice and Bob to answer a question asked by Daniel Litt on Twitter.
Betting games on the outcome of coin flips are used to answer tricky mathematical questions and to motivate the theory.


See also my earlier video where I looked at similar betting games to compute the time taken for random events to occur:    • ABRACADABRA! The magic of martingales  

00:00 Intro
00:52 Coin flips and betting
05:32 Martingale origins
08:09 Martingale definition
15:31 Election odds - martingale example
17:50 Optional sampling
20:40 Martingale betting system
28:10 A Twitter question
36:39 Final thoughts

Music used in the intro, outro and title clips is "Almost Sure" by Alex Gonatas:    • Almost Sure  . I thank him for giving his kind permission to include here