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The Kelly Criterion provides the optimal strategy when betting on random outcomes with known probabilities.
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TIMESTAMPS
0:00 Intro/The Game
1:16 Growth Rates
3:43 People Play Terribly
4:46 The Best Strategy Possible
7:10 The Kelly Formula Is Dangerous
CODE
https://github.com/Duane321/mutual_information/tree/main/videos/kelly_criterion
SOURCES
I first came across the Kelly Criterion in [1], which features it as a powerful example of the relevance and usefulness of information theory. In chapter 6, you'll find an exact and more general discussion of this idea.
Wikipedia, [2], was also useful, as it is frequently. That's where I learned about [3], which was an interesting case study about how bad we are at this game. As an aside, I actually ran the experiment on a friend and didn't find similar results - I guess she was pretty smart! She bet about 3-5 dollars on each flip, with the wagers moving to the larger side of this range as the wealth increased.
[4] is the original paper. It's a nice explanation, but relies on some background knowledge of information theory. If you're curious about the connection to information theory, this is the place to look.
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[1] T. M. Cover and J. A. Thomas. Elements of Information Theory. 2nd edition. John Wiley, 2006.
[2] Kelly Criterion, Wikipedia, https://en.wikipedia.org/wiki/Kelly_criterion
[3] V. Haghani, R Dewey, "Rational Decision-Making Under Uncertainty: Observed Betting Patterns on a Biased Coin", Journal of Portfolio Management, 2016
[4] J. L. Kelly Jr, "A New Interpretation of Information Rate", Bell System Technical Journal, 1956