If you don't make any assumptions about the underlying distribution you're associating with the risk, it can be anything, so I'm not surprised you haven't found

If you don't make any assumptions about the underlying distribution you're associating with the risk, it can be anything, so I'm not surprised you haven't found an explanation. For example, the risk could be dependent on previously values, dependent on unobservable data, completely independent, etc. etc. If you make some basic assumptions about independence, along with some others that I may not understand so well, you can start to grapple with the idea that you should be decreasing the amount you wager on each round as you're hedging against risk. If you make a mistake in your probability estimation in your favor, then great, you win more, but if you make a mistake against, it bites you and you lose more than you would have thought. In the extreme, your "deflation factor" is 0, meaning you wager nothing so you're completely hedged against risk. In terms of the video you provided, he talked about using a sample of 10 to estimate the probability but notice he didn't even mention the variance of such a limited sample. I don't claim to have any deep knowledge of this but Evan Miller's "how not to sort by average rating" post comes to mind in order to get some handle on this particular setup [0]. From the Miller post: What we want to ask is: Given the ratings I have, there is a 95% chance that the “real” fraction of positive ratings is at least what? Miller advocates for using a lower bound Wilson score confidence interval for a Bernoulli parameter. Again, I'm pretty naive when it comes to this stuff but I suspect this is exactly what would be wanted when trying to apply the Kelly criterion in the example from the video you provided. The reality is that risk management is a big subject precisely because the risk model can be complex. The Kelly criterion is meant to be a starting point for complex real world examples, not the destination. I also found a post that has a nice graphic for deflating the Kelly criterion [1], so maybe that might be helpful to you. [0] https://www.evanmiller.org/how-not-to-sort-by-average-rating.html https://www.evanmiller.org/how-not-to-sort-by-average-rating... [1] https://nickyoder.com/kelly-criterion/ https://nickyoder.com/kelly-criterion/ (just above https://nickyoder.com/kelly-criterion/#theory-vs-reality https://nickyoder.com/kelly-criterion/#theory-vs-reality)