Escaping the Odds and a Formula for Life (2024)

I enjoyed the article, well written and engaging.

(It gave me a small sense of reading a recipe blog where the meta is to tell an enormous backstory)

I kind of sympathise with the premise of trying to somewhat soften the economic-worldview (and language) that we are so used to and to extrapolate into our day to day life.

But in the end it still talks about investing in my friends, and that just isn't for me.

> Kelly variants: Betting full Kelly can be psychologically draining, especially with volatile outcomes. Many find that betting half or quarter Kelly reduces emotional swings while still capturing significant long-term growth.

Betting less than Kelly is just as bad as betting more than Kelly! You optimise your expected log growth by betting Kelly.

One problem with Kelly Criterion is that the swings are wild if you apply it. For example if your winning percentage is 55% on a double or nothing bet and you bet according to Kelly 1000 times you are practically guaranteed to have a drawdown of 50% at some point. If you bet 1/2 Kelly the odds of that are about 86% and if you bet 1/4 Kelly they are below 10%.

I've written quick Python script to show the results (1000 bets, 55% winning percentage, starting bankroll 1000, 10000 simulations each).

    Full Kelly:
    Average: 14174823.8 Median: 149660.0 drawdown50: 1.000 drawdown75: 0.939
    1/2 Kelly:
    Average: 145075.3 Median: 42632.0 drawdown50: 0.862 drawdown75: 0.135
    1/3 Kelly:
    Average: 27929.5 Median: 16098.0 drawdown50: 0.330 drawdown75: 0.009
    1/4 Kelly:
    Average: 12146.9 Median: 8916.0 drawdown50: 0.086 drawdown75: 0.000

drawdown50 is a probability of losing 50% of your bankroll at some point and drawdown75 is a probability of losing 75% of your bankroll at some point.

It's a wild ride either way but maybe consider that your utility of money function flattens out much faster than logarithmic one. You may not be able to get 1000 bets in and maybe you don't need 1000x or even 100x your starting capital to get all the money you could ever need.

Yet this article, like thousand others, don't go beyond binary decisions. Binary decisions are fine for many everyday decisions like figuring out whether to get insurance[1] but the Kelly criterion goes well beyond that[2] without changing the fundamentals: estimate a joint probability distribution of the outcome for each alternative, evaluate E(log X) using it, and pick the alternative for which it is highest.

For a deeper introduction, I recommend the somewhat heavy Kelly Capital Growth Investment Criterion[3] which is a well-curated collection of papers on the Kelly criterion and its various uses.

[1]: https://xkqr.org/insurance/?wealth=0&offered=0

[2]: https://entropicthoughts.com/the-misunderstood-kelly-criteri...

[3]: https://www.amazon.com/KELLY-CAPITAL-GROWTH-INVESTMENT-CRITE...