The Kelly Criterion (w/ MathML)

2025-07-20 14:20:21 PDT (last update 2025-07-20 14:26:49 PDT)

I became aware of the Kelly Criterion a while back through YouTube or something. It's a really interesting idea. Imagine that you want to maximize your return over the long term from independent bets in some game.

For example imagine playing poker with a current stack CC of chips. Say that you can make a bet of size cc with expected win probability p>0.5p > 0.5. Let the "fractional return" of the bet be bb: that is, you will get bcbc chips for winning the bet.

The Kelly Criterion suggests that you optimize your long-term return by choosing

c=C(p−1−pb)c = C \left( p - \frac{1 - p}{b} \right)

If you bet more, you will win too little per win over the long term due to excess risk of shrinking your bankroll. If you bet less you will not get the return you "deserve".

There is a fancy proof of optimality of the Kelly Criterion involving log-likelihood.

I am thinking about the Kelly Criterion and variants in the context not just of Poker, but of Yahtzee. I will report here if I figure out anything interesting that is new to me.

There's some math above. Hooray. I have switched my GitAtom blog software to use Python's pandoc library instead of cmarkgfm. It still does Github-flavored Markdown, but has an option to generate MathML. I don't like that Pandoc centers display math, and I'm not sure the HTML renders as well in Chrome or Safari as it does in Firefox. That said, I like using math, so I will likely stick with it for now.