Blog on XTXinverseXTY | John Curcio

KL Divergence and the Kelly Criterion

Sat, 18 Jul 2026 02:09:23 -0400

Portfolio Splitting and the Kelly Criterion

Suppose the Knicks play the Spurs tomorrow.

A bookmaker believes $P(\text{Knicks win}) = p$. He sells two fractional contracts, each fairly priced under that belief:

A $\$1$ Knicks contract that pays $\frac{1}{p}$ if the Knicks win.
A $\$1$ Spurs contract that pays $\frac{1}{1-p}$ if the Spurs win.

(Note: Zero vig $\implies$ fair value = $1)

A gambler believes $P(\text{Knicks win}) = q > p$. He has just $1 but wants to grow it aggressively, so he spends:

The Efficient Market Hypothesis is a Philosophical Razor

Thu, 28 Dec 2023 14:26:53 -0500

I’ve read some inane discussions about the validity of the efficient market hypothesis (EMH). I’ve even participated in some. Proponents warn that cocky retail traders are naive, and detractors point to historical examples of inefficiencies.

I claim this is a category mistake by both parties. The EMH is more like a philosophical razor: you should accept it for a given asset, unless you have some information to the contrary. We might as well call it the efficient market null hypothesis.

Statistical Intuition for Elo Scores

Sun, 11 Jun 2023 21:04:16 -0400

Elo Scoring

Two players have Elo scores $A$ and $B$.

With no info other than that, it’s generally accepted that

$P(A\ beats\ B) = 1 / (1 + 10^{(B - A) / 400})$

If A indeed does beat B, here are the new Elo scores:

$A' = A + K \cdot (1 - P(A\ beats\ B))$
$B' = B - K \cdot (1 - P(A\ beats\ B))$

Where $K$ is a hyperparameter, usually something between 10 and 40.

Inaugural post

Thu, 24 Nov 2022 20:09:36 -0500

Hello, world! It’s me, blog!