Confidence via Capital Growth
Published:
This semester, I took a “special topics” graduate class through CU Computer Science on game-theoretic probability and statistics. “GTP” is a funky emerging branch of math. In its purest form, it argues that we don’t need measure theory to understand probability. Instead of starting with the assignment of probabilities to events (and their unions and intersections) via a measure, GTP starts with betting games, where a player expresses their belief about the probability of an event by betting for or against the event at a given price. If gambling strategies exist which guarantee the gambler a certain gain, then we can define probabilities in terms of (the inverse of) gambler’s certain gain. Theorems about probability (for example, theorems like the law of large numbers which show that some events have 0 probability) can be proven via general gambling strategies.