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A Cowboy’s Charm

Let’s show the counterintuitive fact that poker hands themselves are intransitively ordered by pure preflop equity.

“I don’t remember ever having seen a bird asking an ornithologist how to fly.”

A sequential calibration monitor for probabilistic forecasts.

A small tensor autograd engine and neural network library.

This thesis develops a proof of concept for a non-parametric Bayesian trade structuring system that translates an investor’s distributional views about an underlying asset into an implementable position using listed options. Starting from a market-implied prior recovered from listed option prices, the framework incorporates subjective views as constraints to construct a posterior distribution that deviates minimally from the prior while enforcing the view set. The resulting posterior is then used to derive an optimal target payoff profile under objectives such as expected log growth, and to approximate that payoff using practical option structures under real-world constraints like transaction costs and existing portfolio exposures.

In multiplicative wealth dynamics, “equal and opposite” moves correspond to multiplying and dividing by the same factor, not adding and subtracting equal amounts. We show that if an agent is geometrically risk-neutral in the sense that at any wealth level \(w\), they are indifferent between keeping \(w\) and taking a zero time-average growth bet, then their utility must be affine in \(\ln (w)\), hence \(u(w) = \alpha \ln (w) + \beta\).

Practitioners monitoring deployed probabilistic models face a fundamental trap: any fixed-sample test applied repeatedly over an unbounded stream will eventually raise a false alarm, even when the model remains perfectly stable. Existing methods typically lack formal error guarantees, conflate alarm time with changepoint location, and monitor indirect signals that do not fully characterize calibration. We present PITMonitor, an anytime-valid calibration-specific monitor that detects distributional shifts in probability integral transforms via a mixture e-process, providing Type I error control over an unbounded monitoring horizon as well as Bayesian changepoint estimation. On river’s FriedmanDrift benchmark, PITMonitor achieves detection rates competitive with the strongest baselines across all three scenarios, although detection delay is substantially longer under local drift. Code is available at https://github.com/tristan-farran/pitmon.