We discuss gradient descent based optimisation algorithms, starting from simple gradient descent and slowly making our way to the famous Adam optimiser, motivating adaptations that lead to the optimisers along the way.

Faced with the choice of walking or waiting for a shuttle at Auckland Airport, we explore the optimal strategy in expectation. Starting from a simple deterministic model, we introduce uncertainty in bus headways and discover the inspection paradox: under any variance in arrival times, the expected wait is always longer than the naive estimate of half the mean headway.

We visualise the many different interpretations of the North Pole.

A review of the famous German Tank Problem on estimating the number of German tanks in production conducted by the Allied forces during WW2. A discussion and derivation of the estimator used is also provided.

Discuss and document proofs to a recent article by Gappy on a number of drawdown formulas that are useful in evaluating the probability of drawdown events of portfolios.

We implement Conway’s Game of Life as an exercise in inserting JavaScript into my blog posts.

A summary of the Kelly Criterion and the optimal sizing of bets for maximal expected logarithmic returns.

A generalisation of Q18 from 50 Challenging Problems in Probability.

A cute little trick to solving Fermat’s Little Theorem.