Blog on Anvar A.

Higher or Lower

Wed, 26 Aug 2026 00:00:00 +0000

We discuss the game of higher or lower and an optimal strategy when playing.

Python Micro-optimisations

Sat, 01 Aug 2026 00:00:00 +0000

I provide a series of Python micro-optimisations.

Distance to the Moon

Fri, 01 May 2026 00:00:00 +0000

In light of the recent historic Artemis II launch to return to the Moon for the first time in 50 years, I describe a simple computation of the distance to the Moon from almost first principles.

Arctic Outpost Radio

Mon, 09 Mar 2026 00:00:00 +0000

A short article on Arctic Outpost Radio AM1270, a vintage ratio station broadcasting from the top of the world.

A Review of Descent-Based Optimisation Algorithms

Fri, 20 Feb 2026 00:00:00 +0000

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

Waiting Time and the Inspection Paradox

Tue, 10 Feb 2026 00:00:00 +0000

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.

Poles

Mon, 05 Jan 2026 00:00:00 +0000

We visualise the many different interpretations of the North Pole.

German Tank Problem

Thu, 27 Nov 2025 00:00:00 +0000

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.

Drawdown Formulas

Fri, 21 Nov 2025 00:00:00 +0000

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.

The Game of Life

Thu, 20 Nov 2025 00:00:00 +0000

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

The Kelly Criterion

Thu, 06 Nov 2025 00:00:00 +0000

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

An Even Split in Probability

Sat, 24 Aug 2024 00:00:00 +0000

A generalisation of Q18 from 50 Challenging Problems in Probability.

Fermat's Little Theorem

Fri, 02 Aug 2024 00:00:00 +0000

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