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Simulation Basics: How Odds Tables Are Built
How blackjack odds tables come from simulation and exact calculation: what a simulated round is, how results are averaged, and where the numbers can mislead.
Deeper Maths
Advanced Maths and Simulation
Combinatorics, simulation and risk measures behind the published numbers.
Confidence Intervals for Session Results
Learn how confidence intervals turn blackjack's average result into a range of plausible session outcomes, with a worked illustration and its limits.
Effects of Rules on House Edge: A Table of Changes
A table of approximate house edge changes for common blackjack rule differences, with the assumptions behind them and why the figures vary between sources.
Infinite Deck Versus Finite Deck Calculations
Why blackjack maths often assumes an infinite deck, how that compares to real finite decks, and where the shortcut is accurate or misleading.
Kelly Criterion and Why It Fails Without an Edge
What the Kelly criterion formula says, a worked example with a positive edge, and why it recommends betting nothing when the expectation is negative.
Markov Chains and Dealer Final Totals
How a Markov chain models the blackjack dealer's draw as states and probabilities, with a small worked example and the limits of the simplification.
Monte Carlo Method Applied to Blackjack
An intuitive explanation of Monte Carlo sampling for blackjack: how random trials estimate probabilities, how error shrinks, and what confidence limits mean.
Risk of Ruin Explained
What risk of ruin means, how to compute it for simple bets, and why the chance of losing a bankroll is never zero when the game carries a house edge.
Standard Deviation per Hand in Blackjack
What standard deviation per hand means in blackjack, why it is a little over one unit, and how the spread of results scales with the number of hands.
The Law of Large Numbers at the Table
What the law of large numbers says about blackjack results, why averages settle only over very long runs, and why it does not promise that luck evens out.
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