The mathematics of games of chance

Probability, expected value and simulation, applied to blackjack, roulette and poker. Every claim is checked against the maths or tested in code, and the code is published.

• Blackjack Crash Course: How Card Counting Actually Works

  A plain-numbers guide to card counting: why it works, how the Hi-Lo count and true count are calculated, and what edge a counter can realistically expect.

• Simulating 10 Million Blackjack Hands in Python

  A small, readable blackjack simulator in plain Python: basic strategy versus a Hi-Lo count over ten million hands, with the code and the results.

• House Edge Explained: Casino Games Ranked by Expected Value

  What the house edge is, how to calculate it from the payout table, and how the common casino games compare, from baccarat's banker bet to keno.

• The Math of Variance: Why Players With an Edge Still Go Broke

  Expected value tells you where you end up eventually. Variance tells you how bumpy the road is, and risk of ruin tells you whether you survive it. Worked numbers for a card counter.

• Poker Odds and Equity: A Probability Primer

  The handful of exact probabilities every Texas Hold'em player should know: starting hands, flopping sets, completing draws, the rule of 4 and 2, and pot odds.

• The Gambler's Fallacy and Other Probability Traps

  After five reds in a row, is black due? We checked twenty million simulated roulette spins, and looked at the 1913 Monte Carlo streak and the surprising twist in the hot-hand research.

• Roulette Betting Systems Tested by Simulation

  Martingale, D'Alembert and flat betting, each run for 100,000 simulated sessions on a European wheel. The systems change how you lose, not how much.