Casino Math & Probability

The probability behind casino games: house edge, odds, and expected value worked out in plain numbers so you can see exactly where the math leads.

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La Partage and En Prison: The Two French Rules That Halve the Edge

La Partage and En Prison: The Two French Rules That Halve the Edge

French roulette's La Partage and En Prison rules cut the even-money house edge from 2.70% to 1.35%. Here's exactly how the math works on a single zero.

Roulette Inside vs. Outside Bets: A Risk-Adjusted Comparison

Roulette Inside vs. Outside Bets: A Risk-Adjusted Comparison

Inside bets pay 35:1 and hit once in 37 spins. Outside bets pay 1:1 and hit ~48.6% of the time. Same house edge — wildly different ride. Here's the math.

Fifteen Reds in a Row: When Roulette Streaks Are Math, Not Magic

Fifteen Reds in a Row: When Roulette Streaks Are Math, Not Magic

Stop-Loss and Stop-Win Rules: Math vs. Psychology

Stop-Loss and Stop-Win Rules: Math vs. Psychology

Kelly Criterion for Casino Games: When Math Tells You to Sit Out

Kelly Criterion for Casino Games: When Math Tells You to Sit Out

Flat Betting vs. Progressive Betting: A Variance Comparison

Flat Betting vs. Progressive Betting: A Variance Comparison

Oscar’s Grind: Why a ‘Smart’ Progression Still Loses

Oscar’s Grind: Why a ‘Smart’ Progression Still Loses

D’Alembert: The Pseudo-Conservative Betting Trap

D’Alembert: The Pseudo-Conservative Betting Trap

Paroli (Reverse Martingale): The Math of Riding Streaks

Paroli (Reverse Martingale): The Math of Riding Streaks

Labouchere Cancellation System: The Math of Why ‘Eraser Tape’ Fails

Labouchere Cancellation System: The Math of Why ‘Eraser Tape’ Fails

Fibonacci Betting: Pretty Sequence, Same House Edge

Fibonacci Betting: Pretty Sequence, Same House Edge

EZ Baccarat, Punto Banco, Chemin de Fer: A Probability Comparison

EZ Baccarat, Punto Banco, Chemin de Fer: A Probability Comparison