Every Bet Size, Simulated 100 Million Times

How much should you bet when the odds are on your side, and how much when they are against you? I played 100 million games to test every bet size, from a single dollar to everything you have. Game 1 is the 60% coin. It copies the setup of a real 2016 experiment by Victor Haghani and Richard Dewey: The coin lands heads 60% of the time. You start with $25 and can bet any amount down to a cent, on heads or tails, at even money. Reaching $250 ends the game: that is the most you can win. You get up to 300 flips. That assumes one flip every 6 seconds for the experiment’s 30 minutes. Game 2 is American roulette: The wheel has 38 pockets, 18 of them red. Every bet is on red at even money. You start with $100, and the night ends when you double it to $200 or go broke. Every strategy sees exactly the same coin flips and the same spins, so every comparison is fair. The coin strategies: • Normal: a flat $2.50 on heads every flip • Flat bets of $1, $5 and $10 • A fixed share of your current money every flip: 2%, 5%, 10%, 15%, 20%, 25%, 30%, 40%, 50% and 75% • All in, every flip • The Kelly criterion (20%, the share that grows money fastest), and Kelly that never bets past the $250 cap • The martingale: $1, doubled after every loss • Kelly that bets tails after three heads in a row • A perfect player: the best possible bet for every amount of money and every number of flips left, computed exactly • A control: a copy of Normal on 4 million different games, to show the simulation is fair The roulette strategies: • Normal: $5 on red every spin • Flat bets of $1, $10, $25 and $50 • All $100 on one spin • 10% of your current money every spin • The martingale from $5, with a $500 table limit • Pressing wins: doubling after each win, back to $5 after three wins or a loss • A control: a copy of Normal on 2 million different nights Coin: 4,000,000 games × 19 strategies, plus 4,000,000 control games. Roulette: 2,000,000 nights × 9 strategies, plus 2,000,000 control nights. That makes 100,000,000 games in total. Extra tests outside the 100 million: The coin with 120 flips instead of 300. The coin with no $250 cap. A 55% coin. European roulette with 37 pockets. Roulette stopping at $150 instead of $200. Checks: a separate, plain re-implementation of each game replays the simulator bet by bet. The fixed roulette bets match the exact gambler’s-ruin formula, and every roulette strategy loses the house edge of 2/38 of what it wagers. Limits: The coin and the wheel are idealised. There are no table minimums except where stated. 300 flips in 30 minutes is an assumption. The real players’ figures come from published reports of the paper. The strategies are rules, not real people. Sources: Haghani and Dewey, “Rational Decision-Making Under Uncertainty: Observed Betting Patterns on a Biased Coin” (2016); J. L. Kelly Jr., “A New Interpretation of Information Rate” (1956); standard American and European roulette rules. DISCLAIMER This video is for entertainment and educational purposes only. It is not financial, investment, betting or legal advice, and nothing in it encourages you to gamble. All results come from a computer simulation. Real casino games have a house edge, so over time the house wins, and no bet size or betting system changes that. The 60% coin does not exist in any casino. Never gamble money you cannot afford to lose, and gambling is only legal for adults where you live. If gambling is causing you or someone you know problems, help is free and confidential: in the US call 1-800-GAMBLER (National Council on Problem Gambling); in the UK call the National Gambling Helpline on 0808 8020 133 (GamCare).