Gambling with the Martingale Strategy
Numberphile · Why doubling after losses can't beat the edge
The casino, explained
Casino math, decoded.
Learn how every game really works, practice with free labs that never touch real money, and see the house edge before it sees you.
No real-money gamblingNo casino affiliate linksMath you can verify100% free
What does a casino trip really cost?
Live calculatorExpected loss for the same bet and time, by game. Change the numbers.
Uses typical pace (rounds per hour) and standard house edges. Full calculator →
31
in-depth, math-checked guides
10
free interactive labs & calculators
202
casino terms in plain English
$0
ever asked of you to play or learn
Free labs · virtual chips only
Practice without paying the house
Each lab runs the real game math in your browser. Make mistakes for free, then see exactly what they would have cost.
Blackjack Strategy Trainer
Instant feedback on every decision, a live strategy chart and a weak-spot map that shows where you leak money.
Start drilling →Roulette & Betting-System Simulator
Run 1,000 sessions of Martingale, Fibonacci or D'Alembert and watch what the house edge does to them.
Run a simulation →Slot RTP & Volatility Simulator
See why a 96% RTP game can still empty a bankroll — and how volatility changes the ride.
Spin the math →Hold'em Odds Calculator
Pick any hand and board. Get win, tie and hand-type odds against up to nine opponents.
Calculate equity →Dice & Craps Lab
Roll two dice 10,000 times and watch the bell-shaped truth behind every craps bet.
Roll the dice →Coin-Flip Streak Lab
Think a streak means something is “due”? Test the gambler's fallacy — and try to fake randomness.
Flip coins →
The house edge leaderboard
Not all bets are created equal
The house edge is the share of every dollar wagered that the casino expects to keep over the long run. A 0.5% edge and a 25% edge are different universes.
Compare any game → How house edge works| Bet | House edge | Keep per $100 bet |
|---|---|---|
| Blackjack, basic strategy (good rules) | ≈ 0.5% | $0.50 |
| Baccarat — Banker | 1.06% | $1.06 |
| Craps — Don't Pass | 1.36% | $1.36 |
| Craps — Pass Line | 1.41% | $1.41 |
| European roulette | 2.70% | $2.70 |
| American roulette | 5.26% | $5.26 |
| Baccarat — Tie (8:1) | 14.36% | $14.36 |
| Keno (typical) | 25%+ | $25+ |
Learning paths
Pick a path. Get sharper in an evening.
Start here
New to casino math? Read these six in order.
- House Edge Explained: The Number Every Casino Game Is Built On
- Expected Value (EV) for Beginners: The Math of Every Bet
- How to Play Blackjack: Complete Rules for Beginners
- Roulette Rules & Odds: European vs. American vs. French
- The Gambler's Fallacy: Why Due Numbers Don't Exist
- Responsible Gambling: A Practical Guide to Staying in Control
Math deep-dive
Variance, risk of ruin and why betting systems fail.
- The Law of Large Numbers: Why the Casino Wins Over Time
- RTP vs. Volatility: What Slot Numbers Really Mean
- Bankroll Math and Risk of Ruin: How Long Will Your Money Last?
- The Martingale System: Why Doubling Up Fails (With the Math)
- Betting Systems Tested: Fibonacci, D'Alembert, Labouchère and Paroli
- How Random Number Generators (RNGs) Work in Casino Games
Table-game mastery
Optimal play for the games with the lowest edges.
- Blackjack Basic Strategy: The Complete Chart, Explained
- Card Counting Explained: How It Works and Why It's Hard
- Craps for Beginners: The Best and Worst Bets on the Table
- Baccarat Explained: Banker vs. Player and the Tie Trap
- Video Poker Basics: Pay Tables, Return & Optimal Play
- Poker Hand Rankings & Probabilities (With Odds Table)
Play safe
Budgets, warning signs and the psychology working against you.
Why “e”?
The casino's favorite constant
Take any 1-in-N shot and try it N times. You'll miss every single time about 36.8% of the time — that's 1/e, where e ≈ 2.71828. Bet a roulette number for 37 spins and there's a 36.3% chance it never hits. Our name is a reminder that intuition about luck is usually wrong, and math is usually right.
Try the “at least once” calculator →Fresh guides
All guides →Latest from the academy
Video Poker Basics: Pay Tables, Return & Optimal Play
How video poker works: reading 9/6 and 8/5 Jacks or Better pay tables, what 99.54% return really means, and the hold decisions that matter, with exact EVs.
Read guide →Texas Hold'em Odds: Outs, Pot Odds & the Rule of 2 and 4
Learn Texas Holdem odds: starting-hand math, counting outs, the rule of 2 and 4, pot odds and when a call is profitable, with exact percentages and examples.
Read guide →Sports Betting Math: Vig, Overround and Why Bookmakers Profit
Why a standard -110 line needs a 52.38% win rate to break even, how overround and parlays build in margin, and why even skilled bettors drown in variance.
Read guide →Warning Signs of Problem Gambling (and Where to Get Help)
Chasing losses, hiding spending and gambling to escape stress can signal a problem. Learn the common warning signs, how to raise them and where to find help.
Read guide →How to Set an Entertainment Budget for a Casino Trip
Budget a casino trip like any night out: estimate the expected cost with the theo formula, add a cushion for swings and set firm limits for every session.
Read guide →RTP vs. Volatility: What Slot Numbers Really Mean
RTP sets the long-run cost of a slot and volatility sets the swings. Three machines with the same 96% RTP show why your session rarely looks like the average.
Read guide →
Free starter kit
Get the Casino Math Starter Kit
A printable blackjack strategy card, a house-edge cheat sheet for 30+ bets, and a short weekly email that makes you harder to fool. Free, no spam, unsubscribe anytime.
Watch & learn
Video library →The best videos on casino math
The Trillion Dollar Equation
Veritasium · Includes Ed Thorp's journey from blackjack to markets
The Magic Economics of Gambling
Wendover Productions · How casinos engineer profit from every square foot
Skill challenge · free entry
The monthly Strategy Sprint
Play 50 hands in the Blackjack Trainer. Highest accuracy wins — no purchase, no wagering, judged on skill. Prizes are funded by sponsors and supporters.
Industry & research
Headlines, refreshed daily
- Fresh headlines load here automatically each day. Meanwhile, see the research and regulator sources below.
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Keep the math free and independent
Donations fund hosting, new labs, writers and mathematicians, outreach, and contest prizes. Because we take no casino money, readers keep us honest.
Questions, answered
Is e.casino an online casino?
No. e.casino is an independent educational site. There is no real-money gambling, no deposits and no casino affiliate links. Every lab uses virtual chips that have no value.
Can I win money on e.casino?
Not from gambling outcomes. The labs and simulators are free and have no prizes. Our monthly skill contests are free to enter and are judged on knowledge and accuracy, not chance.
How accurate is the math?
Every figure is derived from first principles or standard published game math, and we cross-check it with our own simulators. Our editorial policy explains how we verify numbers and correct errors.
How does e.casino make money?
Through display advertising, sponsorships and supporter donations. We never take commissions from casinos or betting operators, so nothing on the site is written to sell you a bet.
Is the e.casino domain available for partnership or purchase?
Yes. We welcome inquiries about acquiring or leasing the domain, sponsorship, advertising and partnerships. Use the Partner page to send a confidential inquiry.
18+Gambling should be entertainment, never income. If it stops being fun, free, confidential help is available 24/7 — or take our 2-minute anonymous self-check.