Time-to-Ruin Calculator
Calculate how long your bankroll will last based on playing frequency and bet sizing.
Use this tool →Gambler's Ruin Calculator
The "gambler's ruin" is one of the oldest problems in probability theory, dating back to the 17th century correspondence between Blaise Pascal and Pierre de Fermat. This calculator shows you the exact mathematical probability of going bust before reaching a win goal—and reveals why the house edge makes long-term winning virtually impossible.
🎲 Ruin vs Goal Calculator
Calculate your probability of going bust versus reaching your target
Your starting amount
Target to stop at
Amount per bet
Understanding the Gambler's Ruin Problem
The gambler's ruin problem asks: if you start with a certain bankroll and repeatedly make even-money bets, what is the probability you'll reach a target goal before going broke? This seemingly simple question reveals deep truths about gambling mathematics that every casino patron should understand.
The mathematics behind this problem was studied extensively by mathematicians including Christiaan Huygens in 1657 and later formalized using random walk theory. According to research published in the American Mathematical Monthly, the problem has applications far beyond gambling—in genetics, ecology, and financial mathematics.
Did You Know? Even in a perfectly fair 50/50 game with no house edge, if you have $100 and want to double it to $200 while betting $1 at a time, you have exactly a 50% chance of going bust. But if the casino has even a tiny 1% edge, your ruin probability jumps to about 73%!
The Mathematics Behind Ruin Probability
For a game where you win with probability p and lose with probability q = 1 - p, starting with n units and aiming to reach N units, the probability of ruin is:
When p ≠q (unfair game):P(ruin) = (1 - (q/p)^n) / (1 - (q/p)^N)
When p = q = 0.5 (fair game):P(ruin) = 1 - (n/N) = (N-n)/N
This formula reveals several counterintuitive truths:
- Even fair games are dangerous: In a fair 50/50 game trying to double your money, you have a 50% chance of going bust—not better odds!
- The house edge compounds: A small 2% house edge means you're fighting exponentially worsening odds with each bet
- Bigger goals = higher ruin: Trying to quadruple your money is far more dangerous than trying to win 25%
- Smaller bets help slightly: Betting $1 vs $10 at a time changes your ruin probability (but doesn't eliminate it)
Why Smaller Bankrolls Almost Always Lose
One of the most important insights from gambler's ruin theory is the "David vs Goliath" problem. When two players compete with unequal bankrolls, the player with more money almost always wins eventually—even in a fair game.
Think of it this way: you sitting down at a casino with $500 are playing against the casino's bankroll of $500 million. Even if every bet were perfectly fair (which they aren't), random fluctuations would eventually wipe out the smaller bankroll while barely denting the larger one.
| Scenario | Your Bankroll | Casino Bankroll | Your Ruin Prob (Fair Game) |
|---|---|---|---|
| Small player | $100 | $1,000,000 | 99.99% |
| Medium player | $10,000 | $1,000,000 | 99.01% |
| High roller | $100,000 | $1,000,000 | 90.91% |
And remember: real casino games aren't fair. The house edge tips these already-steep odds even further against you.
The House Edge Multiplier Effect
The gambler's ruin formula shows why house edge matters so much more than most people realize. A 2% house edge doesn't just mean you lose 2% of your bets—it means the mathematical structure of the game is fundamentally tilted against you in an exponential way.
| Win Probability | House Edge | Ruin Prob (Double $100) | Ruin Prob (10x $100) |
|---|---|---|---|
| 50.00% | 0% | 50.0% | 90.0% |
| 49.50% | 1% | 63.2% | 98.2% |
| 49.00% | 2% | 73.1% | 99.7% |
| 48.65% | 2.7% (Roulette) | 79.0% | 99.9% |
| 47.37% | 5.26% (American Roulette) | 87.8% | 99.99% |
The Bottom Line: The gambler's ruin problem mathematically proves what casinos have known for centuries—given enough time, the house edge guarantees that players will eventually lose their bankroll. This isn't pessimism; it's mathematics. Understanding this helps explain why gambling should be viewed as entertainment with an expected cost, not as a way to make money.
Practical Implications
Understanding gambler's ruin has several practical implications:
1. Set Realistic Win Goals
Trying to double your money has significantly lower ruin probability than trying to 10x it. If you're gambling for entertainment, smaller goals mean longer play time and better odds of walking away ahead.
2. Bet Size Matters
Smaller bets relative to your bankroll reduce variance and slightly improve your probability of reaching a modest goal. The standard recommendation of betting no more than 1-2% of your bankroll per bet has mathematical grounding in ruin theory.
3. The Casino Always Has the Bigger Bankroll
No matter how much you bring, the casino has more. Combined with even a small house edge, this mathematical asymmetry guarantees the casino wins over time across all players.
4. Quit While Ahead (If You Can)
The moment you're ahead by your target amount, the mathematics say stop. Every additional bet increases your exposure to the house edge. The discipline to walk away is the only "edge" a player can have.
Related Reading
Expected Value Calculator
The fundamental math concept that determines long-term gambling outcomes.
Use this tool →The MIT Blackjack Team
How card counters briefly flipped the mathematics in their favor.
Read the story →Optimal Stopping Calculator
The mathematics of knowing when to walk away—the 37% Rule for optimal decisions.
Use this tool →
Remember: This calculator is for educational purposes only. If you or someone you know has concerns about gambling, the National Council on Problem Gambling helpline is available 24/7 at 1-800-522-4700.