Time-to-Ruin Calculator

How long will your gambling bankroll last? This calculator reveals the mathematical reality of the "Gambler's Ruin" problem, showing how house edge, bet sizing, and playing frequency combine to determine when a bankroll will be depleted. The answer, for negative expected value games, is always the same: it's not a question of if you'll lose your bankroll, but when.

The Gambler's Ruin Problem: First analyzed by mathematician Blaise Pascal in the 17th century, the Gambler's Ruin proves that in any game with negative expected value and finite bankroll, eventual ruin is mathematically certain given enough time. This calculator helps visualize that inevitability.

Calculate Your Bankroll Survival Time

Select a player profile or customize your own scenario

Player Profiles

Select a scenario to pre-fill values, or customize below

🎰
Casual Gambler
$500 bankroll, $10 bets, slots
🃏
Weekend Warrior
$1,000 bankroll, $25 bets, blackjack
🎲
Regular Player
$2,000 bankroll, $50 bets, table games
💎
High Roller
$10,000 bankroll, $100 bets, baccarat

Your Scenario

Starting Bankroll $500
The amount of money you start with
Average Bet Size $10
Your typical wager per hand/spin/roll
Bets Per Hour 60
Slots: 400-600 | Table games: 30-80 | Poker: 20-35
Hours Per Session 4
How long you typically play per visit
Sessions Per Week 2
How often you gamble (0.25 = once a month)

The Mathematics of Ruin

The time-to-ruin calculation is based on fundamental probability theory. When you play a game with negative expected value, your bankroll follows a predictable downward trend on average, even though individual sessions may result in wins or losses.

Expected Loss Formula

Expected Loss = Bet Size × House Edge × Number of Bets
Time to Ruin = Bankroll ÷ Expected Loss per Unit Time

According to research from the UNLV Center for Gaming Research, this mathematical relationship holds regardless of betting patterns or systems. The only variables that matter are:

  • Bankroll size: Larger bankrolls last longer, but still deplete
  • Bet size: Smaller bets extend playing time but don't change the outcome
  • House edge: Lower edge games provide more entertainment per dollar
  • Playing frequency: Playing less often extends calendar time to ruin

Example Scenarios

🎰 Slot Machine Player
Bankroll: $500
Bet: $2 per spin × 500 spins/hour
House edge: 10%
Expected loss: $100/hour
5 hours to ruin
🃏 Blackjack Player
Bankroll: $500
Bet: $25 per hand × 60 hands/hour
House edge: 0.5% (basic strategy)
Expected loss: $7.50/hour
67 hours to ruin
🎡 Roulette Player
Bankroll: $500
Bet: $10 per spin × 40 spins/hour
House edge: 5.26% (American)
Expected loss: $21/hour
24 hours to ruin
Did You Know? The "Gambler's Ruin" problem was first solved by Christian Huygens in 1657. He proved that in a fair coin flip game (50/50 odds) between two players with unequal bankrolls, the player with less money is more likely to go broke first. With a house edge added, ruin becomes mathematically certain for the player with the finite bankroll, regardless of size.

Game Comparison: Survival Times

How does your game choice affect bankroll longevity? Using a $1,000 bankroll with $25 bets:

Game House Edge Bets/Hour Loss/Hour Survival Time
Blackjack (basic strategy) 0.5% 60 $7.50 133 hours
Baccarat (banker) 1.06% 70 $18.55 54 hours
Craps (pass line) 1.41% 50 $17.63 57 hours
European Roulette 2.7% 40 $27.00 37 hours
American Roulette 5.26% 40 $52.60 19 hours
Typical Slots 10% 500 $1,250 48 minutes
Keno 25% 10 $62.50 16 hours

As the American Gaming Association data shows, slot machines generate the majority of casino revenue precisely because of this math: high house edge combined with rapid betting creates the fastest path to ruin.

Why Variance Doesn't Save You

You might think: "But I've won sessions before! Doesn't that reset things?" The answer is no. According to probability research published by Britannica, the Law of Large Numbers guarantees that your actual results will converge to the expected value over time.

Variance (the ups and downs of individual sessions) creates the illusion of potential profit:

  • You might win on any given day
  • Winning sessions make you feel like you can beat the game
  • But over enough sessions, wins and losses average out to the expected loss

Our Variance Calculator shows this in action: short-term results can vary wildly, but long-term results converge to expected value with mathematical certainty.

Strategies to Extend Playing Time

While you can't change the mathematical outcome, you can extend your entertainment time:

1. Choose Lower House Edge Games

Blackjack with basic strategy (0.5% edge) provides 20x more playing time than typical slots (10% edge) for the same bankroll and bet size. Our Casino Odds Calculator compares all games.

2. Make Smaller Bets

Cutting bet size in half doubles expected playing time. This doesn't change total expected losses (which depend on time played × house edge), but it extends entertainment value per dollar.

3. Set Session Limits

Stop-loss limits don't change expected value but prevent variance from accelerating losses. When you've lost your session budget, stop playing.

4. Play Slower Games

Table games with 40-60 decisions per hour burn through bankrolls much slower than slots with 400-600 spins per hour, even if house edge is similar.

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Remember: This calculator is for educational purposes only. It demonstrates mathematical concepts about gambling bankroll depletion. Understanding these numbers helps explain why gambling should be viewed as paid entertainment, not as an investment or income source. If you or someone you know is struggling with gambling, the National Problem Gambling Helpline is available 24/7 at 1-800-522-4700.