What is gambler's ruin and how does it relate to profit targets?

Gambler's ruin is a probability concept studying the likelihood of reaching either a profit target (goal) or going broke (ruin) before the other. Given finite bankroll and any house edge, the probability of eventual ruin approaches 100% with unlimited play. This calculator shows your odds for specific bankroll-to-goal scenarios.

How do you calculate profit target probability?

For even-money bets, the probability of reaching a goal of N units starting with n units is: P = [(1-(q/p)^n] / [1-(q/p)^N] where p is win probability and q is loss probability (1-p). For a fair game (50/50), it simplifies to P = n/N, meaning starting with $500 targeting $1000, you have exactly 50% chance.

Why is doubling your money so difficult at casinos?

Doubling your money requires reaching a 100% profit target. Even with a 49% win rate (typical for many casino games), the probability of doubling before ruin drops significantly compared to fair odds. The house edge compounds over time, making larger profit targets increasingly unlikely. Mathematics shows you're more likely to go broke than double up.

Does bet size affect probability of reaching my goal?

Yes, significantly. Larger bets relative to your bankroll increase variance. With smaller bets, the house edge has more opportunities to grind down your bankroll, lowering goal probability. With larger bets, you might reach your goal faster but also face higher ruin risk. The optimal approach depends on your specific situation and risk tolerance.

What's the formula for gambler's ruin probability?

For even-money bets with win probability p and loss probability q=1-p: If p ≠ 0.5: P(reaching goal) = [1 - (q/p)^n] / [1 - (q/p)^N], where n is starting units and N is goal units. If p = 0.5 (fair game): P(reaching goal) = n/N. This assumes a random walk model with fixed bet sizes.

Is it ever possible to have over 50% chance of reaching my goal?

Yes, in two scenarios: (1) If you have a mathematical edge (win rate > 50%), as skilled poker players or advantage bettors might have, or (2) If your profit target is very small relative to your bankroll. Starting with $950 and targeting $1000 has much better odds than starting with $500 targeting $1000, even with a house edge.

How should I use this calculator for responsible gambling?

This calculator reveals the mathematical reality behind gambling goals. If you see a 15% chance of doubling your money, that means an 85% chance of losing everything first. Use this to set realistic expectations, understand that most profit targets are unlikely to be achieved, and recognize gambling as entertainment with an expected cost rather than a reliable income source.

Profit Target Calculator | Goal vs Ruin Probability

🎯 Calculate Goal vs Ruin Probability

Enter your bankroll, profit target, and win probability to see the mathematical odds of reaching your goal before losing everything.

Game Presets (Win Probability)

Starting Bankroll ($) Amount you start with

Target Bankroll ($) Goal you want to reach

Win Probability (%) Your chance of winning each bet

Bet Size ($) Amount per wager (even money)

Probability of Reaching Your Goal

37.5%

You're more likely to go broke than reach your target

Reach Goal

37.5%

$1,000 target

Go Broke First

62.5%

Lose everything first

37.5% Goal

62.5% Ruin

$500

Profit Needed

100%

Profit % Target

~50
Avg Bets to Result

1.00%

House Edge

What This Means: Starting with $500 and aiming for $1,000, you have a 37.5% chance of reaching your goal before going broke. The house edge of 1% compounds over time, making ruin more likely than success for ambitious profit targets.

📊 Different Target Scenarios

See how your success probability changes with different profit targets, using the same starting bankroll and win rate.

📉 Bet Size Impact on Success Probability

Larger bets reach decisions faster but with the same probabilities. Smaller bets take longer but give the house edge more opportunities to grind down your bankroll.

Bet Size	Units to Goal	Goal Probability	Avg Bets Needed	Speed

Important: This calculator assumes even-money bets (1:1 payout). For other bet types, the mathematics become more complex. The core principle remains: the house edge makes ambitious profit targets statistically unlikely.

📋 Probability of Doubling Your Money

The classic question: "What are my odds of doubling my bankroll?" Here's the mathematical reality for various games, as documented by the UNLV International Gaming Institute.

Game / Scenario	Win Probability	House Edge	Chance to Double	Chance of Ruin
Fair Coin Flip	50.00%	0.00%	50.00%	50.00%
European Roulette (Even)	48.65%	2.70%	35.14%	64.86%
American Roulette (Even)	47.37%	5.26%	24.53%	75.47%
Blackjack (Basic Strategy)	49.50%	0.50%	45.07%	54.93%
Baccarat (Banker, after comm)	49.32%	1.06%	42.16%	57.84%
Skilled Poker Player (+2%)	52.00%	-4.00%	66.67%	33.33%
Sports Bettor (-110 at 53%)	53.00%	-1.24%	59.39%	40.61%

Key Insight: Even with blackjack's low 0.5% house edge, you still have less than a 50% chance of doubling your money. The gambler's ruin principle shows that any negative expectation, no matter how small, eventually leads to ruin with continued play.

Understanding Profit Target Probability

The probability of reaching a specific profit target before going broke is one of the most important concepts in gambling mathematics. This calculation, rooted in what mathematicians call the gambler's ruin problem, reveals the harsh mathematical reality behind common gambling goals like "doubling up" or "winning back losses."

The Mathematics Behind the Calculator

This calculator uses the classic gambler's ruin formula for even-money bets. According to research from the American Mathematical Society, the probability of reaching a goal of N units starting with n units is:

P(Goal) = [1 - (q/p)^n] / [1 - (q/p)^N]
where p = win probability, q = 1-p (loss probability), n = starting units, N = target units

For a fair game (p = 0.5), this simplifies elegantly to P(Goal) = n/N. Starting with 50 units and targeting 100 units gives exactly 50% success probability. Any house edge, however small, shifts these odds against the player.

Why Doubling Your Money Is Harder Than It Seems

Many gamblers walk into a casino hoping to double their money. The mathematics reveal why this is a losing proposition:

At 49.5% win rate (good blackjack): Only 45% chance of doubling before going broke
At 48.65% win rate (European roulette): Only 35% chance of doubling
At 47.37% win rate (American roulette): Only 25% chance of doubling

Even skilled advantage players with a genuine edge face significant ruin risk. A poker player with a 2% edge (52% win rate) still has about a 33% chance of going broke before doubling their bankroll.

How the House Edge Compounds

The house edge doesn't just take a small percentage of each bet—it compounds over time. As explained by the American Gaming Association, this compounding effect means:

Small edges become significant over many bets
Longer sessions favor the house more strongly
Larger profit targets are exponentially harder to reach
The probability of ruin approaches 100% with unlimited play

The Certainty of Ruin: Mathematical analysis proves that with any negative expectation (house edge), infinite play guarantees ruin with 100% probability. This is why gambling should be viewed as paid entertainment, not an income source.

Practical Applications of This Calculator

Use this tool to:

Set realistic expectations: Understand that doubling your money is unlikely at most casino games
Choose appropriate targets: Smaller profit goals have better success probability
Understand variance: Even with an edge, short-term results can be brutal
Make informed decisions: Know the odds before setting your session goal
Practice responsible gambling: Accept gambling as entertainment with expected costs

The Role of Bet Size

Bet size relative to bankroll affects how quickly you reach a conclusion, but not the fundamental probabilities. Smaller bets mean more decisions before reaching your goal or going broke, which gives the house edge more opportunities to manifest.

For bankroll management, most experts recommend betting 1-5% of your bankroll per wager. This extends playing time and provides more entertainment value, even though it doesn't improve your mathematical chances of reaching ambitious profit targets.

When Can You Beat the Odds?

There are only two ways to have better than 50% chance of reaching your profit target:

Have a mathematical edge: Skilled poker players, advantage bettors with positive CLV, or card counters can have positive expected value
Set very modest targets: Starting with $900 and targeting $1,000 has much better odds than starting with $500 targeting $1,000

For recreational gamblers without a genuine edge, the mathematics are clear: the casino will win more often than you reach your goal.

Frequently Asked Questions

What's the difference between risk of ruin and profit target probability?

Risk of ruin asks "what's my probability of eventually going broke?" (which approaches 100% with continued play at a house edge). Profit target probability asks "what are my odds of reaching a specific goal before going broke?" Both are related through the gambler's ruin mathematics, but they answer different questions. Our Risk of Ruin Calculator focuses on the ruin side of this equation.

Does this calculator work for all types of bets?

This calculator assumes even-money (1:1 payout) bets. For bets with different payouts, the mathematics become more complex. The core principle remains the same: any house edge makes reaching ambitious profit targets unlikely.

Why is my goal probability lower than my win probability?

Because reaching a significant profit target requires winning more bets than you lose over an extended period. A 49% win rate means you lose 51% of bets—that 2% difference compounds over many bets, making net profit increasingly unlikely.

Can I improve my odds by changing bet sizes?

Not fundamentally. Larger bets reach a conclusion faster, while smaller bets extend play. The Kelly Criterion provides optimal bet sizing for those with a proven edge, but without an edge, no betting strategy can overcome negative expectation.

How does this relate to betting systems like Martingale?

Betting systems don't change the underlying probabilities—they just redistribute how wins and losses occur over time. Our Betting System Simulator demonstrates why systems like Martingale eventually fail. The truth about betting systems is that none can overcome the house edge.

What if I have an edge from sports betting?

If you genuinely have an edge (win rate exceeding the break-even threshold), your profit target probability can exceed 50%. Use our Break-Even Calculator to determine your required win rate and Expected Value Calculator to verify your edge.

Should I set a stop-loss or stop-win?

Stop-wins (quitting when ahead) don't change mathematical expectation but can lock in profits during lucky sessions. Stop-losses protect you from catastrophic sessions. Neither changes the fundamental probability of reaching your goal—they just define when you stop playing. Learn more about session planning.

Related Calculators and Resources

Explore these related tools for deeper understanding of gambling mathematics:

Risk of Ruin Calculator - Calculate your probability of going broke given your edge and bet size
Bankroll Simulator - Monte Carlo simulation of bankroll trajectories
Expected Value Calculator - Determine if a bet has positive or negative EV
Kelly Criterion Calculator - Optimal bet sizing for advantage players
Gambler's Ruin Explained - Deep dive into the mathematics behind this calculator
Variance and Expected Value - Understanding short-term swings vs long-term expectation
Gambling Budget Calculator - Set responsible gambling limits based on your finances