Bankroll Calculator

Calculate optimal bankroll requirements and risk of ruin

Bankroll Calculator

BB/100$/hr

Win Rate ($/hr)

Win Rate measures your average profit per 100 hands (BB/100) or per hour ($/hr).

Important Guidance:

If you are unsure or do not have a proven record (min. 300hr+ or min. 10,000+ hands) about your win rate, it's recommended that you leave it at $0/hr or 0 BB/100.

Typical Win Rates:

•Beginner (0-5 $/hr): Learning the game
•Winner (5-20 $/hr): Consistent profits
•Strong Winner (20-50 $/hr): Beating the games
•Crusher (50+ $/hr): Crushing

💡 Find your exact win rate using PokerVis Session Tracking (Pro) under Bankroll Manager.

Std Dev ($/hr)

Standard Deviation (SD) measures how much your results vary by the hour.

Typical Ranges:

•Low (50-100 $/hr): Tight, consistent play with minimal variance
•Medium (100-150 $/hr): Typical for most players
•High (150+ $/hr): Aggressive, high-variance style

💡 Use 150 as a conservative default or estimate around the ballpark will do just fine.

Stakes (BB)

Stakes (Big Blind) The big blind amount from your game. This converts your win rate into actual dollar bankroll requirements.

Examples:

•1/2 game → Enter 2
•2/5 game → Enter 5
•5/10 game → Enter 10
•10/20 game → Enter 20

💡 Just enter the big blind amount - we'll handle the rest. You can also enter your weighted average stakes if you have the data.

Bankroll ($)

Buy-in ($)

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Frequently Asked Questions

Understanding your bankroll calculations, limitations, and best practices

Understanding the Model

The Bankroll Health Calculator uses session-based Monte Carlo simulation to calculate your current Risk of Ruin based on your bankroll, buy-in, win rate, and standard deviation.

The Question: "What's my chance of going broke with my current bankroll and buy-in?"

The Logic:

Real-world poker bankroll simulation:

You start with your actual bankroll (e.g., $25,000)
Each session, you buy in for your typical amount (e.g., $1,000)
Simulate 167 sessions (≈6 months of poker)
Track if you go broke (can't afford another buy-in)
Run 3,000 complete simulations to get statistical confidence
Calculate: What % of simulations ended in bankruptcy?

Two Core Components:

1. Session-Based Monte Carlo Simulation

Unlike traditional continuous models, this simulates REAL poker sessions:

Buy-in management: Each session deducts your buy-in from bankroll
Session simulation: 150 hands per session with normal variance
Catastrophic events: Depth-based cooler probability (see below)
Bankruptcy check: Stop when bankroll < buy-in (can't reload)
Reload logic: If you win/lose, update bankroll and continue

2. Catastrophic Loss Model (Depth-Based)

Real poker includes unavoidable coolers that pure Gaussian models miss:

Buy-in Depth	Catastrophic Prob	Frequency
<100BB	10% per session	1 every 10 sessions
100-200BB	7% per session	1 every 14 sessions
200-500BB	6% per session	1 every 17 sessions
500-1000BB	5% per session	1 every 20 sessions

Why this matters: Set-over-set, AA vs KK, and other unavoidable coolers happen rarely but impact bankroll management. This model is calibrated to live poker reality (~1-2 coolers per 30 sessions). Note: Bluffs, bluff-catches, and hero calls are NOT catastrophic—those are part of your normal variance (edge and standard deviation).

Computational Scale

Metric	Amount
Simulations	3,000 complete bankroll simulations
Sessions per simulation	167 sessions (25,000 hands ÷ 150)
Total sessions simulated	501,000 sessions
Calculation time	~24 seconds

How It Works (Step-by-Step):

Input your stats: Bankroll, buy-in, win rate, standard deviation
Convert to BB/100: Normalizes everything to big blinds per 100 hands
Run Monte Carlo simulation: 3,000 simulations of 167 sessions each
Display your risk: Shows RoR percentage with visual speedometer

⚠️ Model Limitations & Assumptions

This calculator provides mathematically sound guidance but makes important assumptions:

✅ Accounts For:

Session-based gameplay
Buy-in management
Catastrophic coolers
Normal variance
Reload constraints

❌ Does NOT Account For:

Tilt/mental game
Table selection
Skill improvement
Rake and fees
Life expenses

Key Assumptions:

Constant win rate and variance across all sessions
150 hands per session (6 hours at 25 hands/hour typical live)
Catastrophic probabilities based on aggregated player data
No mid-session reloads (one buy-in per session)

💡 Best Practice: Monitor your RoR monthly as stats evolve. If you consistently experience coolers more/less frequently than model assumes, adjust bankroll ±20-30%.

Use as guidelines, not guarantees. Past performance ≠ future results.

Why Session-Based Simulation Matters

Traditional RoR calculators simulate continuous hands, which can produce unrealistic results:

❌ Continuous Model Problems:

Simulates 25K hands non-stop
No buy-in constraints
Goes into negative bankrolls
Misses reload economics
Ignores catastrophic events

✅ Session-Based Benefits:

Models real poker sessions
Enforces buy-in limits
Stops at bankruptcy
Tracks reload ability
Includes cooler probability

Result: More realistic RoR that matches what happens at the tables.

Result: You get your current Risk of Ruin percentage based on 500,000+ realistic poker session simulations, giving you a precise understanding of your bankroll health.

🎯 Accuracy Note: With 3,000 simulations, the calculator provides RoR estimates accurate to within ±0.5%, which is excellent precision for bankroll management decisions. The standard error at this simulation count is approximately 0.3%, making the results highly reliable for practical use.

The Optimal Buy-In Calculator uses Monte Carlo simulation combined with binary search optimization to find the maximum buy-in size that keeps you within your target Risk of Ruin threshold.

Three Core Components:

1. Monte Carlo Simulation Engine

The calculator runs probabilistic simulations of your poker sessions, accounting for:

Your win rate and standard deviation
Normal session variance (modeled as Gaussian distribution)
Depth-based catastrophic loss events (see model details below)

2. Binary Search Optimization

The algorithm systematically searches through buy-in sizes (40BB-1,000BB) to find the optimal amount for your target RoR zone:

Conservative: 0-2% Risk of Ruin
Moderate: 2-5% Risk of Ruin
Aggressive: 5-10% Risk of Ruin

3. Catastrophic Loss Model (Depth-Based)

Accounts for unavoidable coolers (set-over-set, AA vs KK) that vary by stack depth:

Depth	Catastrophic Prob	Frequency
<100BB	10% per session	1 every 10 sessions
100-200BB	7% per session	1 every 14 sessions
200-500BB	6% per session	1 every 17 sessions
500-1000BB	5% per session	1 every 20 sessions

⚠️ Important Notes on Catastrophic Probabilities

•These statistics are based on our team's poker data and experience. Your actual frequencies may vary based on your playing style and deep stack expertise.
•Definition: "Catastrophic loss" only accounts for unavoidable situations where you must go stack-for-stack with strong hands (set-over-set, AA vs KK on dry boards, nut flush vs 2nd nut).
•Does NOT include: Bluff all-ins that get called, calling off with marginal hands, or bluff-catchers. These are skill-based decisions reflected in your win rate and standard deviation, not catastrophic events.
•Individual variance: Catastrophic loss frequency varies greatly between players. Tight players may experience fewer coolers; aggressive deep-stack specialists may encounter more.
•Why we use this data: We selected these probabilities because they provide the closest accuracy for generating personalized recommendations across a wide player population.

💡 Adjustment Guidance

If you experience catastrophic losses more frequently than stated above, consider: (1) Increasing your bankroll requirements by 20-30%, or (2) Reducing your buy-in amount by 15-25% from our calculations.

Despite individual variance, we have high confidence this model applies to the majority of players and provides sound bankroll guidance.

Other Key Model Parameters:

Buy-In Range: 40BB - 1,000BB
Independence Assumption: Each session follows Central Limit Theorem

Computational Scale (Maximum Iterations)

When finding your optimal buy-in, the calculator may run up to:

Metric	Amount
Binary Search Iterations	Up to 20 iterations
Simulations per iteration	750 simulations
Hands per simulation	25,000 hands
Sessions per simulation	167 sessions
Total hands simulated (max)	375,000,000 hands
Total sessions simulated (max)	2,505,000 sessions

Note: Most calculations complete in fewer iterations (typically 10-15). The maximum represents worst-case computational complexity.

Translation: The calculator is simulating the equivalent of multiple professional poker careers to give you statistically reliable buy-in recommendations.

How It Works (Step-by-Step):

Input your parameters: Bankroll, win rate, standard deviation, stake level, target RoR
Binary search begins: Tests buy-in sizes to narrow down optimal range
Monte Carlo runs: For each tested buy-in, runs 750 simulations of 25,000 hands
Risk calculation: Counts how many simulations end in bankruptcy
Monte Carlo validation: Each iteration runs 750 simulations of 167 sessions
Convergence: Repeats until optimal buy-in is found within 1BB precision
Convergence check: Stops when RoR within ±0.05% OR range < 10 BB
Results delivered: Shows you the maximum safe buy-in for your risk tolerance

⚠️ Model Limitations & Assumptions

This calculator provides mathematically sound guidance but makes important assumptions:

✅ Accounts For:

Normal variance
Catastrophic coolers
Multiple sessions
Bankroll depletion

❌ Does NOT Account For:

Tilt/mental game
Table selection
Fatigue effects
Skill changes

💡 Critical: Take a break after losing 2-3 buy-ins, regardless of what the calculator says.

Model assumes perfect mental performance. Use as guidelines, not guarantees.

Result: You get a mathematically-backed buy-in recommendation based on hundreds of millions of simulated hands, not guesswork.

📌 Note: These recommendations include a safety buffer to account for real-world variance (tilt, fatigue, marginal decisions). Highly disciplined professionals with exceptional mental game may be able to play 10-15% more aggressively than our calculations suggest.

The Bankroll Calculator uses parallel Monte Carlo simulation to calculate the exact bankroll you need for your desired buy-in amount across 4 risk tolerance levels.

The Question: "I want to buy in for $X—what bankroll do I need to play safely?"

The Logic:

Inverse bankroll calculation with parallel processing:

You specify your desired buy-in size (e.g., $1,500 = 300 BB at 2/5)
Calculator runs 4 binary searches simultaneously (1%, 2%, 5%, 10% RoR)
Each search finds: "What bankroll achieves this RoR for my buy-in?"
Uses session-based Monte Carlo (167 sessions × 750 simulations)
Returns 4 bankroll requirements—pick your risk tolerance

The calculator completes in 60-90 seconds thanks to parallel processing (4x speedup vs sequential).

Three Core Components:

1. Session-Based Monte Carlo Simulation

Identical engine to the Bankroll Health Calculator—simulates REAL poker sessions:

Buy-in management: Each session deducts your buy-in from bankroll
Session simulation: 150 hands per session with normal variance
Catastrophic events: Depth-based cooler probability (see below)
Bankruptcy check: Stop when bankroll < buy-in (can't reload)
Reload logic: If you win/lose, update bankroll and continue

2. Catastrophic Loss Model (Depth-Based)

Same model used across all calculators—coolers vary by stack depth:

Buy-in Depth	Catastrophic Prob	Frequency
<100BB	10% per session	1 every 10 sessions
100-200BB	7% per session	1 every 14 sessions
200-500BB	6% per session	1 every 17 sessions
500-1000BB	5% per session	1 every 20 sessions

3. Parallel Binary Search (4x Speedup)

Runs 4 independent binary searches simultaneously—one for each risk band:

1% RoR Band (Ultra-Conservative)
Searches range: [buy-in, min(buy-in × 1000, 1M BB)] to find bankroll with 1% bankruptcy risk
2% RoR Band (Conservative)
Typical for professionals with strict bankroll management
5% RoR Band (Moderate)
Standard recommendation for serious players
10% RoR Band (Aggressive)
For shot-taking or players comfortable with higher risk

Each search runs up to 20 iterations with 750 simulations per iteration, converging within ±0.05% of target RoR. Early exits when range width < 10 BB or hits min/max bounds.

Computational Scale (Parallel Processing)

Running 4 risk bands simultaneously (not sequentially) with 120-second timeout per band:

Metric	Amount
Parallel binary searches	4 simultaneous (1%, 2%, 5%, 10% RoR)
Iterations per search	Up to 20 (typically 10-15)
Simulations per iteration	750 simulations
Sessions per simulation	167 sessions (25,000 hands ÷ 150)
Total session simulations (max)	10,014,000 sessions
Calculation time	~60-90 seconds (4x faster than sequential)

Note: Without parallelization, this would take 4-6 minutes. The ProcessPoolExecutor with max_workers=4 runs all bands simultaneously, completing in the time of the longest search (~60-90 seconds).

Search Range: Dynamic upper bound of min(buy-in × 1000, 1M BB) ensures reasonable computation limits while covering realistic bankroll scenarios.

How It Works (Step-by-Step):

Input your target: Desired buy-in, win rate, standard deviation, stake level
Convert to BB/100: Normalizes everything to big blinds per 100 hands
Launch 4 parallel workers: ProcessPoolExecutor submits all 4 bands to worker pool
Binary search per band: Tests bankroll amounts from [buy-in, dynamic max]
Monte Carlo validation: Each iteration runs 750 simulations of 167 sessions
Convergence check: Stops when RoR within ±0.05% OR range < 10 BB
Results delivered: 4 bankroll requirements—choose your risk tolerance

⚠️ Model Limitations & Assumptions

This calculator provides mathematically sound guidance but makes important assumptions:

✅ Accounts For:

Normal variance
Catastrophic coolers
Multiple sessions
Bankroll depletion

❌ Does NOT Account For:

Tilt/mental game
Table selection
Fatigue effects
Skill changes

💡 Critical: Take a break after losing 2-3 buy-ins, regardless of what the calculator says.

Model assumes perfect mental performance. Use as guidelines, not guarantees.

Result: You get a mathematically-backed buy-in recommendation based on hundreds of millions of simulated hands, not guesswork.

Statistical Methods

Monte Carlo simulation is a computational method that uses repeated random sampling to model outcomes under uncertainty. Instead of using mathematical formulas, we run thousands of simulated scenarios to see what actually happens.

Poker Example:

Imagine we want to know: "What's the chance you go broke with a $50K bankroll?"

Instead of complex math, we simulate 750 parallel poker careers with your exact stats:

Each career plays 25,000 hands with your win rate and standard deviation
Normal variance is modeled as random outcomes following statistical distribution
Catastrophic coolers (set-over-set, AA vs KK) are included based on stack depth
We count how many of the 750 careers go bankrupt

If 15 out of 750 went broke, that's a 2% Risk of Ruin.

Why this works: By running hundreds or thousands of simulations, we capture the full range of possible outcomes—from lucky heaters to brutal downswings. The law of large numbers ensures our predictions converge on the true probability.

This same technique is used by financial institutions for risk modeling, weather forecasting, and even casino game design. It's the gold standard for modeling complex systems with randomness.

Risk of Ruin (RoR) is the probability that you'll lose your entire bankroll:

0-2% RoR: 98%+ chance you never go broke (ultra-safe)
2-4% RoR: 96-98% survival rate (acceptable risk)
4-6% RoR: 94-96% survival rate (aggressive)
6-8% RoR: 92-94% survival rate (high risk)
8-10% RoR: 90-92% survival rate (danger zone)

Most professionals aim for 2% RoR or lower to ensure long-term sustainability.

25,000 hands represents a meaningful sample size for statistical accuracy while encouraging regular recalibration as your game evolves.

For Different Player Types:

Online Players (Multi-tabling):

25,000 hands ≈ 2-4 weeks of regular play
4-6 tables × 80 hands/hour = 320-480 hands/hour
Benefit: More frequent calibration catches skill improvements or leaks faster
Recommendation: Recalculate every 25K hands (~monthly)

Live Players:

25,000 hands ≈ 6 months of regular play
~100 hours/month × 25 hands/hour = ~1,000 hours total
Benefit: Perfect semi-annual checkup cycle
Recommendation: Recalculate every 6 months

This Timeframe Balances:

Statistical significance: Enough hands to model variance accurately
Practical relevance: Your edge changes as you improve, learn new strategies, or develop leaks
Realistic projections: Forward-looking analysis, not career-long assumptions
Consistency: All PokerVis calculators (Bankroll, Buy-in, Risk of Ruin) use the same baseline

Why Not 100K+ Hands?

Traditional "100 buy-in rules" assume 100K+ hands with generic, static stats. In reality:

Your game evolves—new strategies, adjusted approaches
Table dynamics shift—different venues, changing player pools
Your skills improve (or stagnate)—edge isn't constant
Mental game fluctuates—tilt patterns, confidence levels

A 6-month projection (or monthly for online players) reflects YOUR current edge, not outdated assumptions from a year ago.

💡 Pro tip: Recalculate regularly as your stats evolve. Yesterday's bankroll needs ≠ today's bankroll needs.

PokerVis encourages active bankroll management, not "set it and forget it" rules from 2008.

Binary search is an efficient algorithm that finds the exact answer by repeatedly cutting the search space in half. Instead of testing every possible value, we intelligently narrow down to the precise number.

How It Works:

Let's say we're finding the bankroll needed for 2% Risk of Ruin:

Start with a range: $100 to $1,000,000
Test the middle: Try $500,000 → Run 750 simulations → RoR = 0.5% (too safe)
Adjust range: Too safe means we can use less. New range: $100 to $500,000
Test new middle: Try $250,000 → RoR = 1.2% (still too safe)
Keep narrowing: New range: $100 to $250,000
Converge: After 10-15 iterations, we find $185,000 gives exactly 2.0% RoR ✅

Efficiency: Without binary search, we'd need to test thousands of values ($100, $101, $102...). With binary search, we find the exact answer in just 10-20 iterations.

Precision: We continue until we reach a tolerance of 0.5% RoR—meaning the answer is accurate within half a percentage point. This ensures reliable recommendations without excessive computation.

The same algorithm is used in everything from computer science sorting to finding solutions in engineering problems. It's one of the most fundamental optimization techniques.

Normal distribution (also called Gaussian distribution) is a statistical pattern where most outcomes cluster around the average, with fewer extreme results on either side. It creates the classic "bell curve" shape.

In Poker Terms:

If your win rate is 5 BB/100 with 100 BB/100 standard deviation:

~68% of sessions fall within ±100 BB of your expectation
~95% of sessions fall within ±200 BB
~99.7% of sessions fall within ±300 BB
Extreme outliers (massive heaters or brutal coolers) are rare but possible

Does poker actually follow normal distribution? Mostly yes, especially over large sample sizes. The Central Limit Theorem states that when you average many independent random events (poker hands), the results naturally form a normal distribution—even if individual hands don't.

⚠️ Important Limitation

Poker has "fat tails" — extreme outcomes happen slightly more often than pure normal distribution predicts. This is why we:

Include catastrophic collision modeling (set-over-set, AA vs KK)
Use conservative Risk of Ruin targets (1-5% recommended)
Suggest recalculating every 100-200 hours as conditions change

While normal distribution isn't perfect for poker, it's the best practical model for variance over thousands of hands. Our additional catastrophic loss modeling accounts for the extreme events that fall outside normal distribution.

Short answer: Monte Carlo simulations use randomness, so results can vary slightly (typically ±0.5%) between runs. This is normal and expected.

Detailed explanation:

Our calculators use Monte Carlo simulation—a method that runs thousands of random poker session simulations to estimate your risk of ruin. Each time you calculate:

We simulate 750 random "poker careers" (25,000 hands each)
Each career has different outcomes due to randomness (variance, coolers, etc.)
We count how many careers go broke to calculate your RoR percentage

Because we use randomness, results vary slightly between calculations—just like if you played 750 real poker careers, each would have different outcomes.

Example:

Run 1: 5.2% RoR
Run 2: 4.8% RoR
Run 3: 5.1% RoR

All three results are statistically equivalent. We're estimating the "true" RoR of ~5%.

Our tolerance:

We accept results within ±0.5% of the target. So if you're targeting 5% RoR:

Anywhere from 4.5% to 5.5% is considered "converged"
This provides fast calculations while maintaining accuracy

Why not make it exact?

We could run 10,000+ simulations for more precision, but:

Calculations would take 10x longer (30+ seconds instead of 3 seconds)
The practical difference is negligible (4.8% vs 5.2% RoR doesn't meaningfully change your bankroll strategy)
Poker variance is already larger (your actual win rate and SD have more uncertainty than ±0.5%)

Bottom line: Small variations between calculations are normal. Focus on the overall magnitude (is it 2%? 5%? 10%?) rather than exact decimals.

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