♠ Card Games Encyclopedia

Poker Variance Simulator: Monte Carlo Visualization

Variance is the hidden force that shapes every poker player's journey. Even the most skilled players experience dramatic swings - crushing downswings that test their resolve and heater runs that inflate confidence. This free variance simulator uses Monte Carlo methods to visualize thousands of possible outcomes, helping you understand what your poker future might look like based on your skill level and game type.

Whether you're grinding Texas Hold'em cash games or battling through Omaha tournaments, understanding variance is essential for maintaining both your bankroll and your mental game. This tool shows you the mathematical reality behind the swings you experience at the tables.

Monte Carlo Variance Simulator

Your expected big blinds won per 100 hands
Typical: 60-80 tight, 80-100 LAG, 100+ PLO
Number of hands to simulate
More paths = more accurate probabilities

Understanding Poker Variance

Variance is a statistical concept that measures how spread out results are from the average (expected value). In poker, variance quantifies the "luck" element - the difference between your actual results and what your skill level suggests you should win. According to research from PokerNews, understanding variance is one of the most important concepts for serious players, as it explains why short-term results often don't reflect true skill.

The standard way to measure variance in poker is through standard deviation, typically expressed as BB/100 (big blinds per 100 hands). A typical No-Limit Hold'em 6-max player has a standard deviation around 70-90 BB/100, while Pot-Limit Omaha players often see 100-140 BB/100 due to the game's higher-action nature.

95% Confidence Range = Expected Win ± (2 × StdDev × √(Hands/100))
Your actual results will fall within this range 95% of the time

Why Monte Carlo Simulation?

Monte Carlo simulation is a computational technique that uses random sampling to model uncertain outcomes. Named after the famous casino in Monaco, it's the same mathematical approach used by financial institutions to model risk and by scientists to simulate complex systems. In this simulator, we generate thousands of possible "poker careers" based on your inputs, revealing the true distribution of possible outcomes.

The technique is particularly valuable for poker because it shows the full range of possibilities, not just averages. As explained in academic literature from institutions like Carnegie Mellon University's poker AI research, understanding probability distributions rather than single-point estimates is essential for rational decision-making under uncertainty.

What This Simulator Shows

  • Multiple outcome paths: Each colored line represents one possible poker journey with your win rate and variance
  • Expected value line: The theoretical average outcome if luck perfectly balanced out
  • Confidence bands: Statistical boundaries showing where results typically fall
  • Downswing probabilities: Likelihood of experiencing various losing stretches
  • Result distribution: How outcomes cluster and spread at your sample size

The Sample Size Problem

One of the most misunderstood aspects of poker is how many hands you need to assess your true skill level. The poker forums at Two Plus Two have extensive discussions on this topic, with the consensus being that most players dramatically underestimate required sample sizes.

Consider a player winning at 5 BB/100 with standard deviation of 80 BB/100. After 10,000 hands - what feels like significant playing time - their results could reasonably range from -30 buy-ins (losing) to +50 buy-ins (crushing). That's the reality of variance. Only after hundreds of thousands of hands does the "signal" (skill) clearly emerge from the "noise" (luck).

Sample Size 95% Confidence Range What This Means
10,000 hands ±32 BB/100 A 5 BB/100 winner could appear to be a -27 BB/100 loser
50,000 hands ±14 BB/100 Still massive uncertainty; winner could show as breakeven
100,000 hands ±10 BB/100 Starting to converge; trends become more reliable
500,000 hands ±4.5 BB/100 High confidence in win rate estimate

Downswings: The Inevitable Reality

Every poker player, regardless of skill, will experience significant downswings. This isn't pessimism - it's mathematical certainty. The only questions are when and how severe. Understanding this reality is crucial for maintaining proper bankroll management and mental resilience.

The poker training site Upswing Poker emphasizes that handling downswings is often what separates successful players from those who go broke. Professional players like Daniel Negreanu have publicly discussed experiencing 30+ buy-in downswings while still being significant long-term winners.

Typical Downswing Probabilities (5 BB/100 winner, 80 SD)

  • 5 buy-in downswing: Nearly 100% probability over 50,000 hands
  • 10 buy-in downswing: Approximately 80-90% probability
  • 20 buy-in downswing: Approximately 30-50% probability
  • 30 buy-in downswing: Approximately 10-20% probability
  • 50 buy-in downswing: Still possible, though relatively rare

How to Use This Simulator

Step 1: Input Your Parameters

Enter your estimated win rate and standard deviation. If you use tracking software like PokerTracker or Hold'em Manager, you can find these stats directly. If not, the presets provide reasonable estimates for different player types.

Step 2: Choose Sample Size

Select how many hands you want to simulate. This might represent your monthly volume, yearly play, or career so far. Larger samples show how results converge toward expected value over time.

Step 3: Run the Simulation

Click "Run Variance Simulation" to generate multiple possible outcomes. Each path represents an equally likely poker journey given your inputs. Study how paths diverge early and (for winning players) tend to converge upward over time.

Step 4: Interpret Results

Pay attention to the downswing probabilities and result distribution. These show the realistic range of outcomes you might experience - not just the idealized expected value. Use these insights to set appropriate expectations and bankroll requirements.

Variance in Different Games

No-Limit Hold'em

The most popular format, NL Hold'em has moderate variance with standard deviations typically between 60-100 BB/100. Tighter, more positionally aware players tend toward the lower end, while aggressive LAG players experience higher variance but potentially higher win rates.

Pot-Limit Omaha

PLO, as covered in our Omaha guide, features significantly higher variance due to closer hand equities and more multi-way action. Standard deviations of 100-150 BB/100 are common, requiring larger bankrolls to weather the storms.

Tournaments

Tournament variance is dramatically higher than cash games because most players lose in each event. ROI (Return on Investment) replaces BB/100, and even elite players can go months between significant cashes. The ICM Calculator helps understand tournament-specific equity concepts.

Psychological Implications

Understanding variance intellectually is one thing; accepting it emotionally is another. Many players know about variance but still tilt during downswings, make poor decisions when running good, or draw incorrect conclusions from small samples. The Expected Value Calculator helps analyze individual decisions separate from results.

Key mental game concepts related to variance:

  • Process over results: Judge decisions by their logic, not outcomes
  • Detachment: View short-term results as data points, not reflections of skill
  • Patience: Trust in long-term mathematics even during painful stretches
  • Humility: Remember that hot streaks can be as misleading as cold ones

Frequently Asked Questions

What is variance in poker?

Variance in poker refers to the statistical measure of how much your actual results deviate from your expected (average) results. Even winning players experience significant short-term losing streaks due to the random nature of card distribution. Variance is measured using standard deviation, typically expressed as BB/100 (big blinds per 100 hands).

How many hands do I need for a reliable sample size?

For cash games, most experts recommend a minimum of 50,000-100,000 hands to get a reasonably reliable estimate of your true win rate. Even at 100,000 hands, there's still significant uncertainty. For tournaments, you need hundreds of events due to higher variance. The variance simulator helps visualize why these large sample sizes are necessary.

Why do I keep losing even though I play well?

Short-term results in poker are heavily influenced by variance (luck). A winning player with a 5BB/100 win rate and typical standard deviation of 80BB/100 can easily experience 20+ buy-in downswings over tens of thousands of hands. This simulator shows that such downswings are mathematically normal and expected, even for skilled players.

What is Monte Carlo simulation?

Monte Carlo simulation is a mathematical technique that uses random sampling to model uncertain outcomes. In this poker variance simulator, we run thousands of simulated poker sessions based on your win rate and standard deviation to show the range of possible outcomes you might experience.

How does standard deviation affect my results?

Higher standard deviation means more volatile results - bigger swings in both directions. A LAG (Loose-Aggressive) player might have SD of 100+ BB/100, experiencing wilder swings than a tight player with SD of 60 BB/100. Higher variance requires larger bankrolls to maintain the same risk of ruin.

Can I trust my results after X hands?

Trust increases gradually with sample size. At 10,000 hands, results are largely noise. At 50,000 hands, patterns emerge but uncertainty remains high. At 100,000+ hands, you can be reasonably confident in your overall direction, though precise win rate estimates still carry significant margins of error.

Related Tools and Resources

Combine this variance simulator with our other poker tools for comprehensive analysis:

Responsible Gambling Reminder

Variance can be emotionally challenging. If you find that poker downswings are affecting your mood, relationships, or financial wellbeing beyond what you're comfortable with, consider taking a break or seeking support. The National Council on Problem Gambling provides resources for anyone struggling with gambling-related issues. Understanding variance should help you play more responsibly - not encourage risky behavior based on "eventually" returning to positive.