Variance in Poker: Understanding and Managing the Swings

Variance is the mathematical measure of how much your results deviate from expected value. In poker, variance creates the swings that can make or break players psychologically and financially. Understanding variance is crucial for proper bankroll management and mental game stability.

What is Variance?

Variance Definition: The statistical measure of how spread out results are from the expected average.

In Poker Terms: How much your actual results differ from your expected winnings over time.

Key Variance Concepts

1. Standard Deviation (σ) - Square root of variance
2. Expected Value (EV) - Your theoretical average result
3. Actual Results - What actually happened
4. Sample Size - Number of hands/sessions played

Mathematical Foundation

Basic Variance Formula

Variance (σ²) = E[(X - μ)²]

Where:

• X = Individual result
• μ = Expected value (mean)
• E = Expected value function

Standard Deviation in Poker

Standard Deviation = √Variance

Practical Application:

• 68% of results fall within 1 standard deviation
• 95% of results fall within 2 standard deviations
• 99.7% of results fall within 3 standard deviations

Variance in Different Poker Formats

Cash Game Variance

Typical Standard Deviations:

Tournament Variance

ROI Standard Deviations:

Calculating Your Variance

Cash Game Example

Your Stats:

• Winrate: 5 BB/100
• Standard deviation: 90 BB/100
• Hands played: 10,000

Expected Results:

• Expected winnings: 500 BB
• Standard deviation: 900 BB
• 68% confidence interval: -400 BB to +1,400 BB
• 95% confidence interval: -1,300 BB to +2,300 BB

Sample Size Requirements

Hands Needed for Statistical Significance:

Variance and Bankroll Management

Kelly Criterion Application

Formula: f = (bp - q) / b

Where:

• f = Fraction of bankroll to risk
• b = Odds received
• p = Probability of winning
• q = Probability of losing

Conservative Bankroll Guidelines

Cash Games:

Tournaments:

Understanding Downswings

Probability of Downswings

For a 5 BB/100 winner with 90 BB/100 SD:

Longest Expected Downswings

Mathematical Expectations:

Factors Affecting Variance

Playing Style Impact

Tight-Aggressive (TAG):

• Lower variance
• Steady winnings
• Fewer big pots

Loose-Aggressive (LAG):

• Higher variance
• Bigger swings
• More big pots

Game Selection Impact

Low Variance Games:

• Tight opponents
• Small pots
• Predictable play

High Variance Games:

• Loose opponents
• Large pots
• Unpredictable play

Position and Variance

In Position:

• Better control
• Lower variance
• More information

Out of Position:

• Less control
• Higher variance
• Difficult decisions

Variance Reduction Strategies

1. Game Selection

Choose games with:

• Weaker opponents
• Deeper stacks
• Better position frequency

2. Playing Style Adjustments

Reduce variance by:

• Playing tighter ranges
• Avoiding marginal spots
• Focusing on value betting

3. Bankroll Management

Conservative approach:

• Larger bankroll requirements
• Move down during downswings
• Never play scared money

4. Volume Management

Optimal volume:

• Play when mentally fresh
• Avoid tilt-inducing sessions
• Quality over quantity

Psychological Aspects of Variance

Cognitive Biases

Recency Bias:

• Overweighting recent results
• Ignoring long-term data

Confirmation Bias:

• Seeing patterns that don't exist
• Attributing results to skill/luck incorrectly

Mental Game Strategies

Variance Acceptance:

1. Understand it's inevitable
2. Focus on decision quality
3. Separate results from process
4. Maintain long-term perspective

Tilt Prevention:

1. Set stop-loss limits
2. Take breaks during downswings
3. Review hands objectively
4. Seek support from poker community

Variance in Different Scenarios

Scenario 1: Tournament Final Table

Situation: 9 players, equal stacks Variance factors:

• ICM pressure
• Short-term luck
• Pay jump significance

Variance impact:

• Single elimination = high variance
• Skill edge reduced
• Luck factor increased

Scenario 2: Cash Game Session

Situation: 6-max $1/$2, 200 hands Variance factors:

• Coolers and bad beats
• Card distribution
• Opponent adjustments

Expected range:

• +/- 4 buy-ins (2 SD)
• Skill edge: 1-2 buy-ins
• Luck factor: 6-8 buy-ins

Advanced Variance Concepts

Skewness in Poker

Definition: Asymmetry in result distribution

Tournament skewness:

• Positive skew (rare big wins)
• Many small losses
• Few large profits

Cash game skewness:

• More symmetric distribution
• Occasional big pots
• Generally balanced

Kurtosis and Fat Tails

Definition: Extreme outcomes frequency

Poker implications:

• More extreme results than normal distribution
• "Black swan" events
• Importance of bankroll management

Variance Tracking and Analysis

Essential Metrics

Cash Games:

• BB/100 winrate
• Standard deviation
• Hands played
• Hourly rate

Tournaments:

• ROI percentage
• ITM percentage
• Average buy-in
• Total tournaments

Software Tools

Tracking Software:

• PokerTracker 4
• Hold'em Manager 3
• DriveHUD
• Hand2Note

Analysis Features:

• Variance graphs
• Confidence intervals
• Downswing analysis
• Bankroll simulation

Variance Simulation

Monte Carlo Analysis

Purpose: Simulate thousands of possible outcomes

Example Simulation:

• 100,000 hands
• 5 BB/100 winrate
• 90 BB/100 SD

Results:

• 68% finish between -400 and +1,400 BB
• 5% chance of losing 20+ buy-ins
• 1% chance of losing 35+ buy-ins

Practical Applications

Bankroll planning:

• Determine required bankroll
• Set move-up/move-down limits
• Plan for worst-case scenarios

Goal setting:

• Realistic expectations
• Timeline adjustments
• Risk tolerance assessment

Managing Variance Professionally

Professional Considerations

Income stability:

• Larger bankroll requirements
• Multiple income streams
• Conservative withdrawal rates

Tax implications:

• Variance affects annual income
• Quarterly payment planning
• Record keeping importance

Staking and Backing

Variance sharing:

• Reduce personal variance
• Share profits with backer
• Professional development

Markup considerations:

• Variance affects markup
• Track record importance
• Long-term relationships

Common Variance Mistakes

1. Underestimating Variance

Mistake: Expecting steady profits Reality: Significant swings are normal Solution: Proper bankroll management

2. Overreacting to Short-Term Results

Mistake: Changing strategy after bad session Reality: Small samples are meaningless Solution: Focus on long-term data

3. Playing Above Bankroll

Mistake: Moving up during heater Reality: Variance can destroy bankroll Solution: Conservative move-up strategy

4. Ignoring Variance in Game Selection

Mistake: Playing highest variance games Reality: Lower variance = more stable income Solution: Balance profit and variance

Variance and Different Player Types

Recreational Players

Characteristics:

• Limited bankroll
• Emotional attachment to results
• Short-term focus

Recommendations:

• Lower variance games
• Smaller stakes
• Focus on fun and learning

Semi-Professional Players

Characteristics:

• Supplemental income
• Moderate bankroll
• Improving skills

Recommendations:

• Balanced approach
• Proper bankroll management
• Variance tracking

Professional Players

Characteristics:

• Primary income source
• Large bankroll
• Advanced skills

Recommendations:

• Conservative bankroll management
• Multiple game types
• Variance minimization strategies

Conclusion

Variance is an inescapable part of poker that every player must understand and manage. Key principles:

1. Variance is inevitable - even the best players experience significant swings
2. Sample size matters - short-term results are largely meaningless
3. Bankroll management is crucial - protect yourself from ruin
4. Mental game is vital - maintain perspective during swings
5. Track and analyze - use data to understand your variance

Understanding variance helps you:

• Set realistic expectations
• Manage your bankroll properly
• Maintain mental stability
• Make better strategic decisions
• Achieve long-term success

Remember: in poker, you're paid for making good decisions, not for winning every hand. Focus on the process, and let the results take care of themselves over time.

Quick Variance Reference

Key Numbers:

• 68% of results within 1 SD
• 95% of results within 2 SD
• 99.7% of results within 3 SD

Bankroll Guidelines:

• Cash games: 30-40 buy-ins
• Tournaments: 100-200 buy-ins
• High variance: Add 50-100% buffer

Mental Game:

• Focus on decisions, not results
• Understand downswings are normal
• Maintain long-term perspective
• Seek support during tough times