Casino Korea

Variance Calculator

Variance is the mathematical concept that explains why gambling results can differ dramatically from expectations in the short term, even while the house edge guarantees long-term losses. This calculator helps you understand how volatility affects your gambling sessions and why short-term wins don't disprove the mathematics of the house edge.

Understanding variance is essential for recognizing why some gamblers win temporarily while the casino always profits over time. High variance games create bigger swings in either direction, giving the illusion that outcomes are controllable when they're entirely random.

Calculate Session Variance

Select a game and session parameters to see how much your results can vary from expected outcomes.

The probability of winning each individual bet
How much you win relative to your bet when you win
Total number of bets in your session

Expected Result

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Standard Deviation

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Volatility Level

Low Volatility Medium High Very High

Key Insight

Visualize Possible Outcome Ranges

See the statistical distribution of possible outcomes for your gambling session.

Probability Distribution of Outcomes

Based on 100 bets of $100 each:

68% of results (1 SD)
95% of results (2 SD)
99.7% of results (3 SD)

Outcome Statistics

Probability of Profit

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Compare Volatility Across Games

See how variance differs across casino games with identical bet sizes and session lengths.

Game Expected Loss Std. Deviation Best 5% Worst 5% Volatility

Understanding the Table

Expected Loss: The average outcome over many sessions of this length.

Standard Deviation: Measures how much results typically vary from the average.

Best 5%: In the luckiest 5% of sessions, you'd gain at least this much.

Worst 5%: In the unluckiest 5% of sessions, you'd lose at least this much.

Note: All games have negative expected value. Higher variance just means bigger swings, not better odds.

Understanding Variance in Gambling

Variance is a statistical measure of how spread out results are from the average. In gambling, variance explains why individual sessions can produce results far different from the expected outcome, even when the house edge guarantees long-term losses.

According to the Encyclopedia Britannica, variance is defined as the average of the squared deviations from the mean. In gambling contexts, this translates to measuring how wildly your bankroll can swing compared to what mathematics predicts.

Variance Formula for Gambling:

Variance = n * p * (1 - p) * (payout + 1)^2

Where:
n = number of bets
p = probability of winning
payout = win amount relative to bet

Standard Deviation = Square Root of Variance

Why Variance Creates the Illusion of Winning

High variance is precisely what makes gambling psychologically addictive. When results can swing dramatically in either direction, winning sessions feel like skill or luck that can be replicated. Research published in the Journal of Gambling Studies (NIH) demonstrates that variable reinforcement schedules (the pattern created by variance) are the most effective at maintaining behavior.

At Kangwon Land, South Korea's only legal casino for Korean citizens, the mathematics of variance operates exactly as described. Some visitors win substantial amounts in individual sessions, which creates stories of success that spread through social networks. What isn't shared equally are the many more losing sessions that the same variance produces.

The Standard Deviation Concept

Standard deviation is the square root of variance and provides a more intuitive measure of outcome spread. The Khan Academy provides an excellent explanation of this concept: approximately 68% of results fall within one standard deviation of the expected value, 95% within two standard deviations, and 99.7% within three.

For gambling, this means that in a given session:

Results beyond three standard deviations are rare but do occur—these are the "big wins" and "crushing losses" that gamblers remember most vividly.

Volatility in Different Games

Casino games vary significantly in their volatility levels. Understanding these differences helps explain why different games feel different to play, even when they have similar house edges.

Low Volatility Games

Blackjack, Baccarat, Craps (Pass Line): These games produce relatively consistent results session-to-session. You won't win or lose dramatically in short sessions, but the house edge still grinds away your bankroll over time. Use our House Edge Calculator to see exactly how much you can expect to lose.

Medium Volatility Games

Roulette, Some Video Poker: These games offer moderate swings. You can have good sessions and bad sessions, but extremes are less common than in high-volatility games.

High Volatility Games

Slots, Keno: High-volatility games can produce dramatic swings. You might lose quickly, or you might hit a significant win. However, the same high variance that allows for big wins also means more frequent losing sessions. Our Session Simulator can visualize this effect.

The Volatility Trap

High-volatility games aren't "better" or "worse" than low-volatility games—they have the same expected loss rate determined by house edge. The difference is entirely in how that loss is distributed across sessions.

Many gamblers prefer high-volatility games because the occasional big win feels more exciting. However, this same variance leads to more rapid bankroll depletion for most players. The Responsible Gambling Council notes that high-volatility games are associated with faster development of gambling problems.

Variance and the Law of Large Numbers

While variance allows for significant short-term deviations, the Law of Large Numbers guarantees that over time, actual results converge toward the expected value. This is why casinos are profitable businesses despite the variance in individual sessions.

The relationship between variance and sample size is inverse: as the number of bets increases, the percentage deviation from expected results decreases. A 100-bet session might vary by 20% from expectations, while a 10,000-bet series might only vary by 2%. Use our Streak Calculator to see how patterns emerge naturally from random variance.

Implications for Gambling Behavior

Understanding variance leads to important insights about gambling:

Variance in Korean Gambling Context

South Korea's strict gambling laws partially reflect understanding of how variance contributes to gambling problems. When a citizen experiences a big win due to favorable variance, they may believe they've discovered a winning method—leading to continued gambling that the house edge eventually punishes.

The enforcement of gambling prohibitions recognizes that variance creates the psychological trap that leads to problem gambling. Our article on gambling debt shows how chasing losses—often caused by unfavorable variance—leads to severe financial consequences.

Important Reminder

This calculator provides educational information about gambling variance. Understanding variance should not be used to develop betting strategies—no strategy can overcome the house edge. Higher or lower variance games all have negative expected value.

If you or someone you know has a gambling problem, seek professional help. Visit our responsible gambling resources or complete our Problem Gambling Self-Assessment.

Frequently Asked Questions

What is variance in gambling?

Variance in gambling measures how widely individual outcomes deviate from the expected average. High variance means results can swing dramatically in either direction, while low variance means results stay closer to the expected outcome. Slots typically have high variance, while blackjack has lower variance.

Why do some gamblers win in the short term despite the house edge?

Variance allows for short-term deviations from expected outcomes. In a small sample size, random chance can produce winning streaks. However, as the number of bets increases, variance's effect diminishes and results converge toward the expected loss dictated by the house edge.

How does standard deviation relate to gambling outcomes?

Standard deviation measures the typical size of deviation from expected results. About 68% of outcomes fall within one standard deviation, 95% within two, and 99.7% within three. This helps quantify how much results can reasonably vary in a gambling session.

Are high variance or low variance games better?

Neither is "better"—both have the same expected loss rate determined by the house edge. High variance games offer bigger swings (both wins and losses) but the same long-term outcome. Low variance games provide more consistent (but still negative) results. The house edge ensures losses regardless of variance level.

Related Tools

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