Variance
Definition
A measure of how much results deviate from the expected value in the short term. High variance games have bigger swings, including longer losing streaks and bigger wins. Low variance games produce more consistent, predictable results.
Variance measures how much your actual results deviate from the expected value over a given number of bets. A low-variance game produces results close to the mathematical expectation, while a high-variance game creates wild swings between winning and losing streaks. Understanding variance is essential for managing your bankroll and your expectations.
Consider two slot machines, both with 96% RTP. Machine A pays small wins frequently (low variance), while Machine B rarely pays but delivers large jackpots when it does (high variance). Over millions of spins, both return 96%. But in a single session, your experience will be dramatically different. Machine A gives steady, predictable play, while Machine B can drain your bankroll quickly or deliver a huge windfall.
Variance is why bankroll management matters so much. Even in a game with a small house edge, short-term variance can produce devastating losing streaks. A blackjack player using perfect basic strategy (0.5% house edge) can easily lose 20 or more consecutive decisions. Without adequate bankroll reserves, variance can knock you out of the game before the math has time to work in your favor.
Mathematically, variance is the average of the squared differences from the mean. In practical terms for gamblers, it determines how much money you need to survive the inevitable swings. Professional gamblers calculate their required bankroll based on the variance of their chosen game and their risk tolerance, typically targeting a risk of ruin below 5%.
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Related Terms
A statistical measure of the spread of results around the expected value. In gambling, it helps predict how much your actual results might differ from the mathematical expectation over a given number of bets.
VolatilityOften used interchangeably with variance, volatility describes how risky a game is. High volatility slots pay less frequently but with larger wins. Low volatility slots pay more often with smaller amounts. Medium volatility offers a balance between the two.
Expected Value (EV)The average amount a player can expect to win or lose per bet over the long run. Calculated as (probability of winning × win amount) - (probability of losing × loss amount). A positive EV means the bet is profitable long-term; negative EV means it loses money.
Gambler's FallacyThe mistaken belief that past random events affect future outcomes. For example, thinking that after 10 red results in roulette, black is 'due.' Each spin is independent and the wheel has no memory. One of the most common cognitive biases in gambling.
Sample SizeThe number of trials or observations in a dataset. In gambling, a small sample size leads to unreliable conclusions. Thousands of hands or spins are needed before results become statistically meaningful.
Normal DistributionA bell-shaped probability distribution where most results cluster around the average. In gambling, short-term results follow a normal distribution around the expected value, with the spread determined by standard deviation.
Bad BeatLosing a hand despite being a heavy statistical favorite. For example, having pocket Aces cracked by a runner-runner flush. Bad beats are a normal part of poker variance, but they often trigger tilt.
Cold StreakAn extended period of losing. Cold streaks are a normal part of gambling variance and do not mean the game is 'rigged' or that a hot streak is 'due.' Managing cold streaks without chasing losses is essential for bankroll preservation.
Hot StreakAn extended period of winning. Due to the gambler's fallacy, players often believe hot streaks will continue, but each event remains independent. The best strategy during a hot streak is to lock in profits, not increase bet sizes.
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Frequently Asked Questions
What is Variance?
A measure of how much results deviate from the expected value in the short term. High variance games have bigger swings, including longer losing streaks and bigger wins. Low variance games produce more consistent, predictable results.
What terms are related to Variance?
Related concepts include: Standard Deviation, Volatility, Expected Value (EV), Gambler's Fallacy, Sample Size, Normal Distribution, Bad Beat, Cold Streak, Hot Streak. Understanding these terms together gives you a more complete picture of the concept.
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