Blackjack Variance Calculator
Calculate session variance, standard deviation, and expected result ranges for your blackjack play. Understand the role of luck vs. skill over different session lengths.
Formula:Session σ = √(Variance × Hands) × Bet Unit
Session Std Deviation
$191.83
19.2 units
Expected Result
$-12.80
P(Profit)
47.3%
Risk of Ruin
49.87%
$
Your total gambling bankroll
$
Standard bet size
60-100 typical for table play
How long you plan to play
Pre-configured rule variations
%
Negative = house edge, Positive = player advantage
Expected Result Ranges for 320 Hands
Expected (Average)
$-12.80
68% Likely Range (1σ)
$-205 to $179
95% Likely Range (2σ)
$-396 to $371
Bankroll Analysis
Betting Units:100 units
Bankroll/Std Dev Ratio:5.2:1
Your bankroll provides moderate protection against variance.
Session Variance Simulator
Monte Carlo simulation with 1,000 iterations
$
Your initial capital
%
Your expected advantage
%
Percentage of bankroll per bet
Total bets to simulate
Key Facts
- •Blackjack variance is approximately 1.15 per hand (bet unit squared)
- •68% of sessions fall within one standard deviation of expected
- •95% of sessions fall within two standard deviations
- •Card counters need 1,000+ betting units to weather variance
- •Short sessions are dominated by luck, not skill or edge
Frequently Asked Questions
What is variance in blackjack?
Variance measures how much your results can deviate from the expected outcome. Blackjack has a variance of about 1.15 per hand, meaning significant short-term swings are normal even with perfect basic strategy. Understanding variance helps set realistic expectations for sessions.
How does variance affect my bankroll needs?
Higher variance requires a larger bankroll to survive downswings. A good rule of thumb is 200-300 betting units for recreational play, and 1,000+ units for advantage players. The variance calculator helps determine your specific risk based on your betting level.
What is the standard deviation in blackjack?
Standard deviation is the square root of variance. For blackjack, it's about 1.07 betting units per hand. Over a session, standard deviation grows with the square root of hands played - so 100 hands has 10x the single-hand std dev.
How many hands until I expect to be profitable?
For basic strategy players with a 0.5% house edge, you're never "expected" to be profitable in the long run. Card counters with a 1% edge need roughly 10,000+ hands for variance to smooth out and results to match expectation.
Try These Examples
Quick-start with common scenarios
How this works
Calculations follow the published mathematics of the game — combinatorics for cards, probability theory for dice, and expected-value accounting for wagers. Results are verified against independent references (primarily Wizard of Odds). No calculation here is an opinion or recommendation; it is arithmetic applied to the rules of the game.
What this tool can’t do
When to consult a professional
This tool computes probability and expected value. It is not a betting system and cannot predict the outcome of any individual wager. If gambling is causing problems for you or someone you know, call the National Problem Gambling Helpline at 1-800-GAMBLER.
Sources
- [1]Wizard of Odds — Michael Shackleford, ASAIndustrywizardofodds.comAccessed Apr 21, 2026
Actuary; widely cited casino-game probability reference. Used for house-edge and EV verification.
- [2]National Council on Problem GamblingOfficial sourcencpgambling.orgAccessed Apr 21, 2026
Responsible-gambling guidance and 1-800-GAMBLER helpline.
Joseph OrdunaFounder & Software Engineer
Full-stack software engineer specializing in embedded systems, web architecture, and AI/ML. Founder of Practical Web Tools. Built the gesture-controlled drone IP acquired by KD Interactive (Aura Drone, sold on Amazon).
Session Std Deviation
$191.83
19.2 units
Expected Result
$-12.80
P(Profit)
47.3%
Risk of Ruin
49.87%