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.