Casino
Blackjack EV Calculator
Calculate blackjack expected value, variance and modeled house edge from an entered distribution of net outcomes. Explore session mean and bankroll assumptions.
Your result
−$0.70
Expected net per hand from entered model
- Modeled house edge
- 7.00%
- Variance in base-bet units²
- 0.9051
- Standard deviation per hand
- $9.51
- Mean over entered hands
- −$70.00
- Session standard deviation
- $95.14
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User-supplied complete net outcome distribution; no basic-strategy or rule-set probabilities inferred.
Expected value, house edge and variance formulas
For each possible net result xᵢ with probability pᵢ, mean μ = Σpᵢxᵢ and variance = Σpᵢxᵢ² − μ². Standard deviation is the square root of variance. Probabilities must sum to 100%. Include naturals, pushes, doubled stakes and splits as distinct final net outcomes when the supplied model contains them.
The illustrative 42% +1, 49% −1 and 9% zero distribution has mean −0.07 base-bet units and variance 0.9051. A $10 base bet gives −$0.70 mean per hand and about $9.5137 standard deviation. These inputs are illustrative, not a blackjack rule-set estimate.
Blackjack house edge needs a complete outcome model
Modeled house edge relative to the initial base bet is −μ. The tool calculates it from your supplied probabilities; it does not infer them from deck count or payouts. Dealer soft-17 rules, double and split rules, strategy and shoe composition affect the actual distribution.
For N independent equal-stake hands, session mean is NμS and session deviation is √N × σS. Use the risk of ruin calculator for a stated drift approximation. A 3:2 versus 6:5 payout chart is insufficient to establish full-game expected value.