Expected Value

The average amount you'd win or lose per bet over thousands of hands. The math underlying every basic strategy decision.

Definition

Expected value (EV) is the long-run average outcome of a bet, weighted by the probability of each result. Positive EV means you profit on average; negative means the house does.

EV  =  sum of (probability of each outcome × payout of that outcome)

Worked example

Say you flip a fair coin and bet $1: heads pays $2, tails loses $1. The EV per bet:

(0.5 × $2) + (0.5 × -$1) = $1 - $0.50 = +$0.50

Each bet has an expected value of +$0.50. Over 1,000 flips, you'd expect to be up roughly $500. Random variance means a single session could be far above or below that, but the average converges over time.

Why EV matters in blackjack

Every blackjack decision has an EV. Basic strategy is the rule that always picks the highest-EV option. When the math says "double," it's because the EV of doubling exceeds the EV of hitting. When the math says "surrender," it's because giving up half your bet has a higher EV than playing the hand out.

EV per dollar wagered is the standard unit. It's like a return rate per bet. A positive EV decision is profitable on average; a negative EV decision still loses money but loses less than the alternatives.

Examples

DecisionEV per $1
Doubling hard 11 vs dealer 6+$0.668
Splitting 8-8 vs dealer 6+$0.394
Standing on hard 12 vs dealer 4−$0.211
Hitting hard 16 vs dealer 10−$0.535
Standing hard 16 vs dealer 10−$0.540
Surrendering hard 16 vs dealer 10−$0.500
Insurance bet (no count, 6-deck)−$0.075

Notice surrender at −$0.500 beats both hit (−$0.535) and stand (−$0.540) on hard 16 vs dealer 10. None of the options are positive EV — that hand is just bad — but surrender is the least-bad. Basic strategy says surrender.

EV vs house edge

House edge is just total EV across all hands and decisions, expressed as a negative percentage. A 0.5% house edge means the average EV of every dollar wagered (across thousands of basic-strategy hands) is −$0.005.

EV is the per-decision lens; house edge is the long-run aggregate. Same math, different scale.

EV in BJNP

The premium tier of Blackjack Navigator Pro shows per-action EV breakdowns: when you face a decision, the app displays the EV of each option (hit, stand, double, split, surrender) so you see exactly why basic strategy recommends what it does.

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