Learn / Expected Value

Expected Value is the average result of a decision, not the result of the next hand.

Expected Value (EV) weights every possible outcome of a decision by its probability. It is the standard way to compare blackjack actions — and it is easy to misread.

What EV measures

A probability-weighted average across every way the hand can end.

For a given action, EV adds up the value of each possible outcome multiplied by its probability. The formula and the way OOB evaluates each action are described in the Methodology.

Average
Not a Forecast
EV describes what an action returns on average across all possible outcomes. A single hand ends in one outcome only.
Comparison
Highest EV Is Preferred
In a given state, the action with the highest EV is the mathematically preferred one. When every available action is negative, the highest EV is the least negative — not a winning hand.
State
EV Depends on the State
The rules, the remaining cards, the player hand and the dealer upcard all change the probabilities, and therefore the EV.
Size
Small Gaps Are Small
The preferred action can be ahead by a very small margin. A higher EV does not mean a large practical difference.
Fraction versus percent

The same value can be written as a fraction of the bet or as a percentage.

OOB’s published states show action EVs as fractions of the original bet, with four decimal places. Multiplying by 100 gives the same value as a percentage of the original bet.

+0.0500 → +5.00% of the original bet
−0.0050 → −0.50% of the original bet
−0.5000 → −50.00% of the original bet
Percent and percentage points are different units.
A change from −0.50% to +0.50% is a change of one percentage point. Pre-bet EV thresholds on this site are quoted as percentages — for example, the 100-Hour Simulated Replay describes a rule with no bet below −1.0% pre-bet EV.
Normalisation on the original bet

Every action EV is expressed per original bet, including any additional wager.

This is the convention stated with every published state: “Per original bet, including any additional wager.” It keeps actions comparable even when they put different amounts at risk.

Stand · Hit
One Unit at Risk
For non-natural hands without side bets, each outcome is a win, a push or a loss of the original bet, so the EV lies between −1 and +1. A natural blackjack is paid as the table rules set and is not covered by this range.
Double
Two Units at Risk
Doubling adds a second unit, so the EV per original bet can lie between −2 and +2.
Split
Several Hands, One Value
Split EV sums the resulting hands, each with its own wager, and is still expressed per original bet.
Surrender
Part of the Bet Given Up
Surrender gives up part of the original bet. Its exact value depends on the hole-card rule in force.
Why a double can show an EV below −1.
In the published state OOB-RS-0008 (10 + 6 against a dealer 10), Double is listed at -1.1414 and Surrender at -0.5387 per original bet. In OOB-RS-0002 (5 + 6 against a dealer 6), Double is listed at +0.6786. These are published values on their stated build, not new calculations.
EV versus realised result

What a decision is worth on average is not what it returns this time.

A higher-EV action can lose the next hand, and a lower-EV action can win it. EV is about the quality of the decision; the realised result also contains chance.

One hand
One Outcome
The realised result of a hand is one of its possible outcomes, not its average.
Many hands
Averages Can Still Drift
Over many comparable decisions, the average realised result is expected to move closer to the EV, but any finite session can differ widely from it.
Simulations
Realised, Not Expected
The One Million Cards and 100-Hour Simulated Replay results are realised results on simulated tracks. They are not EVs and not forecasts.

Positive EV does not remove variance. Risk of Ruin and variance metrics are not available in the application.

Action EV versus pre-bet EV

Two different numbers answer two different questions.

OOB shows the EV of each available action once a hand is dealt. Separately, it estimates the EV of the next round before any card is dealt, and uses that estimate only for the suggested initial bet.

After the deal
Action EV
Calculated for each available action — Hit, Stand, Double, Split, Surrender — from the recorded remaining shoe, the rules, the player hand and the dealer upcard, under the conditioning conventions documented in the Technical Whitepaper. It is used to select the highest-EV action.
Before the deal
Pre-Bet EV Estimate
An estimate of the next round from OOB’s production model, computed from the recorded composition with an empirical calibration inside a defined domain (at least 104 cards remaining and a ten-card density between 26% and 34%); outside that domain the uncalibrated value is used. It is used only for the suggested initial bet.
A positive estimate does not make the next hand positive.
A favourable pre-bet estimate does not make every action EV in the following round positive, and an unfavourable one does not make a hand unwinnable. The internal audit of the production pre-bet EV (Validation Register, V-009) has not reached a verdict.
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Related pages and published evidence.

True Count vs Exact Composition
What a count summarises and what the full composition keeps.
Read the Page →
Reproducible States
Published action EVs with their rules, composition and build.
View State Library →
Methodology
How the action EVs and the suggested initial bet are produced.
Read the Methodology →