The calculation record
Before publishing a percentage, we identify the game or wager, complete rule set, pay table, legal player actions, assumed strategy, deck or wheel model, treatment of pushes and the denominator used. A figure is not transferred to a superficially similar game unless those assumptions also match.
The player house edge is the negative of player EV when both use the same initial-wager denominator.
House edge and expected loss
House edge is normally stated as expected casino win divided by the initial amount wagered. Expected loss then equals total action multiplied by house edge. Games with later optional or required wagers may also be described using element of risk, which divides expected loss by average total money risked. We never compare percentages that use different denominators without labeling the distinction.
This is an average across repeated decisions, not a prediction, stop-loss or statement about the most likely session result.
Exact enumeration and simulation
Where a finite outcome space can be enumerated, probabilities are obtained by counting weighted outcomes under the stated rules. A simulation is used only when it is clearly identified as an approximation. A simulation record should include the random process, number of trials, estimator, uncertainty and seed or reproducibility information when available.
Strategy tables
A strategy cell compares the conditional expected value of every legal action for the displayed player state, dealer information and rules. The action with the highest EV is selected. The current blackjack charts are total-dependent: they group hands by total or pair rather than every exact card composition. Composition-dependent exceptions can therefore exist in one- and two-deck play.
For surrender cells, the chart also states the correct fallback when surrender is unavailable. A rule-matched chart must not be used when a material rule—such as blackjack payout, dealer-hole-card treatment, doubling restriction or split rule—differs.
Calculator validation
Interactive tools are checked at three levels:
- Identity checks: formulas must reproduce simple known examples, such as roulette EV from pocket count and payout.
- Boundary checks: zero values, rule transitions and close strategy decisions are tested explicitly.
- Reference checks: selected outputs are compared with established published analysis for the same complete model.
Stored blackjack profiles are not assembled by adding generic rule adjustments. Each value belongs to the complete configuration displayed beside it.
Rounding
Calculations use greater precision than may be displayed. Percentages and currency are rounded only for presentation. A displayed 0.43% may therefore represent a more precise stored value. Totals may differ by a cent when independently rounded components are added.
Source hierarchy
- Official game rules, regulator material and manufacturer pay tables tied to the exact product
- Reproducible combinatorial analysis or documented simulation
- Established specialist mathematical references used as an independent cross-check
- Clearly labeled illustrative assumptions when exact data are unavailable
A source supports only the model it actually analyzes. See the sources directory and the reference section on each substantive guide.
Limitations and corrections
Casino rules, pay tables and legal availability can change. Posted rules control whenever they differ from the site. Theoretical return does not guarantee an individual result. When a material error is found, we correct the page, update its review date and record the change in the public change log.