Action
The total amount wagered, including money won and wagered again.
Open related lesson →58 defined terms
Casino math glossary.
Plain-language definitions connected to the deeper lessons and calculations that use them.
58 terms
Bankroll
Money deliberately set aside for play; it is an exposure limit, not an advantage.
Open related lesson →Base game
The required wager and settlement structure before optional side bets or progressives are added.
Break-even probability
The win probability required for an offered payout to have zero expected value.
Open related lesson →Buy bet
A craps number wager paid at true odds subject to a commission.
Card removal
Updating probabilities because known cards are no longer available among unseen combinations.
Open related lesson →Coin-in
Total money wagered through an electronic game, not the cash originally inserted.
Commission
A fee charged on a wager, win, or transaction; its basis and timing affect effective value.
Conditional expected value
Expected value recalculated for the information known at a specific decision point.
Open related lesson →Conditional probability
The probability of an event after restricting the sample space to states compatible with known information.
Open related lesson →Confidence interval
A range generated by a stated statistical procedure to communicate sampling uncertainty.
Open related lesson →Configuration
The exact approved rules, pay table, denomination, features, and settings used by a game.
Correlation
The extent to which two results tend to move together rather than independently.
Open related lesson →Covariance
A signed measure of how two outcomes vary together; it affects combined variance.
Open related lesson →Decision rate
The number of resolved wagers or meaningful game decisions per unit of time.
Denominator
The amount used as the base of a percentage, such as initial wager or average total action.
Dealer qualification
A minimum dealer hand required for specified comparisons or wagers to settle normally.
Element of risk
Expected casino win divided by average total money wagered, often used when later wagers vary.
Enumeration
Counting every compatible outcome exactly rather than estimating by random simulation.
Expected loss
Total action multiplied by the applicable house edge under the same model and denominator.
Open related lesson →Expected value (EV)
The probability-weighted average net result of all mutually exclusive outcomes.
Open related lesson →Fair odds
The payout that makes a wager break even before commissions or other costs.
Open related lesson →Feature contribution
The portion of a game’s theoretical return produced by a specified bonus or feature.
For-one payout
A return convention that may include the original stake; five-for-one commonly means four units of net profit.
Gambler’s fallacy
The false belief that independent outcomes must quickly balance after a streak.
Open related lesson →Hit frequency
The share of trials producing an award under a stated definition, including awards smaller than the wager when rules count them.
Hold
An observed accounting ratio based on money retained relative to buy-ins or handle; it is not synonymous with house edge.
House edge
The casino’s expected win expressed as a percentage of a clearly stated wager denominator.
Open related lesson →Implied probability
The break-even probability encoded by an offered payout before adjustments for pushes or multiple prizes.
Open related lesson →Independent events
Events for which observing one does not change the probability distribution of the other.
Open related lesson →Initial wager
The amount committed before later decisions add, remove, or multiply exposure.
Jackpot baseline
The reset or reference value already included in a base return before meter growth is added.
Open related lesson →Maximum aggregate payout
A cap on the total amount payable from one hand, round, or linked set of wagers.
Monte Carlo simulation
Randomly sampling a defined model many times to estimate an outcome distribution.
Open related lesson →Mutually exclusive outcomes
Outcome categories constructed so no single trial can belong to more than one category.
Natural
A qualifying initial-card result with special settlement, such as a two-card blackjack.
Net payout
Profit excluding return of the original stake; a 3:1 net payout wins three units plus the stake back.
Optimal strategy
The legal decision policy with the highest expected value under the exact stated rules.
Outcome distribution
Every possible net result paired with its probability.
Pay table
The complete schedule mapping qualifying outcomes to awards, including footnotes and caps.
Open related lesson →Place bet
A removable craps wager that a selected number appears before seven, paid at posted odds.
Progressive
A prize meter that changes as eligible wagers are made or jackpots are awarded.
Open related lesson →Push
A settlement returning the applicable stake with neither net win nor loss.
Qualification
A condition that must be met before a hand, feature, payout, or wager is eligible.
Random number generator (RNG)
The system producing values mapped to outcomes in an electronic game’s approved implementation.
Return to player (RTP)
Expected prizes divided by total qualifying wagers under a specific model and configuration.
Open related lesson →Risk of ruin
The probability of reaching a defined bankroll boundary under a stated game, staking rule, and horizon.
Open related lesson →Sample size
The number of observations or simulated trials used to estimate a quantity.
Open related lesson →Side bet
An optional wager with its own event definition and pay table, even when it uses the base game’s cards.
Standard deviation
The square root of variance, expressing result spread in the original units.
Open related lesson →Stopping rule
A predeclared condition ending future action; it controls exposure but does not improve prior wagers.
Open related lesson →Theoretical loss
Another name for expected loss under a specified amount of action and house edge.
To-one payout
A net-profit convention: five-to-one normally means five profit units plus return of stake.
True odds
The fair net payout implied by the underlying win and loss probabilities.
Variance
The probability-weighted squared spread of outcomes around expected value.
Open related lesson →Vigorish (vig)
A commission or pricing charge; in craps its collection basis and timing can materially change the effective edge.
Volatility
A practical description of how concentrated or dispersed a game’s result distribution is.
Wagering requirement
Qualifying action required before a bonus or related winnings become withdrawable.
Open related lesson →