A to Z of terms
Fifty entries, grouped by first letter. Twenty-four of the twenty-six letters carry at least one entry. Each entry gives a one-line plain-language gloss and its topic chapter; entries carrying a figure also name the base that figure is measured against.
A
Ante
A fixed amount every player puts up before a hand is dealt, forming the pot the hand is played for.GAMES AND RULES
Advantage
The share of each amount staked that one side of a game expects to keep once every outcome is weighted by its probability. per unit stakedHOUSE ADVANTAGE
B
Bankroll
The total amount set aside for play, against which the spread of results over many trials is measured.VARIANCE AND STREAKS
Binomial distribution
The distribution of the count of successes in a fixed number of independent trials that each succeed with the same probability.VARIANCE AND STREAKS
Bookmaker's margin
The amount by which the prices offered on every outcome of a market sum to more than one whole probability. per unit stakedODDS AND PRICES
C
Combination
A selection in which order does not matter; the count of six-from-forty-nine selections is 13,983,816.LOTTERIES AND DRAWS
Come-out roll
The first roll of a dice sequence, which either settles the bet at once or fixes the number the sequence must then repeat.GAMES AND RULES
Cumulative probability
The probability that a result falls at or below a stated value, found by adding the probabilities of every outcome up to it.PROBABILITY
D
Decimal odds
A price stated as the total return per one unit staked, so that its reciprocal is the implied probability. per unit stakedODDS AND PRICES
Dependent events
Events where the outcome of one changes the probability of another, as when cards are dealt without replacement.PROBABILITY
E
Even-money bet
A bet returning one unit of profit per unit staked, quoted as 1/1, 2.00 or +100.ODDS AND PRICES
Expected value
The probability-weighted average of every outcome of a bet; on a 37-pocket wheel it is minus one part in thirty-seven. per unit stakedPROBABILITY
F
Fair game
A game whose expected value is zero, meaning the prize paid matches exactly the true odds against the result.PROBABILITY
Fractional odds
A price stated as profit against stake, so 5/1 returns five units of profit for one unit risked.ODDS AND PRICES
G
Gambler's fallacy
The belief that a run of one outcome makes the opposite outcome more likely on the next independent trial.PROBABILITY
Gambler's ruin
The result that a player with finite funds facing a negative expectation and unlimited trials is eventually certain to reach zero.VARIANCE AND STREAKS
H
Hit frequency
The proportion of trials returning anything at all, set independently of how much is returned in total. per spinGAMES AND RULES
Hold
The proportion of the amount staked that a game or table retains once play has finished. per unit stakedHOUSE ADVANTAGE
House edge
The expected loss per unit staked, fixed by the gap between the prize a game pays and the prize a fair game would pay. per unit stakedHOUSE ADVANTAGE
I
Implied probability
The probability a quoted price corresponds to, found by taking the reciprocal of the decimal price.ODDS AND PRICES
Independent events
Events whose probabilities are unaffected by one another, so past results carry no information about the next trial.PROBABILITY
J
Jackpot
A prize accumulating from a fixed share of each amount staked until a stated result occurs. per unit stakedGAMES AND RULES
K
Kelly criterion
A staking formula maximising the long-run growth rate of funds; it returns a stake of zero whenever the expected value is negative.VARIANCE AND STREAKS
L
Law of large numbers
The result that the observed proportion of an outcome approaches its probability as trials rise, while the absolute gap need not shrink.PROBABILITY
Long run
The count of trials at which expected loss grows large relative to the spread of results around it.VARIANCE AND STREAKS
M
Margin
The share of the total staked on a market that its prices are expected to retain once every outcome is covered. per unit stakedODDS AND PRICES
Martingale
A staking pattern doubling the stake after each loss; it changes the distribution of results and leaves the expected value unchanged.VARIANCE AND STREAKS
N
Negative expectation
A bet whose probability-weighted average outcome is a loss, which is the condition of every commercially offered game of chance.HOUSE ADVANTAGE
O
Odds
A statement of the ratio between the ways a result can fail and the ways it can occur, or of the price paid for it.ODDS AND PRICES
Overround
The amount by which the implied probabilities of all outcomes in a market exceed one hundred per cent. per marketODDS AND PRICES
P
Pari-mutuel
A pool system combining all stakes, deducting a fixed share, and dividing the remainder among winning tickets. per unit stakedLOTTERIES AND DRAWS
Par sheet
The internal specification of a game listing every symbol weight, every prize, and the return the two together produce.GAMES AND RULES
Permutation
An arrangement in which order matters, counted before dividing out the orderings to reach a combination.LOTTERIES AND DRAWS
Probability
The proportion of equally likely outcomes producing a stated result, written as a number between zero and one.PROBABILITY
Q
Quinella
A pool bet requiring the first two finishers in either order, settled from the pari-mutuel pool for that bet type.LOTTERIES AND DRAWS
R
Random number generator
The mechanism selecting a game's outcome; a certified one produces results passing tests for uniformity and independence.GAMES AND RULES
Regression to the mean
The tendency for an extreme run of results to be followed by results nearer the average, with no correcting force involved.VARIANCE AND STREAKS
Return to player
The proportion of total amounts staked a game returns as prizes over the long run; its complement is the house edge. per unit stakedHOUSE ADVANTAGE
S
Sample space
The complete set of outcomes a trial can produce; one die has six, two dice have thirty-six.PROBABILITY
Standard deviation
The typical distance of a result from the average, growing with the square root of the count of trials.VARIANCE AND STREAKS
Streak
A run of identical consecutive results, whose probability falls geometrically with length but which is ordinary across many trials.VARIANCE AND STREAKS
T
Trial
One repetition of a game or bet, the unit in which counts, probabilities and expected values are stated.PROBABILITY
True odds
The odds corresponding exactly to a result's probability, against which the odds actually paid are compared.HOUSE ADVANTAGE
Turnover
The total amount staked over a period, which is the base a per-unit-staked figure is multiplied by. per unit stakedHOUSE ADVANTAGE
U
Unit
The stake size a figure is expressed in; percentages here are stated per unit staked unless another base is named.HOUSE ADVANTAGE
V
Variance
The average squared distance of results from their mean; its square root is the standard deviation.VARIANCE AND STREAKS
Virtual reel
A mapping assigning unequal numbers of internal positions to the visible symbols of a reel, setting their true probabilities.GAMES AND RULES
Volatility
How widely a game's results spread around its return, set separately from the return itself.VARIANCE AND STREAKS
W
Wager
An amount staked on a stated outcome under stated terms.HOUSE ADVANTAGE
X
No entry in this index begins with X.
Y
No entry in this index begins with Y.
Z
Zero
The pocket or pockets on a wheel belonging to neither even-money group, and the entire source of the wheel's edge.HOUSE ADVANTAGE