Glossary of terms

Three names for one quantity

House edge, return to player and overround describe the same underlying fact from three trades. The table converts between them.

Terms

Astragalus

The ankle bone of a sheep or goat, thrown as a four-faced randomiser in the ancient world; the direct ancestor of the die.

Bankroll

The total amount a player has available across a period of play, as distinct from the amount staked on any one bet.

Combination

A selection where order does not matter. Written C(n,k) and central to lottery and card counting.

Decimal odds

A price written as the total returned per unit staked, stake included. The implied probability is one divided by it.

Dependent trials

Plays where the result of one changes the distribution of the next, as when cards are dealt without replacement.

Edge

The share of each unit staked that a game retains on average over the long run. See the house edge guide.

Expected value

The probability-weighted average result of a bet, found by multiplying each outcome by its chance and adding.

Fractional odds

A price written as a to b: win a for every b staked. The implied probability is b divided by (a+b).

Gambler's fallacy

The belief that an outcome is due after a run of the opposite; it treats independent trials as if they had memory.

Hit frequency

How often a game returns anything at all, which may be less than the amount staked.

Hold

The share of money brought to a game that an operator actually retained over a period; larger than the edge because stakes are recycled.

Implied probability

The probability a quoted price corresponds to once converted, before any margin is removed.

Independent trials

Plays whose distributions do not depend on what came before, as with dice, wheels and number generators.

Law of large numbers

The result that observed proportions converge on their probabilities as the number of trials grows.

Margin

The operator's theoretical share of a market, expressed as the overround relative to the summed book.

Overround

The amount by which the implied probabilities of every outcome in a market exceed one hundred per cent.

Paytable

The list of outcomes and their payouts that defines a game's arithmetic entirely.

Pseudorandom number generator

A deterministic algorithm producing a sequence that passes statistical tests for randomness.

Return to player

One hundred per cent minus the house edge, stated as a long-run average over very many plays.

Rollover

A jackpot pool carried into the next draw because no ticket matched; it raises the pool without changing the odds of matching.

Sample space

The complete set of possible outcomes of a play, such as the thirty-six ordered results of two dice.

True odds

The payout that would make a bet break even in the long run: n-1 to 1 for an event occurring once in n cases.

Variance

How widely results scatter around expectation; it grows with the square root of the number of plays while expected loss grows in proportion.

Virtual reel

An internal list of stop positions, which may weight symbols differently from how they appear on the visible strip.