glossary

bankrollentry

The sum set aside for play. Distinct from handle: a bankroll can be staked many times over, and the house edge applies to the staking, not to the sum.

combinationentry

A selection in which order does not matter. Written C(n,k); the basis of every draw-lottery probability.

decimal oddsentry

A price expressed as the total return per unit staked, stake included. Implied probability is its reciprocal.

dependenceentry

The condition in which one trial changes the probabilities of the next, as when a card is removed from a shoe.

expected valueentry

The probability-weighted average result of a wager, per unit staked. Negative for every commercial game.

fractional oddsentry

A price expressed as profit against stake, such as 5/2. Carries the same information as decimal and moneyline.

free oddsentry

A supplementary craps wager paid at the true odds of the point, and therefore the rare wager with an expected value of exactly zero.

handleentry

The total amount staked over a period, as distinct from the money brought to the game. The denominator of house edge.

hit frequencyentry

How often a machine returns anything at all, independent of how much. A component of volatility rather than of return.

holdentry

An accounting figure: the share of money brought to a game that was not carried away. Larger than house edge because money is restaked.

house edgeentry

Expected loss per unit staked, expressed as a percentage. A property of the payout table, fixed before play.

implied probabilityentry

The probability a quoted price corresponds to. Across a market these sum to more than one.

independenceentry

The condition in which one trial tells you nothing about the next. True of wheels, dice and draws; false of card shoes.

law of large numbersentry

The theorem that the average of independent trials converges to their expectation as the number of trials grows.

moneyline oddsentry

A price expressed relative to a hundred units, positive for outsiders and negative for favourites.

overroundentry

The amount by which implied probabilities across a market exceed one. The market equivalent of a house edge.

pari-mutuelentry

A structure in which prizes are shares of a pool after a fixed deduction, rather than fixed amounts.

probabilityentry

The share of equally likely outcomes in which an event occurs, between zero and one.

random number generatorentry

The process that determines a machine outcome at the moment of the request; the animation that follows is presentation.

return to playerentry

The complement of house edge: the long-run share of stake returned. Meaningful only over very large numbers of rounds.

rolloverentry

A jackpot carried into the next draw, raising that draw's expected value without changing anyone's probability of winning.

ruinentry

The absorbing state of an exhausted bankroll, after which favourable variance cannot help.

sample spaceentry

The complete enumerated set of equally likely outcomes. Every figure on this site begins with one.

standard deviationentry

The square root of variance, in the same units as the result. Grows with the square root of the number of rounds.

varianceentry

The expected squared deviation from the mean; the measure of how widely results scatter around expectation.

virtual reelentry

An internal list of positions mapped onto physical reel stops, decoupling a symbol's appearance from its probability.

volatilityentry

How a machine's return is distributed between frequent small wins and rare large ones. Independent of RTP.