--- title: "Chance & Odds Index" url: https://gagamblinghelpline.org/ description: "A plain reference index of terms, probabilities and worked figures from the mathematics of games of chance: expected value, house edge, odds notation, variance and draw." --- # Chance & Odds Index House Advantage ## [House edge](https://gagamblinghelpline.org/terms/house-edge/) The house edge is the share of each amount staked that the rules of a game are expected to retain once every outcome has been weighted by its probability. It is fixed entirely by the difference between the prize a game pays and the prize a game with no edge would have to pay for the same result. On a wheel of thirty-seven pockets that pays 35 to 1 on a single number, that difference works out at exactly one part in thirty-seven, or 2.70 %. per unit staked The figure is derived in full, from the pocket count upward, on the [House edge](https://gagamblinghelpline.org/terms/house-edge/) entry. ## From the journal [01**How Casino House Edges Work and Player Strategies**Sep 14, 2026](https://gagamblinghelpline.org/how-casino-game-house-edges-work-common-mistakes-and-better-approaches/) [02**Why Is SweepstakesTable the Best for Low Wagering?**Aug 18, 2026](https://gagamblinghelpline.org/why-is-sweepstakestable-the-best-for-low-wagering/) [03**Best Sweepstakes Casinos for Daily Free Coins (2026)**Aug 16, 2026](https://gagamblinghelpline.org/best-sweepstakes-casinos-for-daily-free-coins-2026/) [04**Why Is Kanggiten the Best for Highly Tailored Launches?**Aug 15, 2026](https://gagamblinghelpline.org/why-is-kanggiten-the-best-for-highly-tailored-launches/) [05**Top 7 Sweepstakes Casinos for Promo Codes**Aug 15, 2026](https://gagamblinghelpline.org/top-7-sweepstakes-casinos-for-promo-codes/) [06**Top 3 Alternatives of SOFTSWISS for Game Aggregation Services**Aug 15, 2026](https://gagamblinghelpline.org/top-3-alternatives-of-softswiss-for-game-aggregation-services/) [07**SweepsPulse for High RTP Slots: Why It's the Best Choice**Aug 14, 2026](https://gagamblinghelpline.org/sweepspulse-for-high-rtp-slots-why-it-s-the-best-choice/) [08**Top 3 Alternatives of Soft2bet for White-Label Casino Platforms**Aug 11, 2026](https://gagamblinghelpline.org/top-3-alternatives-of-soft2bet-for-white-label-casino-platforms/) More [09**Top 5 Sweepstakes Casinos for Gold Coin Packages**Aug 06, 2026](https://gagamblinghelpline.org/top-5-sweepstakes-casinos-for-gold-coin-packages/) [10**SweepsPulse for Purchase Bonuses: Why It's the Best Choice**Aug 03, 2026](https://gagamblinghelpline.org/sweepspulse-for-purchase-bonuses-why-it-s-the-best-choice/) [11**Crypto Withdrawals: What to Look for in a Sweepstakes Casino**Aug 02, 2026](https://gagamblinghelpline.org/crypto-withdrawals-what-to-look-for-in-a-sweepstakes-casino/) [12**Top 3 iGaming Platforms for Deep Crypto Integration**Jul 28, 2026](https://gagamblinghelpline.org/top-3-igaming-platforms-for-deep-crypto-integration/) [13**The 10 Best Sweepstakes & Social Casinos for Daily Rewards**Jul 27, 2026](https://gagamblinghelpline.org/the-10-best-sweepstakes-social-casinos-for-daily-rewards/) [14**Playtech vs Kanggiten for Live Casino Studios**Jul 22, 2026](https://gagamblinghelpline.org/playtech-vs-kanggiten-for-live-casino-studios/) [15**Top 5 WhatsApp Business API Platforms for Small Businesses Who Need Enterprise Security**Jul 22, 2026](https://gagamblinghelpline.org/top-5-whatsapp-business-api-platforms-for-small-businesses-who-need-enterprise-security/) [16**10 WhatsApp Marketing Software Tools to Compare Before You Buy**Jun 24, 2026](https://gagamblinghelpline.org/10-whatsapp-marketing-software-tools-to-compare-before-you-buy/) ## Topic chapters - Probability (10) - Lotteries and Draws (4) - Odds and Prices (8) - House Advantage (10) - Variance and Streaks (11) - Games and Rules (7) ## Long-form chapters - [Probability and expected value](https://gagamblinghelpline.org/topics/probability-and-expected-value/) - [How the house edge is calculated](https://gagamblinghelpline.org/topics/how-house-edge-is-calculated/) - [Odds notation and implied probability](https://gagamblinghelpline.org/topics/odds-notation-and-implied-probability/) - [Variance, spread and why streaks are ordinary](https://gagamblinghelpline.org/topics/variance-and-streaks/) - [Independence and the gambler's fallacy](https://gagamblinghelpline.org/topics/independence-and-the-gamblers-fallacy/) - [Return to player and lottery prize funds](https://gagamblinghelpline.org/topics/return-to-player-and-lottery-prize-funds/) - [How games of chance are designed](https://gagamblinghelpline.org/topics/how-games-of-chance-are-designed/) - [A history of lotteries and betting](https://gagamblinghelpline.org/topics/history-of-lotteries-and-betting/) - [The development of gambling regulation](https://gagamblinghelpline.org/topics/development-of-gambling-regulation/) ## Letters carrying entries [A](https://gagamblinghelpline.org/terms/#A) [B](https://gagamblinghelpline.org/terms/#B) [C](https://gagamblinghelpline.org/terms/#C) [D](https://gagamblinghelpline.org/terms/#D) [E](https://gagamblinghelpline.org/terms/#E) [F](https://gagamblinghelpline.org/terms/#F) [G](https://gagamblinghelpline.org/terms/#G) [H](https://gagamblinghelpline.org/terms/#H) [I](https://gagamblinghelpline.org/terms/#I) [J](https://gagamblinghelpline.org/terms/#J) [K](https://gagamblinghelpline.org/terms/#K) [L](https://gagamblinghelpline.org/terms/#L) [M](https://gagamblinghelpline.org/terms/#M) [N](https://gagamblinghelpline.org/terms/#N) [O](https://gagamblinghelpline.org/terms/#O) [P](https://gagamblinghelpline.org/terms/#P) [Q](https://gagamblinghelpline.org/terms/#Q) [R](https://gagamblinghelpline.org/terms/#R) [S](https://gagamblinghelpline.org/terms/#S) [T](https://gagamblinghelpline.org/terms/#T) [U](https://gagamblinghelpline.org/terms/#U) [V](https://gagamblinghelpline.org/terms/#V) [W](https://gagamblinghelpline.org/terms/#W) [Z](https://gagamblinghelpline.org/terms/#Z) Twenty-four of twenty-six letters hold at least one entry. X and Y hold none. ## Figures at a glance - Single number, 37 pockets, paid 35 to 1 **2.70 %** per unit staked - Single number, 38 pockets, paid 35 to 1 **5.26 %** per unit staked - Dice sequence, pass on 7 or 11 **1.41 %** per unit staked - Two-way market priced 1.91 each side **4.50 %** per unit staked Each figure is derived on the chapter that states it. ## Editorial policy Figures are derived on the page that states them, and each is printed with the base it is measured against. [Read the method](https://gagamblinghelpline.org/method/) ## Topic chapters ## Probability What a probability is, how outcomes are counted, and how a bet's average result is worked out. [Cumulative probability](https://gagamblinghelpline.org/terms/#C) The probability that a result falls at or below a stated value, found by adding the probabilities of every outcome up to it. PROBABILITY [Dependent events](https://gagamblinghelpline.org/terms/#D) Events where the outcome of one changes the probability of another, as when cards are dealt without replacement. PROBABILITY [Expected value](https://gagamblinghelpline.org/terms/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 staked PROBABILITY [Fair game](https://gagamblinghelpline.org/terms/#F) A game whose expected value is zero, meaning the prize paid matches exactly the true odds against the result. PROBABILITY [Gambler's fallacy](https://gagamblinghelpline.org/terms/#G) The belief that a run of one outcome makes the opposite outcome more likely on the next independent trial. PROBABILITY [Independent events](https://gagamblinghelpline.org/terms/#I) Events whose probabilities are unaffected by one another, so past results carry no information about the next trial. PROBABILITY [Law of large numbers](https://gagamblinghelpline.org/terms/#L) The result that the observed proportion of an outcome approaches its probability as trials rise, while the absolute gap need not shrink. PROBABILITY [Probability](https://gagamblinghelpline.org/terms/#P) The proportion of equally likely outcomes producing a stated result, written as a number between zero and one. PROBABILITY [Sample space](https://gagamblinghelpline.org/terms/#S) The complete set of outcomes a trial can produce; one die has six, two dice have thirty-six. PROBABILITY [Trial](https://gagamblinghelpline.org/terms/#T) One repetition of a game or bet, the unit in which counts, probabilities and expected values are stated. PROBABILITY ## Lotteries and Draws Counting selections, dividing pools, and how a draw game's return is fixed before any tier is set. [Combination](https://gagamblinghelpline.org/terms/#C) A selection in which order does not matter; the count of six-from-forty-nine selections is 13,983,816. LOTTERIES AND DRAWS [Pari-mutuel](https://gagamblinghelpline.org/terms/#P) A pool system combining all stakes, deducting a fixed share, and dividing the remainder among winning tickets. per unit staked LOTTERIES AND DRAWS [Permutation](https://gagamblinghelpline.org/terms/#P) An arrangement in which order matters, counted before dividing out the orderings to reach a combination. LOTTERIES AND DRAWS [Quinella](https://gagamblinghelpline.org/terms/#Q) A pool bet requiring the first two finishers in either order, settled from the pari-mutuel pool for that bet type. LOTTERIES AND DRAWS ## Odds and Prices How prices are written in the three common notations, and what a price implies about probability. [Bookmaker's margin](https://gagamblinghelpline.org/terms/#B) The amount by which the prices offered on every outcome of a market sum to more than one whole probability. per unit staked ODDS AND PRICES [Decimal odds](https://gagamblinghelpline.org/terms/#D) A price stated as the total return per one unit staked, so that its reciprocal is the implied probability. per unit staked ODDS AND PRICES [Even-money bet](https://gagamblinghelpline.org/terms/#E) A bet returning one unit of profit per unit staked, quoted as 1/1, 2.00 or +100. ODDS AND PRICES [Fractional odds](https://gagamblinghelpline.org/terms/#F) A price stated as profit against stake, so 5/1 returns five units of profit for one unit risked. ODDS AND PRICES [Implied probability](https://gagamblinghelpline.org/terms/#I) The probability a quoted price corresponds to, found by taking the reciprocal of the decimal price. ODDS AND PRICES [Margin](https://gagamblinghelpline.org/terms/#M) The share of the total staked on a market that its prices are expected to retain once every outcome is covered. per unit staked ODDS AND PRICES [Odds](https://gagamblinghelpline.org/terms/#O) 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](https://gagamblinghelpline.org/terms/#O) The amount by which the implied probabilities of all outcomes in a market exceed one hundred per cent. per market ODDS AND PRICES ## House Advantage The structural difference between the prize a game pays and the prize a fair game would pay. [Advantage](https://gagamblinghelpline.org/terms/#A) 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 staked HOUSE ADVANTAGE [Hold](https://gagamblinghelpline.org/terms/#H) The proportion of the amount staked that a game or table retains once play has finished. per unit staked HOUSE ADVANTAGE [House edge](https://gagamblinghelpline.org/terms/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 staked HOUSE ADVANTAGE [Negative expectation](https://gagamblinghelpline.org/terms/#N) A bet whose probability-weighted average outcome is a loss, which is the condition of every commercially offered game of chance. HOUSE ADVANTAGE [Return to player](https://gagamblinghelpline.org/terms/#R) The proportion of total amounts staked a game returns as prizes over the long run; its complement is the house edge. per unit staked HOUSE ADVANTAGE [True odds](https://gagamblinghelpline.org/terms/#T) The odds corresponding exactly to a result's probability, against which the odds actually paid are compared. HOUSE ADVANTAGE [Turnover](https://gagamblinghelpline.org/terms/#T) The total amount staked over a period, which is the base a per-unit-staked figure is multiplied by. per unit staked HOUSE ADVANTAGE [Unit](https://gagamblinghelpline.org/terms/#U) The stake size a figure is expressed in; percentages here are stated per unit staked unless another base is named. HOUSE ADVANTAGE [Wager](https://gagamblinghelpline.org/terms/#W) An amount staked on a stated outcome under stated terms. HOUSE ADVANTAGE [Zero](https://gagamblinghelpline.org/terms/#Z) The pocket or pockets on a wheel belonging to neither even-money group, and the entire source of the wheel's edge. HOUSE ADVANTAGE ## Variance and Streaks How far results scatter around their average, and how that scatter behaves as trials accumulate. [Bankroll](https://gagamblinghelpline.org/terms/#B) The total amount set aside for play, against which the spread of results over many trials is measured. VARIANCE AND STREAKS [Binomial distribution](https://gagamblinghelpline.org/terms/#B) The distribution of the count of successes in a fixed number of independent trials that each succeed with the same probability. VARIANCE AND STREAKS [Gambler's ruin](https://gagamblinghelpline.org/terms/#G) The result that a player with finite funds facing a negative expectation and unlimited trials is eventually certain to reach zero. VARIANCE AND STREAKS [Kelly criterion](https://gagamblinghelpline.org/terms/#K) 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 [Long run](https://gagamblinghelpline.org/terms/#L) The count of trials at which expected loss grows large relative to the spread of results around it. VARIANCE AND STREAKS [Martingale](https://gagamblinghelpline.org/terms/#M) A staking pattern doubling the stake after each loss; it changes the distribution of results and leaves the expected value unchanged. VARIANCE AND STREAKS [Regression to the mean](https://gagamblinghelpline.org/terms/#R) The tendency for an extreme run of results to be followed by results nearer the average, with no correcting force involved. VARIANCE AND STREAKS [Standard deviation](https://gagamblinghelpline.org/terms/#S) The typical distance of a result from the average, growing with the square root of the count of trials. VARIANCE AND STREAKS [Streak](https://gagamblinghelpline.org/terms/#S) A run of identical consecutive results, whose probability falls geometrically with length but which is ordinary across many trials. VARIANCE AND STREAKS [Variance](https://gagamblinghelpline.org/terms/variance/) The average squared distance of results from their mean; its square root is the standard deviation. VARIANCE AND STREAKS [Volatility](https://gagamblinghelpline.org/terms/#V) How widely a game's results spread around its return, set separately from the return itself. VARIANCE AND STREAKS ## Games and Rules The specifications, mappings and rules that decide what a game returns and how often it returns it. [Ante](https://gagamblinghelpline.org/terms/#A) A fixed amount every player puts up before a hand is dealt, forming the pot the hand is played for. GAMES AND RULES [Come-out roll](https://gagamblinghelpline.org/terms/#C) 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 [Hit frequency](https://gagamblinghelpline.org/terms/#H) The proportion of trials returning anything at all, set independently of how much is returned in total. per spin GAMES AND RULES [Jackpot](https://gagamblinghelpline.org/terms/#J) A prize accumulating from a fixed share of each amount staked until a stated result occurs. per unit staked GAMES AND RULES [Par sheet](https://gagamblinghelpline.org/terms/#P) The internal specification of a game listing every symbol weight, every prize, and the return the two together produce. GAMES AND RULES [Random number generator](https://gagamblinghelpline.org/terms/#R) The mechanism selecting a game's outcome; a certified one produces results passing tests for uniformity and independence. GAMES AND RULES [Virtual reel](https://gagamblinghelpline.org/terms/#V) A mapping assigning unequal numbers of internal positions to the visible symbols of a reel, setting their true probabilities. GAMES AND RULES ## Recently added entries The eight entries written most recently, in the order they were written. This index keeps no publication calendar. [Overround](https://gagamblinghelpline.org/terms/#O) The amount by which the implied probabilities of all outcomes in a market exceed one hundred per cent. per market ODDS AND PRICES [Pari-mutuel](https://gagamblinghelpline.org/terms/#P) A pool system combining all stakes, deducting a fixed share, and dividing the remainder among winning tickets. per unit staked LOTTERIES AND DRAWS [Par sheet](https://gagamblinghelpline.org/terms/#P) The internal specification of a game listing every symbol weight, every prize, and the return the two together produce. GAMES AND RULES [Regression to the mean](https://gagamblinghelpline.org/terms/#R) 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](https://gagamblinghelpline.org/terms/#R) The proportion of total amounts staked a game returns as prizes over the long run; its complement is the house edge. per unit staked HOUSE ADVANTAGE [Virtual reel](https://gagamblinghelpline.org/terms/#V) A mapping assigning unequal numbers of internal positions to the visible symbols of a reel, setting their true probabilities. GAMES AND RULES [Volatility](https://gagamblinghelpline.org/terms/#V) How widely a game's results spread around its return, set separately from the return itself. VARIANCE AND STREAKS [Wager](https://gagamblinghelpline.org/terms/#W) An amount staked on a stated outcome under stated terms. HOUSE ADVANTAGE ## Editorial note Two conventions govern everything printed here. The first is that a percentage is meaningless without the quantity it is a percentage of, so every figure on this site is printed with the base it is measured against: per unit staked, per spin, per draw, per market. A 4 % figure per unit staked and a 4 % figure per hour of play are not the same number and cannot be compared. The second is that every figure is derived on the page that states it, from assumptions written out in full, rather than asserted or attributed to an outside authority. Applying those conventions to commercial games produces one plain arithmetic result, which is stated here once rather than repeated on every page. Every game offered commercially pays less on a winning result than a game with no edge would have to pay. That gap is not an incidental feature of any particular game; it is the mechanism by which the game produces revenue, and it is fixed in the rules before any play occurs. Because the gap is fixed and each trial is independent of the last, the expected result of continued play is a loss proportional to the total amount staked, and the proportion of trials that finish in loss approaches certainty as the count of trials rises. No sequence of stakes, no pattern of timing and no run of prior results alters that arithmetic, and nothing on this site should be read as suggesting otherwise. This index describes how these figures are calculated and where the rules that fix them came from. It does not describe how to play any game, and it recommends nothing.