Odds and Maths Terms: RTP, House Edge, Variance Defined
Clear definitions of 22 odds and maths terms, from RTP and house edge to expected value and the gambler's fallacy, with worked numbers from real games.
On this page
These are the terms behind every number on the Odds page. A few of them describe the same thing from different sides: RTP and house edge always add up to 100 percent, and volatility and hit frequency explain why two games with the same RTP can feel nothing alike.
Entries link to a longer page where a definition is not enough on its own, usually because it needs a worked example. The figures used are read from the game engines in the Cashout Arcade repository and match the published odds. Coins are virtual and have no cash value, so none of this describes money you could win.
How the main terms fit together
Take a 100-coin bet at a 50 percent chance in Dice. The fair multiplier is 2x, but the game pays 1.94x. Expected value is 0.5 times 194, or 97 coins back. That is a 97 percent RTP and a 3 percent house edge. The volatility is the spread around that average, and the hit frequency is simply the 50 percent of rounds that pay.
For the longer explanations, see What Is RTP? Return to Player Explained With Examples, House Edge Explained: How Casinos Make Their Money and Volatility in Casino Games: Why Results Swing. Words for casino games themselves are in Casino Game Terms: Slots, Tables and Arcade Games Defined.
Terms
RTP
Return to player. The percentage of all coins wagered on a game that it pays back over a very long run of rounds. A 97 percent RTP returns 97 coins per 100 wagered on average and keeps 3. Read the full RTP entry
House edge
The share of every wager the game keeps on average, equal to 100 percent minus the RTP. Most Cashout Arcade games have a 3 percent house edge. It is an average over many rounds, not a charge taken each round. Read the full House edge entry
Volatility
How widely a game's results swing around its average. High volatility means rare, large wins and long dry spells. Low volatility means frequent small wins. Two games can share one RTP and feel completely different. Read the full Volatility entry
Variance
The statistical measure behind volatility, calculated as the average squared distance of results from the mean. Its square root is the standard deviation, which is in the same units as the payout and easier to read.
Hit frequency
How often a round returns anything at all, or more than the stake, depending on how the game defines a hit. It is not the same as RTP. A game can hit often and still pay little, or hit rarely and pay a lot. Read the full Hit frequency entry
Expected value
The average result per round if you could play it endlessly, found by multiplying each outcome by its chance and adding them up. For a 100-coin bet in a 97 percent RTP game, expected value is 97 coins returned, or minus 3 coins. Read the full Expected value entry
Probability
The chance of an event, written as a number from 0 to 1 or as a percentage. A fair coin landing heads has a probability of 0.5, or 50 percent. Probabilities of all possible outcomes of one event add up to 1.
Odds (as a ratio)
A way of stating chance as a ratio, such as 1 in 37 or 36 to 1. Odds of 1 in 37 correspond to a probability of about 2.7 percent. Betting odds and probability are related but not the same thing, so check which one a source means.
Payout ratio
What a winning round returns for each coin staked. In Cashout Arcade a payout multiplier includes your stake, so 1.94x on a 100-coin bet returns 194 coins, a net gain of 94. The average payout ratio across all rounds is the RTP.
RNG
Random number generator. Software that produces the unpredictable numbers a game uses to decide results. Digital games use pseudo-random generators, which are statistically random but follow a calculation. Cashout Arcade draws each result on its server. Read the full RNG entry
Seed (random number)
The starting value fed into a pseudo-random generator. The same seed always produces the same sequence, which is how tests replay results. Seeds are also used by provably fair systems, where they are committed to before play.
Provably fair
A system, common in crypto casinos, in which the operator publishes a hash of a secret seed before play and reveals the seed afterwards, so a player can check the result was not changed. It proves consistency, not a fair edge. Read the full Provably fair entry
Server-authoritative
A design in which the server, not the player's device, decides every result, and the app only displays it. This is how Cashout Arcade works. The animation on screen cannot change the outcome, but you rely on the published odds rather than a verifiable hash.
Basic strategy
The play that gives a skill-based game its best possible return, worked out by calculating every decision. In Cashout Arcade's Blackjack, basic strategy returns 97 percent, while never doubling returns 95.6 percent. Read the full Basic strategy entry
Bankroll
The total amount set aside for play. Bankroll management means deciding in advance how much you are willing to lose, since the house edge makes the expected result negative. It limits losses; it does not create an advantage. Read the full Bankroll entry
Max win cap
A ceiling on what one round can pay. In Cashout Arcade no round pays more than 50,000 times the bet, or more than 250,000,000 coins. Games with a smaller top prize reach well below that, and the cap is a limit, not a prize.
Independent events
Events where one outcome has no effect on the next. Roulette spins, dice rolls and coin flips are independent, so past results say nothing about the following one. Ignoring this leads to the gambler's fallacy. Read the full Independent events entry
Gambler's fallacy
The mistaken belief that a result is due because it has not happened recently, such as expecting heads after five tails. For independent events the chance on the next try is unchanged. Read the full Gambler's fallacy entry
Law of large numbers
The rule that the average of many independent trials drifts toward the true expected value as the number of trials grows. It explains why a 97 percent RTP shows up over thousands of rounds but not in a single session. Read the full Law of large numbers entry
Martingale
A betting system that doubles the stake after every loss, hoping one win recovers everything. It cannot change the house edge. It raises the amount at risk quickly and ends in one large loss when a long losing run arrives. Read the full Martingale entry
Sample size
The number of rounds a result is based on. Small samples are noisy: a player can be far above or below the RTP after 50 rounds. Claims about a game being generous or tight need thousands of rounds before they mean anything.
Fair multiplier
The payout that would make a bet break even, equal to 1 divided by the probability of winning. A 25 percent chance has a fair multiplier of 4x. Cashout Arcade pays 0.97 divided by the probability instead, which is the house edge.