Probability Basics Glossary Probability & Statistics Terms

Two events are called independent when the result of one has no effect at all on the probability of the other. Every spin of a slot is independent, so no matter how many times you lost just before, the win probability of the next spin is the same. Forget this and you fall into the gambler’s fallacy.

The probability that independent events all happen together is found by multiplying their individual probabilities. For example, if the chance of a 7 on one reel is 1/25, the chance of a 7 on all 3 reels is 1/25 × 1/25 × 1/25 = 1/15,625.

The probability that an event does not happen is found by subtracting the event’s probability from 1. It is easiest to calculate “the chance of the bonus triggering at least once in 300 spins” as 1 minus the chance of it never triggering (bonus frequency).

A list of all possible outcomes and the probability of each is called a probability distribution. A slot’s probability distribution looks something like “0x at 70%, 0.5x at 10%, 2x at 8% … 10,000x at 0.0001%,” and RTP and standard deviation are calculated from it.

The amount you lose on average over the long run. You find it by multiplying total bets by the house edge. If you bet a total of 1 million on a game with 96% RTP, the expected loss is 40,000. Actual results can be much larger or smaller than this depending on luck.

The RTP a provider publishes is a mathematically designed theoretical value, while the return you actually get from playing is the actual (observed) value. With few spins the two can differ greatly, and they only get close after a very large number of spins (law of large numbers).

When measuring results, the number of observations is called the sample size. Even if you see a record in a community saying “this game’s real RTP is 120%,” if it covers only a few thousand spins, the sample is too small and it is likely just chance.

A range drawn around a measured value, such as “there is a 95% chance the true value lies within this range.” In slots, it is used to estimate the range the actual return will fall into over a certain number of spins (volatility index).

An extreme value far from the other outcomes. A win of several thousand times your bet in a slot is a typical outlier. In high-volatility slots, outliers make up a significant part of the RTP, so it is hard to feel the average in short sessions.

A math design document that lays out a slot machine’s reel strip composition, the probability of each combination, payouts, RTP, and hit rate. PAR is known to stand for “Probability Accounting Report.” It is usually not made public, but regulators and testing labs use it to verify the game (virtual reels and reel strips).

Not every outcome comes up with equal probability; instead, the frequency of each symbol or multiplier is set differently. For example, among multiplier symbols, weights are set so that 2x appears often and 500x appears very rarely.

RTP broken down by win size. In low-volatility games, small wins make up most of the RTP, while in high-volatility games rare big wins and bonuses take a large share. Even with the same RTP, a different pay distribution makes the game feel completely different to play.

The share of total RTP that comes from bonuses such as free spins. For example, if 40 percentage points of a 96% RTP come from the bonus, the base game return while you don’t see the bonus is lower, around 56%. The higher the bonus contribution, the higher the volatility.

A spin that ends with no win at all. If the hit rate is 25%, then on average 3 out of every 4 spins are dead spins. The higher a game’s volatility, the more often long stretches of dead spins occur.

This is when you bet 1,000 and get back 300, yet the screen and sounds celebrate as if it were a win. In reality, you lost 700. Research suggests such effects make players feel they win more often than they really do, and countries such as the UK have banned celebrating losses disguised as wins (UKGC).

Total bet amount multiplied by the house edge, which the casino industry calls “theo.” Casinos often set customer tiers and perks based on this theoretical loss rather than on how much the player actually lost.

The share of the money players put in that the casino actually kept. Unlike the house edge, which is a theoretical value, this is an actual accounting figure, and because the same money gets re-bet many times, it comes out higher than the house edge. The hold rate for Nevada slots is around 7% per year (Nevada).

Numbers that look random, generated by a computer using a mathematical formula. Because a formula is used, they are strictly speaking not truly random, but with a good enough algorithm they are statistically indistinguishable from random. The RNG in most online slots is a certified pseudo-random number generator.

A pseudo-random number generator starts its calculation from a starting value called a seed. The same seed produces the same sequence of numbers, so making the seed unpredictable is the key to security. Provably fair games publish the server seed and the player seed so results can be verified.

The sequence of numbers produced by a pseudo-random number generator will eventually repeat exactly from the start. This length is called the period. A good generator has an unimaginably long period (for example, 2 to the power of 19937 minus 1), so repetition is not a problem in practice.

Random numbers obtained from unpredictable physical phenomena such as thermal noise, radioactive decay, or quantum effects of light. They come close to true randomness, but they are slow, so they are usually used together to create the seed for a pseudo-random number generator.

A distribution in which every value in a set range comes up with exactly the same probability. The numbers an RNG draws follow a uniform distribution, and the game converts these numbers into reel positions or outcomes while applying weights.

The process of checking, with several statistical tests, whether the numbers produced by an RNG show any bias or pattern. Testing labs draw millions of numbers and examine their distribution, sequences, correlations, and more, and only RNGs that pass are certified.