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Casino games mathematics

Casino Games Mathematics and Payout

What is a payout percentage?

Return to player or payout represents the percentage of the total bet amount that the casino has returned to the players, as wins. The value displayed on our website and inside our games, is the THEORETICAL AVERAGE PAYOUT. This is calculated using the formula of total win amount per total bet amount, after simulating all possible game results or a very large number of gameplays (over 10 million), using the current reel configuration of that game and the current paytable values.

The calculated PAYOUT is equal to the total amount of wins registered at your casino per total amount of bets registered at your casino.

The calculated PAYOUT within a game may not match the AVERAGE PAYOUT of that game, until the number of rounds played in that game at your casino will be very large. With the number of gameplays at your casino increasing inside a certain game, the calculated PAYOUT will tend to get more and more closer to the AVERAGE PAYOUT of that game. For verification purposes, you can refer to the law of large numbers on WikiPedia.
We estimate that at least 10,000 gameplays are needed to be played in a game, in order for the calculated RTP to be within +-5% range of the theoretical RTP.

The PAYOUT may also go over 100% for some games, for a short period of time, depending on how the RNG worked and how it granted the prizes to the players. This is how any real money and licensed casino works and every casino owner must have a money reserve to cover these potential wins. Consider the scenario where a player wins the largest prize from a slot game... he hits 5 of a kind and wins bet x3000 for example. For the statistics to reflect a profitable RTP on that game, many gameplays will need to be played. With the number of gameplays increasing, the casino will gain back any amount that it lost and eventually make a considerable profit.
The risk can be minimized by lowering the bet values or by lowering the volatility of the game (this is done by requesting us to adjust the paytable values so that the highest paying symbols will pay less, but if we modify the paytable values, then the payout will change).

For non-regulated casinos (fun-currency, sweepstakes), the mathematics of the games may differ and the games may have a payout pool from which they pay money, as long as there are money in that pool.

What does RTP mean?

RTP means Return to player which is the same as the payout.

What does house edge mean?

The house edge represents the built-in advantage that the casino will gain, over time. In other words, it is the average profit of the casino from the total bets. This is equal to 100% - PAYOUT. For example, if a game has a PAYOUT of 98.53%, then the house edge for the casino will be equal to 1.47%

What is a hit frequency?

Hit/Win Frequency is a value that describes how often a win (with a minimum value=0.001 CREDITS) will be awarded to the player, in average. If a game has a hit frequency of 20%, this means that 20% of the times, or 1 out of 5 times, the player will win SOMETHING.

What is a bonus frequency?

The bonus frequency is a value that describes how often the bonus round of a current game will be triggered, in average. A value of 10% means that 10% of the times, a bonus round will occur, which means 1 out of 10 spins.

Can the RTP of a game be changed?

The RTP of each game is a number that is influenced by all possible game results and the game rules and paytable values (if applicable).
In order to modify the RTP, the game rules and/or the paytable values need to be changed. For games that have a paytable (slots, video pokers), the RTP can be adjusted by us, one time, before your casino will go live. This can be done free of charge. It is not possible to change the RTP of the other games (table card games, roulette) unless we make significant change to their rules.
Please note that it is not possible to change the RTP of any game from our backend administrator panel, because it is against GLI-19 certification requirements to be able to do this. GLI-19 certification is required to run legally a casino in any top jurisdiction. Companies who claim to offer the option of changing the RTP from backend, either do not have GLI-19 certified software/games, either modify the games to work with a manipulated RNG.

What happens when the RTP(payout) of a game is modified?

Adjusting the RTP percentage means to make modifications to the game rules and/or to the game paytable (if applicable). After that, the new game rules must be simulated in order to determine the new RTP percentage. Only our company has access to these simulators and they are not distributed with the purchase of the games.
For example, in the slot games, if we lower the paytable values, the RTP will become lower, but we do not know by how much unless we resimulate all possible combinations of the reels using the new paytable values. In roulette games, the only way to lower the RTP is to lower the multiplier values of the winning bets or by introducing a fee on every win. In the table card games, the RTP can be lowered by introducing more decks of cards (in some games) or by introducing a fee on every win or by lowering the multiplier values of the winning bets.

Can I adjust the RTP percentage?

You can adjust the paytable values and then, indirectly affect the RTP of the game, but you will not know by how much your game RTP increased or decreased, unless you run a simulation on a large pool of data. We do not provide any simulators with the purchase of our games. We provide no assistance for such modifications and we cannot tell you if the new payout percentage is correct, unless you buy our services of adjusting the payout percentage or you buy our "Payout/House edge Calculator for slots" software addon.

Can I adjust the HIT frequency percentage?

No. This statistic is mainly dependant on the composition of the reels in the slot games. In order to adjust it, you need to redesign the reels composition and run a simulator on a large pool of data, in order to determine the new value. Making changes to the reels composition are also not permitted unless you buy the games with source codes. We offer this adjustment as a service, the price being listed on our website.



BY CASINOWEBSCRIPTS PUBLISHED 11 October 2016

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