What is “Fairness” for an Internet casino game?
Fairness for an Internet casino game is defined by four operational principles.
Operational Principle #1
The game must operate in a manner that is indistinguishable, in principle, from the same game as offered in a brick and mortar casino.
This item is often misunderstood to mean that the game must act in a manner exactly like the associated brick-and-mortar (B&M) casino game. Many B&M casino table games follow procedures for shuffling and dealing that cannot or are not replicated online. In games like blackjack and baccarat, multiple rounds may be dealt between shuffles. Moreover, physical elements in B&M casinos undergo wear and tear that may induce bias. These include dice, roulette wheels, keno balls and the wheel-of-fortune. The auditor understands that in an Internet casino shuffling usually occurs after each round and that all event outcomes are determined by a random number generator. However, other elements of the game, such as the rules, pay tables, bonus features, and game play should match the associated B&M casino version.
Operational Principle #2
The game and its random number generator must pass a suite of statistical tests designed to detect bias.
One of the standard tests for each game is to measure its “Return-to-Player” (RTP). Each game has a fixed theoretical value of its RTP that can be used as a baseline value. The more rounds that are played, the closer the actual RTP should be to the theoretical value. The auditor may consider the probabilities of various subsets of events from the game. The auditor compares the events that occur in actual game play against the expected number for each event. The primary tools for this type of analysis are the chi-squared statistic and the binomial distribution. Bias can also occur in a correlative fashion; the auditor may analyze events in successive rounds of play. The random number generator (RNG) used should be one of the industry standards. The implementation of the RNG into the games should safeguard the outcomes, while insuring the values produced are uniformly distributed over the required interval.
Operational Principle #3
The game can have no operational flaws that allow the house edge to be changed by the player or casino.
One of the most cited causes of dissatisfaction among players at Internet casinos is the belief that a game can be modified in real time to yield the desired result against an individual player. Likewise, many Internet casinos are extremely cautious with players they believe may be using mathematical tools, systems, or “bots” to beat their games. It is the responsibility of the auditor to consider the issue of whether each player is experiencing the same mathematical model during each round of play. If the auditor concludes that the model is stable and accurately represents the game, then neither the player’s dissatisfaction with his results nor the Internet casino’s fear of bots or systems are legitimate concerns. The auditor is obligated to express an opinion if asked, supported by facts, in response to concerns about game outcome manipulation. The auditor’s obligation is to act in a manner to safeguard the game and not to side with either the casino or player in any disputes.
Operational Principle #4
The game must remain statistically stable over time.
Changes to the rules or payouts of existing games may negate previous auditing. The auditor may be tracking the long term RTP, or other statistics, of the game over a period of months or years. If the auditor is not aware of the change, he may raise a red flag that a game is not operating correctly. Modifying the game may introduce unexpected bugs, including making the game distinguishable from its B&M counterpart, creating a bias, or making the game susceptible to abuse by players or the casino. The auditor looks towards statistical stability as evidence that audits previously performed continue to describe the current game. The longer the game is stable, the more evidence the auditor can collect to re-confirm his opinions and conclusions and the easier it will be to recognize and address issues going forward.
What is “Return to Player” and why is it important?
Return to Player (RTP) for a casino game is given by the formula:
Amount Wagered by Player – This is the amount of the initial wager by the player. Many games allow or require additional wagers to be placed after the initial wager. For example, Three Card Poker requires a “Play” wager for the hand to compete. Blackjack allows additional wagers for doubling or splitting. For purposes of computing the RTP, these additional wagers are not considered.
Total Amount Wagered by Players – For the period over which the audit takes place for a specific game, each initial wager for each round by each player is tallied to give the total amount wagered by all players.
Amount Returned to Player – Conceptually, this is the net amount the player wins (positive number) or loses (negative number) in a round.
For most table games, if the player wins the round then his original wager is returned. The amount wagered is not counted in the return, just the net amount won. If the player loses, then the amount returned is a negative number — he loses the total amount wagered for the round, again this is the player’s net result for the round. One way of thinking about the return for table games is that it equals (total amount returned) – (total amount wagered).
For slot machines and video poker return is simpler to define. The original wager is forfeited once it is placed. The amount returned to the player is the amount won based purely on the pay table for the game and the result of the round.
Total Amount Returned to Players – For the period over which the audit takes place for a specific game, the amount returned for each round by each player is tallied to give the total amount returned to the players.
For the purpose of auditing, each game has a theoretical RTP that is known in advance. As with all gambling, there will be runs of good and bad fortune by the players. The auditor computes the RTP using actual game play data given in the log files and compares that to the theoretical RTP for that game. The more rounds that are played, the more the auditor expects these two numbers to closely match up. The auditor knows the reasonable range of values for the RTP computed from the log file data given the number of rounds played and the theoretical RTP.
The RTP is a helpful baseline statistic to verify that a game is operating properly.