Understanding RTP
For casino players, a few numbers are more important than the often-quoted Return to Player (RTP) percentage. This metric represents the statistical likelihood that a game will pay back its players over an extended period. But how is this critical value calculated? The answer lies in complex mathematical modeling, computer simulations, and advanced statistical analysis.
At its core, RTP is a measure of a casino game’s expected value and house edge expressed as a percentage of all money wagered. An RTP of 96%, for instance, means that for every $100 bet, the game will theoretically pay back $96 to players over an extremely large number of plays.
Calculating this long-term average payout percentage is no simple feat, as it requires considering every possible outcome of a game and its associated probabilities and payouts. Let’s examine the methodology behind RTP calculations for some of the most popular casino games.
Slots
Modern slot machines, whether online or in land-based casinos, are essentially sophisticated computer programs running intricate probability models. To calculate the RTP, game developers must first define the exhaustive list of all reel combinations and map each to its corresponding payout on the pay table.
For a simple 3-reel, 10-payline slot, there might be 1,000 potential combinations on each reel spin. But for the increasingly popular 5-reel video slots with 20–50 paylines, the number of possible outcomes balloons into the millions or even billions.
With the list of outcomes defined, the next step is assigning accurate probability values to each result based on the game’s math, reel compositions, and rules. The software can then simulate millions upon millions of slot spins, tracking payouts versus wagers to calculate the ultimate expected return.
Finally, the cumulative payouts from all simulations are divided by the total simulated wagers to yield the RTP percentage. Regulatory testing labs will run these RTP simulations over shortened and full game cycles to certify the results.
Video Poker
Video poker games like Game King’s 9/6 Jacks or Better present another modeling challenge. Not only do the RTP calculations need to factor in probabilities of different dealt hands, but also the optimal player strategy for each situation.
By defining the detailed decision strategy for every possible starting hand, video poker games become akin to their live table counterparts. The RTP then hinges on players making mathematically perfect decisions every time.
To calculate these numbers, the software will first determine the probability of receiving each possible starting hand. It then must map out the optimal strategy for holding/discarding cards, as well as the probabilities and payouts for all potential resulting hands.
Tracking each permutation and combining the results determines the overall expected return if played with a basic strategy. Games with more player choices and deviations from optimal play will have more complex models.
Roulette
While slots rely on virtual reels and video poker hinges on strategy, the RTP calculations for roulette integrate concepts like wheel physics, betting options, and the differing dynamics of American versus European wheels.
First, developers must encode details like the wheel dimensions, number of slots/pockets, and diameter and weight of the ball to accurately simulate its landing probabilities. The software can then simulate billions of spins to map probabilities to each exact wheel section.
With those granular outcome probabilities defined, the available roulette bets come into play. The model must consider all the different inside/outside bets, and their payouts per the established rules, and factor in the house edge mechanics of any rule variations.
Ultimately, the weighted sums of simulated outcomes versus all possible wagers per the game’s betting options and payouts determine the RTP for each of the American and European roulette variants.
Blackjack & Table Games
For table games like blackjack, baccarat, and casino poker, the RTP process combines elements of video poker’s strategic decision trees with the outcome probability models used in roulette and craps.
The first step is mapping out the probability of each initial dealt hand or roll of the dice based on the game’s rules, number of decks in play, etc. Blackjack models might separate the player and dealer upcards while craps factors in all potential two-dice roll combinations.
Next, the potential player decision paths must be enumerated for every possible situation — hitting, standing, splitting, doubling down, and so on. Each unique decision path has differing probability outcomes based on the implemented game rules and payouts.
Comprehensive RTP models will simulate every unique combination deal/roll, assess the optimal player decision strategy, and track the weighted expected values versus all possible wagers per the game’s betting limits.
The output is a calculated bankers’ expected value and corresponding player RTP for each table game under variable house rules and perfect basic strategy.
Randomization, Audits, and RTP Reporting
Of course, the RTP values for any casino game are only as robust as the underlying random number generator (RNG) and randomization models. Modern casino games employ cryptographically secure PRNGs and certified randomization processes to prevent patterns or player prediction of outcomes.
Leading testing agencies like eCogra, Gaming Laboratories International (GLI), and BMM will audit and certify each game’s RTP calculations, randomization, and other statistical metrics before approving for casino use. These independent laboratories exist to objectively validate return statistics and game fairness on behalf of regulators.
Finally, once a game’s RTP is officially certified, casinos in regulated markets must report that percentage prominently alongside the rules and pay tables. This transparency helps players understand the long-term expected value and make educated decisions on which games to play.
While the mathematical foundations of RTP seem daunting, this metric ultimately boils down to representing the built-in house edge for casino games over the long run. With higher RTP percentages, players can expect to lose less of their bankroll in theory.
However, no RTP value can predict the outcome of any individual session since casino games remain forms of gambling at their core. Skilled video poker players may overcome low RTP games through optimal strategy, while even high RTP slots are susceptible to unlucky streaks.
By understanding how RTP gets calculated through probability models, software simulations, and independent auditing, players can leverage this information wisely alongside considerations like volatility, jackpot potential, betting preferences, and pure entertainment value.
