Serena Petersen and Anton Kuhlmann

Successful Slots And Math Design

Slot machines! People love them. Math? Not so much. The casino industry secret: there are unique math models behind every slot machine. Casinos have a variety of games on their floor with a range of experiences to suit every type of player. It’s common for a player to have a great experience on one slot game and a not-so-great session on a different game. What makes one slot game better than another? The math behind each game plays the ultimate role.

The creation of each new slot game starts with the initial game concept. The early design stages are fueled by the desired game features and mechanics. Most designers have an idea in mind of how they want their game to play, including game volatility and frequency of features. This initial concept then leads to further gameplay choreography, matching the math and gameplay to the overall theme of the game. The slot designer uses past and current knowledge of proven game successes to create new innovative titles that resonate with players. This industry insight coupled with a deep understanding of slot game conventions, game theming, art styles and math design comprise the slot designer’s tool belt.

Having a math background allows a slot designer to understand how the game mechanics interact. This allows for a better cohesion of the desired features and the math experience. Knowing how the math balance interacts when incorporating an additional feature allows the slot designer to vet their ideas quickly and efficiently. Otherwise, designers might spend months of trial and error attempting to make an idea work only to find it doesn’t. Instead, the designer spends most of their time optimizing gameplay to attract and retain players.

What keeps a player coming back? Winning! This win is based off the math design of the game. A common misconception is that the math balance of the game is primarily focused on the RTP (return to player). Typically, RTP represents a percentage of the wager the player expects to get back. As a gaming mathematician, RTP isn’t a goal as much as it is a constraint. Although it’s easy to maintain the RTP, the challenge becomes making it fun.

For example, let’s take a couple of games at 90 percent RTP. The first being an extreme low volatility game, and the second, an extreme high volatility game. In the first game, the player wagers $1 and wins $0.90 on every spin. This is a perfect 90 percent RTP game, but would anyone play this game? Of course not.

Here’s another one: the player wagers $1 and wins nothing 999 spins out of 1,000. But on average, every 1 in 1,000 spins awards the player $900. Again, it’s clearly a 90 percent game, and some players might try their luck chasing the BIG WIN. But how long will someone play a game that pays them absolutely nothing before throwing in the towel? At 1 in 1,000, it isn’t unlikely to go several thousand spins before getting a win. Of course, these represent extreme examples, and all slot games fall somewhere in between.

Math design across multiple game features is a balancing act. How often should free spins be triggered, and how much should they pay on average – not only average, but how often should they pay BIG? How often should those wilds hit the screen, and how many of them? Interactions between many different game features affect how the game plays. Implementing a high-quality math design that properly balances all features will make or break a successful game.

The universal rule of give and take governs the possible math balance. If the free games always pay out huge, then they can’t happen very often. If the win potential of that game feature is too volatile, then players will get a huge win every once in a while, but be disappointed most of the time. Sure, the player that hits the huge win will come back, but what about the hundreds of players that don’t? A solid slot math model will keep a player returning, but there are many games with the same features and game theme that have a vast performance gap on the casino floor. The games that win the battle have a math experience that matches player expectation while creating excitement, anticipation and retention.

In summary, while often overlooked or oversimplified, the math model is the most important part of any slot game. It drives the entire experience, which dictates everything that happens, including player retention. Luckily, there are the few superhero slot mathematicians who love making and playing these games. A math designer’s goal is to create a great experience where everyone wins. Show me the money!

Serena Petersen and Anton Kuhlmann are Game Mathematicians. Consulting Game Design and Math at Jackpot Designs, LLC. They can be reached at