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Fantasma Games: The ghosts of departed quantities

By Lewis - 19 August 2021

Tianzhi Zhou, Product Owner and Game Mathematician at Fantasma Games, details the nuanced and vital role of math in the game development process. Tianzhi believes math offers as prominent a route for differentiation as other design elements, albeit one in which it is most difficult to innovate.

Who is responsible for the creation and implementation of math in the developer team? What is their remit?

The Game Designer, Math Designer, Game Mathematician; the title changes from studio to studio but ultimately there is a math guy or girl that will oversee the math model for each slot.

Depending on the size of the studio, there may be several math experts that work under the lead mathematician. Their remit is to create the math model for each slot, and to also push the boundaries and come up with new concepts and profiles.

To do this, they must have a very good understanding and knowledge of probability theory, random process and statistics. Equally important is knowing how the game’s math profile impacts the player experience and how this can be used to deliver more thrills and added entertainment value.

What role does math play in the game development process?

The math profile is the blueprint for the game or, more specifically, the gameplay. It decides the mechanics and features of the game as well as its basic set-up including the number of reels, symbols and how the slot will evaluate and pay.

Once the initial profile has been created, the math used for generic data aspects such as the pay table, reel grids and line patterns is fine-tuned, as are game-specific configurations that affect the frequency and value of the slot’s features.

Once this has been done, the math profile is communicated to the rest of the team. Important math metrics like volatility, hit rate and feature value must guide other areas of development such as graphics, animations and sound.

What comes first in the creative process – the concept or the math?

It can be both. The concept for a slot can come from anywhere – it could be a story, a theme, an art concept, a new mechanic or simply a phrase or saying. Of course, the math profile will ultimately underpin the slot and deliver the exciting gameplay players are looking for.

How has math evolved for online slots in recent years with the proliferation of developers and operators?

Math is becoming more complex, more volatile and more niche as player preferences and expectations change and mature. Developers are also using math as a point of innovation in order for their slots to stand out from the hundreds of others that hit the market each month.

I think this is a positive for players, as studios are having to push the boundaries and deliver new experiences that will engage and entertain players.

How does math influence gameplay?

Math has a massive influence on the gameplay, and this is why it is so hard for developers to create a math profile that appeals to the widest possible range of players. This is because math impacts key game aspects such as hit rate, feature trigger rate and value as well as volatility.

For example, a slot with a low hit rate can be perceived as cold; a slot with a low free spins trigger rate can feel grindy and a slot with volatile free spins can seem harsh. This is why we have to look at the math model as a whole and not on a per metric basis.

It is impossible to nail all of these aspects, so it really comes down to a balancing act between them. What is really important, though, is that the math and the design come together in a way that is cohesive and delivers a seamless player experience.

Does math offer as prominent a route for differentiation as sound or design?

Absolutely. New math profiles and mechanics can definitely make a slot stand out from others. A new evaluation system, way of triggering a feature and, of course, a never seen before bonus all have massive player appeal.

That being said, math is probably the hardest area in which to innovate. Not only do you have to be creative, you also need a vast knowledge of slots both as a designer/mathematician and as a player. Oh, and a bit of luck in order to bring this all together and create a blockbuster game.

Is quirky and innovative math overlooked? Do players appreciate it?

I don’t think it is overlooked. In fact, I think players are more willing than ever to try slots that have different math profiles, mechanics and features. The challenge is ensuring the game has been designed and developed in a way that keeps players wanting to come back for more.

Slots that have been designed to be different just for the sake of it rarely top the charts for long. Players might be drawn to them in the first instance, but once the novelty has worn off they will return to slots that deliver a more consistent and rewarding experience in the long-term.

How is new technology shaping how developers approach slot math?

It is allowing us to bring games to market much faster than before. Not only that, but games that are more mathematically complex. This is because we can now use technologies that have a much faster computational speed, allowing us to run large scale simulations at pace.

This in turn means we can calculate and certify more complex math profiles easily and quickly, and this really reduces the time it takes to move a slot from concept to launch.

How has math enabled Fantasma to create unique and distinctive titles? Could you name any examples?

Fantasma has looked to innovate in the area of math from day one. Take Hero Hunt, for example. The game features a unique level up system that unlocks more features as the player accumulates experience points.

To do this, we had to create seven individual math profiles for the seven levels of the game. This brings in elements of progression and reward and combines it with a feeling of adventure and exploration, something that had not been achieved in a slot game before.

Then we have Elemento. This slot features a unique feature area that surrounds the 7×7 gameplay grid. The layout is only possible because of a super smart math design that makes the mechanics clear to follow but also very versatile. The features trigger in the designated area but there is a complex chain of events that takes place.

We are seeing more titles with exceptionally high RTP in the online slot market. Unlike land-based casinos, online casinos do not have alternate forms of income beyond the titles they offer. Do you believe there should there be a minimum industry standard for RTP online?

A standard that protects players is definitely a good idea but I also want to make clear that I believe the online slot market is actually much fairer and transparent that the land-based market.

Then there is the sheer volume of online slots in the market; unlike the land-based sector where players only have a small number of machines to choose from in a gambling venue, when online they have thousands – if they have a bad experience with one game, they will simply play another.

This means online slot developers must deliver a superior player experience and that in turn ensures they are meeting the highest possible standards.

What is the next evolution in slot math?

Multiplayer slots that you can play with or even against your friends and family. And mark my words, it won’t be long before slots such as these hit the market.