Serena Petersen and Anton Kuhlmann

Slots for Fun or Fortune

Casinos! People love the thrill and excitement they offer. The high intensity atmosphere of slots, the massive buffet and of course WINNING make the casino exciting. Winning keeps a player coming back to the same game again and again for another shot to win big. The variety of slots provides gameplay options for all types of gamblers on the casino floor, from a consistent gambler to a Vegas vacationer.

With so many games on the floor it can be difficult to know how a game will play. Hiding behind all the spinning reels, game themes and catchy music is the game’s math model. It determines the reel layouts, pay tables, bonus frequencies and everything else that happens in the game. One game may have lots of small wins, lower volatility and amazing game immersion, while another game has rare wins, high volatility and HUGE WIN opportunities. Luckily, there are some hints that can help identify the style of gameplay players prefer.

In general, slot math models fall into two broad categories commonly termed “Entertainment” or “Gambler.” Catering to these two player types, games are carefully tuned to have a specific style of gameplay. Although not apparent on the surface, the targeted math design provides a dramatic difference in the gambling experience.

A gambler game targets the loyal core player, where the primary focus is the big win opportunity. This core player consistently returns, hoping to leave with a bigger wallet. Big money, big money, big money! These games often have simpler presentations, shorter animations and quick transitions allowing the player to get back to spinning. Medium-sized wins keep the player’s bankroll going while they chase the bonus game for the MASSIVE payout. The dream: win big and buy a yacht!

While not always the case, there are a few key elements that help identify gambler games. Gambler games use strong themes, large animals or mythical creatures. Many of the new gambler games have Asian themes featuring lots of gold and red. Lower line counts or “Ways” pays are great candidates for this type of experience. Also, simple mechanics with a single bonus game yield higher potential payouts when landing the right combination on screen.

The math behind these gambler games will sacrifice hit-rate in exchange for big win frequency. The gambler player doesn’t mind a low hit-rate if it leads to a sizeable win. In fact, repeatedly winning less than the bet amount is more likely to agitate the gambler. The gambler is content to wait out the dry spell, maintaining their bankroll with uncommon medium wins until the big win presents itself. These math game design decisions create a high volatility game with large win potential. Because high volatility games can have long losing streaks, players need a sizeable entry bankroll to ensure a good experience.

The other major type of math model targets the entertainment player. These games are for players who want to be entertained. Welcome to Vegas! The casino is full of slots based off movies, TV shows, board games and video games. They target players who identify with the intellectual property giving them a soft and lengthy gambling experience that leaves the player captivated and surprised with the latest technology and multiple bonus rounds. Frequent random features with nostalgic video clips offer small- to medium-sized wins at a regular cadence. These work very well with tourists and new players, where the identifiable theme and entertainment value resonate more than prior gambling experience.

Slot games in the entertainment group are usually easy to identify. The mega-cabinets with the newest I.P. content almost always fall into this category. However, not all entertainment math models are on the newest cabinets. Some are on standard cabinets without I.P. and are identified by frequent bonuses, high line counts and tall reels.

Although big wins are rare in these games, almost every spin gives a win. They come from a plethora of game features with video clips, sounds, animations and player immersion. The math design focuses on giving the player frequent bonuses for longer player engagement. The high hit-rate and frequent features will generally yield a low volatility math model. Often described as a “dribbly” play experience, generally the bankroll will last for a long time without the large “ups and downs” associated with a gambler game. The bankroll will decrease slowly subsidized by small-line payouts and minor wins from the random features or triggered bonuses. As a tradeoff for these longer sessions, large wins are less common.

Ask anyone about his or her favorite slot, and they will say they like “the one with the big wheel,” “the fish game,” or “that one movie.” Recognizing these games as either gambler or entertainment styles of math design reveals valuable player preference information. These preferences are key to providing future experiences that resonate with players. Thus, the unique math models behind each casino game must key into this resonation to keep the player returning again and again.

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