Unleashing the Power of Logic and Mathematics in RPGs: Enhancing Gameplay through Strategic Thinking

Solving a logical-mathematical puzzle

When Gandalf and the fellowship arrived at the entrance of the Mines of Moria, the Doors of Durin stopped their progress. Gandalf stepped forward and translated the Sindarin text: 

The Doors of Durin, Lord of Moria. Speak, friend, and enter. I, Narvi, made them. Celebrimbor of Hollin drew these signs.

Gandalf initially misunderstood these simple instructions. With a little help from the hobbit, Merry Brandybuck, and a re-translation, the wizard understands what he needs to do next. He speaks the Sindarin word for friend and the Doors of Dorin opened.

In my mind, this is the first example I think of when I think of the history of puzzles in role-playing games. Certainly, they’re others in the other fantasy novels, but this is the first one that I think of.

In this episode, Gandolf is forced to use his Logical-Mathematical intelligence (LM), as set forth in the works of Howard Gardner. This intelligence focuses on the ability of players to puzzle things out in their minds. This could be as simple as arithmetic or it could be as complex as a multi-piece physical puzzle box. Once again, these abilities are staples in the RPG space. We use them all of the time as we add modifiers to dice rolls and try to puzzle out a three-dimensional space during combat. So how can we utilize these abilities more in our RPG adventures? 

Game Masters can facilitate the use of Logical–Mathematical intelligence in their adventures by first recognizing those players in their group that are strong in this area. Then they can plan encounters that utilize the strengths of this intelligence. Finally, they can encourage engagement by providing toys and manipulatives that will help maintain engagement in LM players.

Recognizing Logical-Mathematical Intelligence in your players

LM intelligence manifests itself in how players interact with challenges out in front of it. These players will use numbers and logic to reason out how something works. They will also look for patterns in disparate ideas and actions so they can better understand them. Once they have gathered all of this information, they will use mathematics and reasoning skills to create something new. 

As your players come to the table, listen for those who are quick at adding up damage or even the sum of their dice rolls plus modifiers. These are players who have a hard time giving up the wooden puzzle box that you placed in front of all your characters to solve. They might even keep a Rubik’s cube in their bag. You might even recognize your LM players during times when you are not at the table. For example, this might be the friend who has a hard time keeping quiet once they have figured out a movie mystery.  Their facility with making connections and working with numbers will help you quickly identify them as LM players. 

Activities and Encounters for LM Players 

In order to tap into the logical and mathematical skills of LM players, Game Masters can try the following things: 

  • Puzzles
  • Riddles (here are some simple instructions on creating your own riddle)
  • Games
    • Mancala
    • Chess
    • Checkers 
    • Tic-Tac-Toe 
    • Connect 4 
    • Dominoes 
  • Researching handouts for clues 
  • Simple science experiments 
  • Visual timelines of events 
  • Mysteries
    • Even small mysteries where the GM provides short clues that over time allow players to guess what is coming up (more ideas on small mysteries below)
  • Maps and miniatures to help players make strategic plans
    • 3D terrain 
  • Legend of Zelda-style puzzles (Game Designer Toolkit has a great video on this
  • A picture that subtly includes an out-of-place object that players must notice 
  • Mazes 
  • Secret Codes or words written in a non-native alphabet 
  • Have players create symbols and signs for Thieves’ Can’t 
  • GMs can use analogies as they describe an encounter
  • Have players keep track of the damage done to monsters 

Small Mysteries 

Small mysteries come in two forms. The first is foreshadowing. Game Masters will provide clues that prepare players for the scenes that are coming up. For example, you tell the players: “You notice the large padded footprints of a big cat.” Then in a later description, you add, “While walking through the trees you identify a clump of black hair wedged between two tree branches.” Even later still, the party comes across a number of corpses and you point out: “The wounds on the victims indicate that they were all looking away when whatever attacked them first hit them.” With all of this setup, the players will not be completely caught off guard when they run into a pack of panthers with illusion powers. Even better, they will be really excited if they figure it out first and then found out they were right. 

Your small mysteries might also help players to recognize that a previous idea was wrong. So the party following the big cat from the example above has guessed that the creature was a displaced beast from the first two clues (that is, the footprints and the black hair). They look at each other and say, “Illusion Panthers ;).” However, when they find the tracks again and the massacred victims, you might steer them away from their previous idea by adding that they find six-inch-long spikes embedded in the victims and nearby trees. Now they know they are tracking a manticore and might need to get some reinforcements. 

The second type of small mystery occurs when players have multiple choices in front of them. Game Masters need to differentiate the choices. One way to understand these choices is to think of the classic dungeon. When the characters reach a T-junction with paths going left and right, GMs will ask them which direction the characters want to go. Without any additional description, the players have no way of making an educated decision. One way is as good as the other. However, the GM can describe the junction as follows:

You reach a T-junction with a hallway going right and a hallway going left. A quick glance down the hallway shows that it descends like a ramp towards a distant door. You also notice the blood on the floor as though something that is bleeding has been dragged across the floor. Then to the left, you see the hallway continues to a large wooden door. From that direction, you can hear a rhythmic ticking sound that hits you with its regular beat. Which way would you like to go?

With these differentiated descriptions, you have given your characters a mystery. What was being dragged down the hall to the right? What is making the ticking sounds to the left? Worse yet, is it some sort of countdown? These descriptions will hopefully hook your players and help them to make a decision with a reason. And Reasoning is what we are trying to engage with our LM players.

Focusing Toys and Materials 

Some players find it easier to pay attention when they have something in their hands. The following items might help an LM player to focus on the game. However, you will want to make sure that they don’t become a distraction from the game, but if they help, use them. 

Conclusion 

Capitalizing on Logical-Mathematical Intelligence at your table makes for a lot of fun. Game Masters can include puzzles and mysteries (big and small). You can introduce physical puzzles and mazes. You can take some of the mental load often placed on the Game Master and hand it to another player. By paying attention to LM intelligence, you will (like the Doors of Durin) allow your friends to enter into the game.

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