Relative Numbers

Today I’m going to discuss some very mathy game design theory. If that’s not your thing, it’s probably best to steer clear now.

Working on Shadow Throne and some other prototypes, I realized I was making use of something I’ll call relative numbers in my games. After giving it a little thought, I realized that these numbers show up in many games, and for good reason. Today I’ll spend some time explaining what relative numbers are, give a few examples of how they show up in games, and finish by discussing why you might want to include relative numbers in your game.

What are Relative Numbers?

I use the term relative numbers in a pretty abstract sense. I basically mean any number where there aren’t specific absolute values that determine outcomes. (See, I told you it was abstract!)

I think it might be a little easier to explain what I mean using an example. I’ll discuss many more examples below, but this is a simple one that shows the difference between a relative number system and an absolute number system.

The actual cost of power plants in Power Grid is determined by the players. Image from Board Game Geek.

The actual cost of power plants in Power Grid is determined by the players. Image from Board Game Geek.

In Dominion, buying a new card requires a player to achieve an absolute number, printed on the bottom left of the card. In Power Grid, power plants are auctioned, so buying one requires a relative number, determined by how much other players are willing to push up the price. The same power plant can cost radically different amounts of money in two plays of Power Grid, which is a good indication than the number is relative.

Relative Numbers in Action

I first became aware of relative numbers because two games I’ve worked on use them in different ways. Once I became aware of them, I started seeing relative numbers all over the place. Here are a few examples of where they show up in games.

Winning score. The victory conditions for many games, especially Euro games, involve getting the most points. To win the game, you don’t have to reach a specific number of points, you just have to beat the next closest player. This makes many games revolve around a single relative number.

Race to the finish. Other games end when one player reaches a certain position or a certain score. Here, the goal isn’t relative, but the game still revolves around a relative number: time. Rather than trying to achieve the biggest score, players try to reach an absolute number in the fewest turns.

Auctions. Auctions show up in many games, and take many forms. But they ultimately all revolve around relative numbers. To win an auction, you don’t need to achieve a set, specific number, you just need to beat your opponents.

Combat. Whether combat involves rolling dice, playing cards, or is deterministic (like in Small World), it often requires you to beat your opponent’s strength, making it a relative number system. (Though note that there are many examples of absolute number combat systems, too.)

Mini-games. Often times, players will be rewarded for doing best in one area of a game. The longest road card in Settlers of Catan is a great example of this.

In Alhambra, players score points by having the most buildings of various colors. Image from Board Game Geek.

In Alhambra, players score points by having the most buildings of various colors. Image from Board Game Geek.

This is one of the first relative numbers I discovered while working on my tech company deck building game Techies. Each hand, players determine turn order based on how much hype they generate for their company. The player with the most hype goes first, then the second most, etc. While relative numbers often translate directly into victory points, they don’t have to.

Stocks. Many games have players trying to bet on which “stock” will do best. Here, the relative numbers are at least partially outside the control of the players, and it’s the players’ job to determine which will outperform the others.

This is the other form that helped me recognize relative numbers. In Shadow Throne, one of three colors wins each hand. Each card a player plays will make its color a little more likely to win and reward the player if that color ends up winning. In essence, players are both influencing which color wins at the same time they’re betting on which color they think will win.

Once I noticed relative numbers, I started seeing them everywhere. I tried to cover many types with the above examples, but I’m sure there are many I missed. Let me know if you have more examples in the comments!

Valuable Relative Numbers

So, why did I start seeing relative numbers everywhere? Because they add a lot to games! Below are some of their many benefits.

In 7 Wonders, military cards force you to pay attention to your neighbors. Image from Board Game Geek.

In 7 Wonders, the military race forces you to pay attention to your neighbors. Image from Board Game Geek.

Player interaction. Relative numbers are a great way to get players to care about what each other are doing in an indirect way. Rather than tearing each other down, relative numbers often encourage players to try to outperform each other. Relative numbers are also a good way to focus player interaction to prevent the game from getting too chaotic.

Re-evaluating absolute numbers. Relative numbers have the tendency to infect the absolute numbers around them. If you’re only 1 point behind the leader, a 2 point and 5 point card are equally valuable to you. But once you’re 3 points behind, that 2 point card isn’t looking so great. Shifting the real value of absolute numbers keeps players on their toes and the game feeling fresh.

Sense of progression. If players are building an engine, or simply getting more powerful as the game goes on, relative numbers keep things fair and simple while still contributing to the overall trajectory of the experience. An exciting early game card becomes a weak late game card, giving the players a real sense that the game is moving towards an exciting conclusion.

Dynamic experience. With relative numbers, no two games will be the same. A winning hand one turn will lose horribly the next. This not only keeps the game interesting over the course of a single play, it adds to the replayability of the game over multiple plays. In fact, when relative numbers involve competition between players, fun meta-games can also develop as players get to know a game better over time, letting the game grow with the players.

Relatively Speaking

In Arboretum, a player only scores a suit if she has the sum of the ranks of that suit in her hand is greatest among players. Image from Board Game Geek.

In Arboretum, only the player with the highest count of a suit in hand scores that suit. Image from Board Game Geek.

I think relative numbers are a great inclusion in many game designs, and encourage you to think about them as you work on your games. Honestly, there’s a good chance that if you look at a design you’re working on, you’ll find relative numbers already in there! But being able to identify them and understanding how they work can only make you a stronger designer.

Before I sign out for today, I do want to give one word of warning. While I think relative numbers contribute a lot to interesting, dynamic gameplay, it’s best to use them sparingly. If you put too many relative numbers in your game, it can become confusing and feel too chaotic. Find a place to include a relative number or two in your game, then support those areas with absolute numbers. Your players will thank you, even if they don’t realize why.

Thanks to my generous Patrons whose support and encouragement made this article possible.

Leave a comment

5 Comments

  1. Really enjoy the post. I feel you only describe one type of stock mechanic and missed price mechanics. (Market Mechanic Lecture: Prices is a supplemental primer on pricce mechanics).

    One way of using stocks (as described in your post) is you bet on a stock and see what happens e.g Speculation. Another way of using stock is to buy and trade them with other players to communicate information.

    My buying the stock tells you I have information suggesting future success.
    You selling the stock suggests you have information on the some sort of failure or you think I am overestimating future success.

    Price mechanic games based on communicating information are based on the efficient market hypothesis where each indvidual player has limited information on each stock.

    If the information is from an endogenous mechanic – the relative value will be manipulated by the players. Or, the information that alters relative value can come from exogenous events – e.g. a dice roll/card draw that adds or removes resources.

    When you trade stocks in a price mechanic game like Post Position the relative values players agree upon communicates their inside information. In Post Position the information being traded is on the order the horse will finish the race. (The game calls them bets, but in reality they are naked stock shorts). A player willing to pay a high price for a stock (bet) signals they have information a horse will do well and the player who sells a stock (bet) to that player has information the horse will do poorly.

    Games centered on price mechanics awards the players who more successfully gathered information relative to other players, allowing them to profit on their trades.

    Reply
  2. Wow! Thanks for this analysis, Mr. Fristoe. I never noticed this before. . . Simply that there was this flexible value I really enjoyed playing with. Now that I have a name and a clear perspective on the relationship between absolute and relative numbers, I can’t wait to go back to a few of my earlier designs and see what kind of tweaks and adjustments can be worked in for clean up. 🙂

    Reply
  1. Weekly Update V | The Formalist Post
  2. Game Elements: Goals | The Best Games Are Yet To Be Made
  3. Game Elements: Scoring | The Best Games Are Yet To Be Made

Leave a Reply

Your email address will not be published. Required fields are marked *