# Identical vs Equivalent

I often say that board games are the combination of psychology and mathematics. More exactly, they use mathematics to induce specific psychological reactions: tension, angst, euphoria, excitement, satisfaction, all just because your number will be lower than your opponents’. Fascinating, isn’t it?

Now let’s take that vision of games and look at them through a game design lense. A game’s elements (be they components, theme, or mechanisms) are not the point: they are tools to create a specific experience. Sure, all of these elements are important pieces, but the sum of the parts are what’s important.

This sheds light on one easy pitfall of design: to look for identical alternatives rather than equivalent: too often, I hear playtesters suggest alternatives, and designers turn them down because of some minor mathematical differences. This is especially true when we talk about streamlining, about suggestions that could simplify an entire system but are turned down because that one action would now give 4 rocks instead of 3. Is that a meaningful difference?

I talked about one similar situation in this blog’s very first post, when we had included 5 different ways for tokens to score, and 4 different mini-games, which were technically different, but did not affect the game’s experience or the players’ decisions at all.

Another example is from the roleplaying games side: in 13th Age, players roll obscene amounts of dice for damage. The designers strongly suggests to instead either (a) take the average damage, (b) roll one die and multiply it by the number of dice, or (c) roll two or three dice and take the average for the rest.

These are all mathematically different: the static number obviously stands out, but even multiplying one die leads to much swingier results than the standard die roll, which itself is swingier than just rolling a few and averaging the rest. However, while all are mathematically different in how extreme the results will tend to be, the game does not change much between the two. You could have a group where each player chooses a different way of calculating damage, and it wouldn’t make much of a difference: while not identical methods, they are by and large equivalent.

When designing, every design element should be there for a reason. During your process, it’s important to look for equivalent alternatives, which could fill the same role in the design, without being identical.

For example, High Rise, Lords of Waterdeep, London, and Cleopatra and the Society of Architects all have a Corruption mechanism: some things you do are stronger, but come with this negative token you then have to manage, and try not to have the most of. They all have a different associated mechanism, but they all have the same impact: give some actions a delayed, and uncertain cost. If you took any two and switched the Corruption mechanisms, they would mostly still feel the same. There would be differences, but I’m not sure they would be that meaningful.

Of course, the difference between identical and equivalent is very subjective, and highly context-dependent: you might disagree with my example above. Yet, I would still suggest you err on the side of openness, especially early in your design process: it’s so easy to try something, and, if it doesn’t work, to just CTRL+Z the change.