Mathematically Equivalent Rules

Why Change A Rule?

Genesis is at a point that it plays great with people who know how to play it and people have started actively requesting it at games nights (Always a good sign that a prototype is approaching being ready for publishing!) However I’m finding a noticeable proportion of new players are having a hard time with the game in places and sometimes it’s a downright unenjoyable experience.

Why Not Change A Rule?

The game is working great. People are really enjoying it and it’s working smoothly and well. The balance is approaching where I want it. Games have emotional high points that I’m pleased to deliver. Feedback is generally good.

How Do We Change Something without Changing It?

We use a mathematically equivalent rule!

Let me give an example:

For most abilities timing doesn’t matter, they can go off more or less simultaneously. However for a few the order makes a difference so these each have a speed from 1-10. You resolve all speed 10 abilities, then speed 9, then speed 8 and so on.

A sticking point for the game was that some players would read the rules, but then treat speed 1 as the fastest and speed 10 as the slowest. When quizzed on how this happens a reason emerges: Players intuited that speed 1 goes 1st and 2 goes 2nd and so on.

So the mathematically equivalent rule in this situation is to simply multiply all speeds by 10. Now cards are speed 10, 20, 30 etc. The problem just disappears, while there’s a reason to intuit 1 is faster than 10, there’s no equivalent to believe 10 might be faster than 100.

Critically this doesn’t change how the game is resolved at all – the same abilities go in the same order under both sets of rules. There is no situation in which using one rule rather than the other changes the outcome (in terms of game state) – but using one rule rather than another changes the outcome (in terms of ability to grasp the rules first time) so it’s clearly a better choice.

I’m pretty sure I’m not the first designer to go through this specific process. In fact as a teenage player some years ago I always thought it was a bit silly that Robo Rally used speeds that were multiples of a hundred. It seemed pointless to busy up the cards with extra digits that were always predictably meaningless. But seeing the difference in how players react: Now I get it.

I wonder just how often designers worry at some problem, hit upon a solution and then realise they’ve seen that solution before but didn’t recognise it as a solution because the problem doesn’t exist in that game?

Another Problem

Presently Genesis abilities often choose targets based on their power and can sometimes modify their power. For instance an ability might be something like “All champions with a power of 5 or less gain +3 power”

Abilities always target based on a cards natural power – under no circumstances will they select a target based on its total modified value. So in the above example if a power 6 card was reduced to 5 by some other ability, it wouldn’t get a +3. The +3 is only for champions with 5 or less printed on the card.

This seemed like a fairly solid rule to me, certainly compared to previous iterations where some things cared about unmodified values and others cared about final values. “Always unmodified” didn’t strike me as difficult.

I dramatically underestimated how complex that’d be for players with different backgrounds. There are a lot of different ways in which people think and some portion of players just can’t grasp “always unmodified” as a rule.

But if we flip it over to abilities like “All champions with a level of 5 or less gain +3 in combat” it becomes easy. It’s exactly the same rule, but moving away from “modified power” and “unmodified power” to two values called different things makes it much easier to intuit.

Alright, but how do we apply this to design in general?

The commonality between situations helped by this sort of intervention is that they have the following traits:

1) The rule works really well for people who understand it.
2) A portion of players play the rule incorrectly.
3) These incorrect plays are due to intuiting a competing rule and the incorrect intuition is known.

From there the rule can be modified to remove the intuited rule as a valid interpretation without changing the thing that’s making it work well for a lot of players.

In the first example the intuition was “1 means 1st” so the modification is to get rid of 1.

In the second example the intuition was “If this alters power I can use it to get the right power to use this other thing that cares about power” so the modification is to stop using the word power to refer to what are essentially two different things.

Sometimes it’s better to embrace the intuition wholesale and actually change the rule to match whatever people intuit that it is. It was an option to change powers to say 1st, 2nd etc. if all powers were in play every turn I’d probably have done that – but in this case avoided it because the notion that 2nd goes 1st (because 1st isn’t in play) might prove equally unintuitive with players trying to execute one of the unmarked powers before it.

So if you’re working on a game, have a quick scan of your playtester feedback and see if you’ve got situations like that. It’s easy to dismiss “We got this rule wrong but then read it again and then it played fine” as something that worked itself out, but it’s perfectly possible to use it to improve the odds that more people will get it right first time.

After all, some players won’t give your game more than one chance 😉

2 thoughts on “Mathematically Equivalent Rules

  1. Interesting article. One thing that was fascinating to me is that in both cases, the solution that I figured you were building to was not the one you settled on. For example, if new players think speed 1 goes first and speed 10 goes last, my solution was simply to bow to their perception. Have lower numbers go before higher numbers. And if modified vs unmodified power is troublesome, why not have your abilities simply include the word “printed”? So your card would say “All heroes with printed power 5 or higher gain +3 power.” I think that would remove a lot of ambiguity. Anyway, just food for thought. Thanks for writing out your thoughts, always interesting to get inside the head of a designer!

    • The problem with just making 1 go first is that some players were correctly intuiting that the highest number goes first. Since some playesr were seeing it each way around I needed to change it to a system that everyone would percieve in the same way.

      Funny thing about the word “printed” is that it was actually there at the start! I had some things that ran of printed power and some that ran off power. In a previous iteration that was confusing and I winnowed the game down to the point that everything ran off printed power so the distinction was no longer necessary. Following that people reported being annoyed by the printed direction because they all said printed power so the distinction was percieved as unecessary. Removing it gets us to the version of the game at the start of this post 😉

      If the alternate solution hadn’t worked I’d have gone back to “Printed power” since “It annoys some pedants” is better feedback than “People can’t play the game” but as it is the new solution is working great 🙂

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