RPG mechanics as math problems
The first category of mechanics are essentially math problems - mechanics that for any given situation have a correct solution on what to do to maximise your outcome.
oWoD Automated Fire
First one of these is Automatic Fire from Vampire the Masquerade:
This attack basically gives you a lot of extra dice to a roll, but makes the roll Difficulty higher. It's basically a move you want to use either when you need a hail mary, or the Difficulty is already so low it doesn't matter much. For other scenarios, whether or not to use this move would require running the numbers, but there is still a definitive yes or no answer to whether using it is a good move or not. Figuring it out for certain however requires some complicated math of using your AnyDice-fu.
DOGS Growth
DOGS presented a similar math problem to its players when it came to Growth.
DOGS is a system in which you have stats that take form of multiple dice of a given size - "3D4", "4D6", etc. When you undergo Growth, you get to either increase the number of dice for a given stat, or increase the size of those dice - so from "3D4" you can go into either "4D4" or "3D6". Turns out there is an optimal way of progressing through those dice to get the best result on average:
So for example, 3D6 gives you on average 0.5 higher roll than 4D4, while 5D8 is better than 7D4 by 5 whole points on average. The game doesn't explain those concepts to the players and it's simple and abstract enough that these things shouldn't matter, but for a problem-solving player it's a solvable mechanic.
Mouse Guard and optimal combat
Mouse Guard is a system with its own little combat / conflict engine that relies on picking actions (Attack, Defend, Feint and Manoeuvre) and seeing how they interact with one another. Attack lowers opponent's Disposition (HP essentially), Defend heals your Disposition, Manoeuvre is a way to get an advantage on next rolls, while a Feint is like an Attack with caveats - if played against an Attack, Feint does nothing, but if played against a Defend, Defend does nothing.
During our first game of Mouse Guard we soon learned that this setup creates a simple First Order Optimal Strategy - just always Attack. Attack vs Attack or Defend gets you closer to resolving the conflict, Attack trumps Feint, and Manoeuvre often isn't useful enough to trump dealing damage to an opponent. Attack, Attack, Attack!
FOO (First Order Optimal) Strategy
Towards the end of the game this has ended up being such a simple and optimal strategy that for our next game of Mouse Guard we had to switch the rules to give Attack a hard counter not to devolve every conflict of any type into "press A to win if you press it faster than your enemy".
Cortex and marginally useful SFXs
Recently our group picked up the modular system Cortex. We only played a few sessions of it so far, but one thing that stood out to me was how "starchy" (boring) some of its special powers were.
First of all, Cortex is another mixed-die system that puts a big emphasis on making pool of dice and manipulating your dice. So if you're Iron Man, you can have say, Eccentric Billionaire at D10, Ganius Scientist at D12 and Mk1 Iron Man Suit at D6 and roll those all together to do something.
On top of that, one module you can use in Cortex are Power SFX (special effects). Those are some extra powers your character can use that are tied to a Power Set that can alter the game a bit. So for example you can be Tony Stark with Iron Man Power Set, and one of your SFX could be "Immunity" where you spend a Power Point to negate a specific attack, simple enough.
However, a lot of those SFX are boring dice manipulators. For example - Focus lets you take two dice and turn them into one bigger die. Boost lets you shut down one power to increase the die on another die. Dangerous gives you an extra small die to roll, but changes the size of other dice. Multipower lets you use more than one dice from a given pool but they all are decreased a step or more. Versatile lets you split one die into two or more smaller dice. The list goes on.
I've ran some numbers and a lot of these powers are marginally useful. Say, turning 3D8 into 2D8+2D6 with Versatile gives you an average roll that's 0.42 higher, but gives you 0.45 smaller Effect and 0.2 more Hitches. Without going into what those are, those numbers are marginally useful. Sometimes the numbers increase marginally, sometimes they decrease, but from what I've seen it's not a big effect overall.
Unfortunately to get those numbers I had to spend a few hours programming and debugging a Cortex dice simulator. It's hard to make an informed decision as to whether a power is useful or not without a chart, and trying to play a game well that's filled with unknowable probabilities would just be the case of blind luck.
One way or another - the stat-focused SFX and similar mechanics can be one of two things - either boring because they don't change much about the roll, or having an optimal way to play it, in which case you're not engaging with the mechanics, you're solving a math problem. Either way the mechanics become irrelevant because they're either "use them always", "don't bother with them ever", or "use them under specific circumstances". Since Cortex is based on complex math with no glaringly obvious answer, I honestly can't be bothered to use these SFX.
Honourable mention - Exalted, Paranoia Combat
Honourable mention in this category should also go to Exalted. I won't elaborate much on it since this section is already getting long, but there are two things that are worth mentioning that make this epic game of sword and sandal capital H Heroes boring: Paranoia Combat and Minuscule Incremental Charms.
Paranoia Combat was a strategy from 2nd edition Exalted where the optimal way of winning the Rocket Tag combat was to turtle up and play in the most boring way possible.
Minuscule Incremental Charms were special powers you could buy with XP that would give you just small bonuses to rolls or change tiny things that were rather boring in themselves. Things like Triumph-Forged God-Body that gave you double-9s on Athletic rolls instead of double-10s, or Wyld-Forging Focus that started wyld-shaping at a higher phase. All of those were such small tweaks that they might not be worth the mental load, and weighing their effect vs XP cost would be a small math problem in itself.
Gaming mechanics for profit
Most RPG mechanics that you can game for profit I've come across were focused on being able to farm XP, or at least streamline the way you earn XP. While not a problem in itself (who cares if the party got more XP if they're having fun doing it - you're not competing with anyone), it can start to become a problem when it draws too much attention away from doing things in the game and having fun and onto "brrrr the number goes up"
Chronicles of Darkness - punch me in the face for XP
I've covered this one before in the "Punch me in the face for XP - the failure of CoD beats system" article, so I won't repeat much here. Basically, in Chronicles of Darkness you can basically earn XP by being beaten up a bit at the start of every scene, and some systems like Mage the Awakening 2nd Edition even call out a similar way to farm magic XP.
In a similar vein, the systems also let you earn XP by a number of other ways, like turning fails into botches. This can create some animosity between players when someone is invested in some scene going well, while other players are there to mess things up just to farm up some extra XP - "I failed to impress this character, I opt to botch it instead and make them hate us. Too bad they knew something about your lost sister, guess we'll never find what they knew!".
DOGS - Growth vs Consequences optimisation
Another entry for DOGS, this time about maximising the rate at which your character growths, as opposed to optimising how they grow.
DOGS is a system where you Grow when you suffer Consequences as a result of a conflict you had. To become stronger, you have to get into conflicts, get beaten up a bit, etc. However, Consequences can also have lasting effects if they are bad enough - if you roll too high on them, you may even have to step down your stats, essentially netting you zero, or potentially giving you some net negative sessions. Once again, there is a mathematically optimal way of playing:
Which is basically to get a 3D4 Consequence - it has the best chances of being a net gain. You get such small Consequences by essentially keeping non-violent in conflicts, which to an extent is a "mechanic as a metaphor" for the system.
Mouse Guard and farming Checks
Mouse Guard is a system where you grow your character by practice - aka the more you use a skill, the better you get essentially. As with any such system, the first way of farming it is by doing things all the time, which can encourage you to hog the spotlight. This can be a bit of a problem, but then there is more.
The game is broken up into two parts - the GM turn and the players' turn. During the GM's turn (which lasts about half of the session, not "a turn"...) you can earn "Checks", which you spend during the players' turn to do things and make rolls. You earn those Checks by using your Traits against yourself ("I am Small, therefore I have problems lifting this large log!"). You can use a Trait against yourself once per roll, which means the more you act and roll on GM's turn, the more Checks you can earn to act more during the players' turn.
Moreover, during a conflict you can easily earn a lot of Checks if you play in a very boring way. Essentially, during a conflict you pick actions to take - Attack, Defend, Feint and Manoeuvre. When you Defend, you essentially try to recover your HP. Since the conflict only ends when one of the party's HP goes down to zero, if you turtle up you will be rolling for a long time, letting you earn Checks for every roll. In a lot of cases you can also earn a lot more Checks during a fight under specific circumstances - breaking a tie in enemy's favour or giving an enemy more dice in a vs conflict. So if you play like a turtling asshole and have enough dice, you can in theory earn a lot of Checks.
This strategy has one counter though, Feinting makes you unable to roll Defend. You can try anticipating it though by throwing an Attack that trumps Feint into the mix to make your opponent have to Defend and recover. It's not perfect, but it can work...
While that turtle Defence is an extreme example, I have played in some sessions where a less extreme form of Check farming was involved, which later resulted in pretty neat things being accomplished during the players' turn.
Conclusions
There are a number of games out there that rely on math obscurity to give a sense of depth or agency. However, solving the game mechanic from a mathematical sense is only so fun, and once solved the complexity is replaced with an optimal way to play the game, which isn't fun. Making the math behind it harder is not making the choices more meaningful, just the decisions harder to make informed. Try pruning such mechanics from your game if possible.
Similarly, there are games that can be exploited by players to gain some disproportionate amount of XP and what have you that detract from the game by rewarding boring play.
Or in other words - if you are designing a new game system, try asking a math nerd or a game developer to break it. They might do the math and show you how balanced your system can be, and you can guide your players to playing the game well with that math as well.
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I would love to hear your homebrew fix for mouse guards combat system.
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