# Calculation Burden

At present my computer game fix is Tales of Maj’Eyal, a delicious open source roguelike. It’s probably the board gamer in me that gets on so well with turn based board games that do their best to generate a fair portion of interesting decisions. I like Tales because of how well it leverages the advantages of being a computer game, for instance various achievements unlock races and classes for character building. In most roguelikes I find death a frustrating exercise in “go back to the beginning” but in Tales I’d find myself unlocking things that made me think “I can’t wait to die!”

I enjoy the cross-proliferation of ideas between platforms. I got a lot out of Risk: Legacy transitioning unlockable content to the board game world and I can see plenty of other places where board and computer game designs have influenced each other. Pondering on this (As I had yet another paradox mage explode in an uncontrolled burst of temporal feedback) made me wonder what it would look like to implement Tales as a board game, which lead me to this equation:

damage = (0.3 * (physpow + cun*45 + dex*45) * ((sqrt(base_dmg / 10) – 1) * 0.5 + 1) * (sqrt(eff_talent_level / 5) / 2 + 1)))^1.04

This is the damage calculation for how much damage a rogue wielding a dagger in their primary hand assuming they have at least one rank of lethality. Assuming that they don’t have any other equipment or talents other than dagger mastery or lethality. Before applying the type resistances, armour and armour hardiness of the target. Obviously the general purpose calculation is a good deal more complicated.

Can you imagine the game that would ask players to make calculations of this nature?

Yet I can play the game, actually I’ve been playing the game for a good while without knowing exactly how the calculations for a great deal of the things within it actually worked. I think this is an important feature of gamers: Players are able to play and enjoy games that have a mathematical complexity above the level that they are willing (or able) to calculate by hand.

The more I thought about it, the more obvious it became that the vast majority of games that I enjoy are to some extent designed around this purpose. I started looking through my games with the lens of “How does this game create mathematically complicated situations without at any point asking any player to do any arithmetic in a manner that they’d notice?” and coupling this with the question “How does this game give meaningful feedback to allow a player to understand and learn from the results of their actions even if they’re not familiar with the model that generated that feedback?”

To pick a game on the shelf at random, let’s say Merchant of Venus, there’s plenty of insight into the game to be had this way. The goods roughly follow a rule demanding that goods are bought for a fraction of their sale value that is smaller the higher their sale value is, but the game never needs to state the exact equation in the rules. The player never needs to understand it either as intuitively the trade off between a good that offers a better return as a % of capital invested against a good that offers a better absolute return makes sense in a game characterised by a limited space to store goods.

Similarly the shape of the board offers a significant disadvantage to going 4th. Three unexplored planets are accessible from the starting position and the benefit to being the first to uncover a new civilisation at the start of the game is significant. In most games the first three players will set off towards these three and the fourth player will move to chase whichever one has made the least progress, disadvantaging those two players as they enter a race for this position rather than having their plans progress unopposed. The 4th player will always be in this race, wheras players starting in more advantageous positions will not. The exact impact of this is hard to compute, but no player needs to compute it, the disadvantage is obvious to whichever player is last to reach an undiscovered civilisation without comprehending the model that generated the result.

I choose the second example because it’s highly unlikely to have been a conscious choice on the part of the designer. I can’t imagine the line of thinking that goes “I’m going to make it suck to go 4th, I hate things that are 4th, fireworks are awful.” It’s more to illustrate that simple mechanics generate complex models whether the designer intends it or not, so these considerations cut both ways. We can do wonderful things by implementing mechanics that are made possible by intricate underlying structures and then implementing them in such a way that the player never has to compute them, but we can also create unintended effects by creating systems that we don’t understand all of the consequences of.