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Most people who have any interest at all in competitive gaming dislike randomness in games, but many still think that a small amount of it can be a good thing. That makes me really mad because it's obvious that the main problem with randomness - it punishes players for decisions that were actually optimal given their information - is inherent and universal; scaling down the degree doesn't change its nature. And all of the argued benefits of randomness are at best things you don't need randomness to get.
One of the most obvious arguments people make for RNG is that it helps keep every match fresh. However, games like Dominion and Prismata and even Chess960 refute the idea that in-game randomness is necessary for this.
How to create variety in a deterministic game
The randomness argument: "in a completely deterministic game, if you're even a little bit more skilled than someone else you'll win nearly all the time. It'll be hard to find opponents you can have a balanced winrate against".
Prismata is again a great counterexample. This is a deterministic pure strategy game with no hidden information or any other "randomness by another name" mechanics, and it has extremely high performance variance. From my experience as a near top player in Prismata I'd say a 200 elo advantage is something like a 70% winrate. I had a couple of wins against top players when I was about average level, and frequently lost to players 500 points below me when I was in the top 20.
How to replicate Prismata's performance variance
There's also an occasionally raised argument that randomness actually increases player enjoyment directly. It tends to go something like, "uncertainty is essential for engagement; if you know what's going to happen it can't be exciting". This is wrong because you don't know what's going to happen even without randomness. Try playing a game of chess and 10 moves in tell me if you know what the game is going to look like 10 or even 2 moves later.
Personally, by far the most exhilarating game I've ever played is the deterministic perfect-information (and turn-based!) Go.
This is an argument I've heard before: "randomness gives players a chance to come back after a mistake. This keeps the whole game interesting instead of making it get stale as soon as someone takes a significant lead".
This one is really ironic because this is actually a problem mostly created by randomness. Something exists called *resignation* which is the real solution to being behind; the only reason this argument even gets raised is because of games where you feel you can't resign because you might still win through luck. I used to play a card game called Spellweaver with a lot of randomness, and I had loads of experiences where I knew I was behind and I was no longer enjoying the game, but I couldn't resign because there was that one card in my deck that could turn around the game if I drew it; I had to hang on until the bitter end incase that happened. It was actually the randomness that was causing my misery. When I fell hopelessly behind in Go or Prismata I always just resigned and I was never dissatisfied beyond the inherent dissatisfaction of losing.
It's also not at all impossible to have a deterministic and fair game where comebacks are possible and commonplace. In fact strategy games are really the only genre that tend to lack comebacks without randomness. Fighting games usually have no randomness and comebacks are an everyday experience.
I discuss comebacks more in my page on feedback loops.
This might be surprising, but there's actually a pretty understandable argument that randomness helps make games deeper. Making the right decision a matter of probability can make it far harder to know what the right decision is; Spellweaver was actually a good example of this. There were a lot of common situations where the decision depended on what cards you wanted to assume the enemy might have, and so you could never really prove what the optimal decision was. Top players disagreed. And when I tried to create my own card game, I learned the hard way that removing hidden information, intended to make the game more deterministic and fair, actually trivialized most of the decisions and it just came down to deck matchups or draw luck.
But this doesn't mean that randomness is in any way necessary to create a sufficiently deep game, just that it can be one way to slap a bandaid on an otherwise dreadfully shallow game. The deepest game in the world is still Go as far as I'm concerned, and by orders of magnitude. So this doesn't make randomness a good thing or even a necessary evil, just a crutch that can cover for some of the weaknesses of an uninspired design by replacing it with other problems.
So no, randomness is not okay, and yes, it's possible to make a deterministic game with enormous depth, variety of experience, uncertain outcomes in unequal matches, very "exciting" to play, and doesn't bore the losing player.