Randomness Helps the Weaker Party

I am still playing several rounds of Elements per day, and the perverse randomization really strikes me at times. If I could just have the expected value of my deck, I would win a lot more than I do. As it is, I have seen a 1/12 chance fail to come up 54 times in a row. Which has a 1% chance of happening, so it must be happening more often than I notice.

If you do not understand the math on why randomness helps the weaker party, it requires the assumption that “losing” and “losing big” have no different consequences. Let’s say the other person is 20% better than you, however you would measure that. On average, he should win every single time you two are opposed. Now add some randomness: if you both do better or both worse, it is a wash and you still lose; if he does better than usual and you do worse, you get crushed; if he does worse than usual and you do better, you win at least half of those games. Adding randomness lets the worse party win what would otherwise be a guaranteed loss.

This was first driven home for me in pen-and-paper RPGs. Randomness benefits the monsters, as do things that exploit it like critical hits and fumbles and auto-hits/-misses on 20s/1s. The average goblin may have a life expectancy of six seconds, but he still hits on a natural 20, and depending on your system/edition/house rules, that may also be a crit. If you just checked the attack bonus against your armor, every goblin would always miss. Similarly, if you hit a goblin with a critical hit, so what, it was dead in one hit anyway; if you hit a PC with a critical hit, that could matter. If the goblin fumbles, it dies unarmed instead of armed; if a PC fumbles, that could matter.

This is great for the player if something is really hard and you only need to do it once. You can keep throwing yourself against that wall until the dice come down ridiculously in your favor. “Achievement unlocked!” and you can move on. If you want to beat the last StarCraft II mission easily on the highest difficulty, you can save and reload every time the Nydus Worms appear somewhere inconvenient; those are random from a limited pool, so you can eventually get them to appear in spots where they will instantly be destroyed. It’s not sporting, but there are surely many who thought that mission was trivially easy, others who thought it was near-impossible, because of the randomization. On the other side, this is horrible for the player if the difficulty is high and then you add randomness. That can make it randomly impossible, with the added bonus of making you wonder whether you actually earned that victory or just got the lucky equivalent of that Nydus Worm save-scumming I described.

If you have a fair amount of randomness, adding more trials brings you closer to the expected value. This is why you play best-of-whatever. Over a large number of attacks, that critical hit chance might come to a 5% damage bonus. The longer the fight and the more trials, the more skill can overcome perverse random events. Compare basketball to soccer/football or hockey. Basketball games have scores like 96-84; if a referee messes up a call, oh well, that’s few-point swing, which is upsetting when it matters but it usually balances out or does not matter. World Cup games frequently end 1-0, and more than 10 goals would be a ridiculous game. One odd occurrence, one bad referee call, and that changes the entire tournament.

You will occasionally see books or movies that recognize the high randomness, high consequences nature of real life combat. These tend to be dark and jarring, but you would have thought one random bullet would have caught Batman in his utterly unprotected mouth by now. You will not find many games with one hit kills and no respawn (feel free to refresh).

: Zubon

5 thoughts on “Randomness Helps the Weaker Party”

  1. Nice explanation Zubon. I remember reading that competitive fps games often disable criticals for this very reason.

    Mind you I can see a justification for randomness. Take the example you have given of a player who is 20% better and without randomness they win every game. I imagine (although the precise maths eludes me) that there is an appropriate level of randomness you could add that would see the better player win just 20% more games. The competition is no longer a white wash but instead each player wins on average according to his/her skill level.

    Poker is an example of a game with a very high level of randomness and yet no-one doubts that better players always win out in the long run.

  2. yeah I was immediately in love with elements, but once I got my Entropy/Aether deck fleshed out (my own damn fault) the coin-toss nature of the game thereafter caused me to walk away never to look back. :\

  3. The basketball / netball / european handball family of sports still suffer from “randomness”, but in the opposite direction. In soccer, you very rarely score. The ideal in basketball is that you never fail to score on your turn. Though in basketball you typically have a lot more “fail to score” cycles than you’ll have “score” events in soccer, and this mitigates the effect of a single mistake event. Even 10-20 “events” per game is enough that +/- 2 or 3 can be absorbed unless the teams are so evenly matched it’s not funny.

    Aussie Rules Football is interesting in that scoring events vs not scoring events are both sufficiently frequent that simply reading the scoreline tells you a lot about who controlled the game.

    The real skill with randomness in game design is to make the changes subtle. The randomness needs to “random walk” the game state in a manner that makes the players chase it / adapt to it. The bigger the stake, the more likely a single random event – no matter how unlikely – can trump player skill.

    You also need to design on the assumption that “stupidly unlikely” events will happen eventually. This doesn’t matter so much for games which reset frequently, but for a “campaign” game that is intended to continue in the case of failure, there needs to be a player-controlled abort where the player can cut their losses in the face of overwhelming bad luck.

    1. You also need to design on the assumption that “stupidly unlikely” events will happen eventually.
      If there is a possibility of a one-shot kill crit, it will eventually happen to any character. If this is old D&D, with the chance to not survive a resurrection attempt, you can work out the exact chance that, on any given attack, your character will be permanently killed. Multiply that by the number of enemies you expect to face…

  4. The other part of the randomization argument is when to apply randomization and when not to. I agree that randomization is necessary to prevent both predictable outcomes and discouraged newbies, but developers need to learn when random events are exciting and engaging, and when they’re just plain irritating.

    Compare WoW to FFXI in regards to their crafting systems. Long ago you could fail at crafting and gathering on a fairly regular basis, and the average orange-difficult node produced a few failed attempts before it was completely drained. It served no purpose other than to produce uncertainty, and the result was nothing but frustration. So they changed it. FFXI had crafting system that factored in not only a random value, but also the direction you were facing, the phase of the moon, the time of day, the day, and whether you had woken up on the left side or right side of your bed that morning. And it sucked. And as far as I know, it was never fixed. Was it a mysterious system that a few people really enjoyed divining the algorithm of? yes. But most of the people who used it just got pissed off and frustrated.

    My extended point here is that randomization should more often than not be used exclusively for things that yield some positive effect. Random fails that add nothing but frustration are pointless. Random critical effects that give you an unexpected bonus are awesome. People are psychologically rooted in the concept of control, and if they can’t control something they need to at least be able to predict it. The last part of this rule should be that if they can’t predict it, then it should at least yield some benefit to them when it happens so they aren’t surprised in an offputting way. The only exceptions I see to this are Missing in PVP and random traps in dungeons THAT ARE FUNNY. Random death sucks, but if you unexpectedly witness your character being simul-sliced into ten pieces by hidden blades, at least you got a chuckle :)

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