Just a Thought on Randomness

Humans are terrible when it comes to randomness. They're bad at recognizing it; they are terrible at producing it. I think most people realize this so I'm not going to go on about it at any length. Instead, I want to provide an example which I find amusing.

Years back, a video game named Fire Emblem came out for the Game Boy Advance handheld console. It was a tactical role-playing game in which units fight one another. Whenever units attacked one another, they had a chance to hit and a chance to get a "critical hit." As is common in anything with randomness, people often complained about how they were unlucky in it. Quite often, people would say they thought the game's random number generator (RNG) was biased.

They were right. Kind of. You see, the game developers knew people feel this way when playing games. They knew no matter how perfectly random results might be, people would think they saw patterns in it. To try to reduce the unpleasantness this creates, the developers decided to rig the chance to hit rolls. Instead of rolling one random number from 1-100 for the percent chance to hit, they made it so the game rolled two numbers from 1-100 and averaged them.

Yeah, that's right. If you have a displayed 99% chance to hit, the only way you'd miss is if you rolled the 1% chance twice, If the opponent had a displayed 10% chance to hit, their actual chance to hit would be much lower. Yet people playing the game routinely complained about the RNG being biased against them.

I thought that was amusing enough to share.


  1. People are extremely bad at estimating risk, too. I think it's because we're wired to see patterns so we invent them on the skimpiest amounts of input. Then emotions take over...

  2. Strange that the game developers would persist in using the "% chance to hit" terminology, when it clearly is no such thing.

    Stat nitpick: if they're averaging the two rolls, a displayed 99% chance to hit should miss on (100,100), (100,99), & (99,100), right? Still far from a true 99% chance. In general, a displayed N% chance to hit (with N>50) will miss on (201-2*N)*(200-2*N)/2 permutations out of 100^2 possibilities, hitting more often than the displayed chance.

    On the low side of the curve, a 1% displayed chance to hit will hit only on (1,1). For N<=50, it will hit on (2*N)*(2*N+1)/2 permutations out of 100^2, always less than the displayed chance. The combination of the two segments creates a sigmoid curve.

  3. HaroldW, good catch. The chance of missing with a (displayed) 99% hit rate is 9,997/10,000 as there are three cases like you describe. And to be more precise, I believe the game rolls from 0 to 99, not 1 to 100. That doesn't change anything in function though.

    And yeah, the result is a sigmoid curve. I didn't know the name of it until you mentioned it. I'm pretty sure the reason the devs use it while displaying the incorrect values is just to make players feel better. In the game, your characters will generally have higher stats than the enemies (as you have to face more of them than there are you). That means the player tends to be rewarded by this system while the enemies are punished. That, to an extent, combats the perception bias where people think the RNG is "out to get them." I am sure if the game showed accurate values, more people would complain about the RNG than they do with the false ones.

    By the way, there were several more games in the series which use this same system. They've all been better received than the ones which didn't. It seems a lot of people like being lied to in this way.

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