People Don’t Understand Probabilities – Case RECON

Okay, I’ve said that before, but here’s a good example from RECON, a pretty old RPG published by Palladium, even if its outside of the Palladium family.

The game has three “major characteristics”: alertness, strength and agility. Making a character starts with rolling d100 for each of them, but if the total of the three characteristics is less than 100 or any of them is less than 30, you can declare the character “4-F” and reroll the whole character again.

What does this actually mean?

How many people have a characteristic below 30? Gladly, this is quite easy to calculate. Its just 1-(1-0.29)^3 = 0.642089. Okay, so that would mean almost two thirds of people are unfit for service.

“Okay,” you might be thinking to yourself, “but that’s only for game balance reasons”. Sure, you might think that way, but it actually shows a great misunderstanding about humans. This would still mean that even within the army, there are so vast differences between people that some person can be three times as strong as someone else.

But okay, lets look at the other rule. How often is the total less than 100, but none of the characteristics is under 30? This isn’t quite that trivial to figure out, but at the same time it isn’t that complicated. First, we know that if one characteristic is 40, at least one of the other two would need to be less than 30 to make the total less than 100 (40 + 30 + 30 = 100).

So, the lowest possible is 30 + 30 + 30 (= 90) and the highest possible is 99 (33 + 33 + 33 for example). The latter can be attained by a variation of different numbers, such as 39 + 30 + 30, and I bet there’s a way to calculate these, but since I’m a coder, I used a few minutes to make this little piece of code:

$total = 0;

for($i = 30; $i < 40; $i++)
        for($j = 30; $j < 40; $j++)
                for($k = 30; $k < 40; $k++)
                        if($i + $j + $k < 100) $total++;

echo $total;

Before I tell you the result (which was actually somewhat smaller than I expected, but not that much), I'd like you to think about this for a second. How many often does this rule come into play? If you consider that the range is about 10 out of hundred for each characteristic, you might think that it's about 1 in 1,000 (0.1^3), which is not very accurate, but a good starting point.

The actual number is 220 out of 1,000,000. So, basically never, or at least not frequently enough to warrant a rule.

This makes me feel that the rules were never actually even tested in a meaningful way. They were just made based on a hunch. Sure, its an old game (from the 80s), so its ancient technology, but has the ability to assess probabilities really improved? One would hope that after being inundated in games for the last decades, many people are better at it, but I doubt it.

Would you have assessed the probabilities correctly or anywhere near that?

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