Friday, November 11, 2011

The Psychology of Probabilities

In a conversation regarding saving throws I had, someone argued that magic users had better saving throws versus spells than the other character classes, hence it wasn't worth attempting to cast a Light spell on their eyes.  When you work out the numbers, though, a level 1-5 magic user has only a 35% chance of saving and a 6-10 level magic user still has less than 50-50 odds.  When you throw initiative into the mix, the chance of coming out on top is better, but it's by no means decisive.  Since we're gambling, D&D is, after all, governed by chance, I'd say cast the spell on a spell caster.  They may do better than average at saving but it's still not great.

That left me wondering about the psychology of probability.  It seemed like the fact that a character had better than average odds of success was taken to mean that they had good odds of success, which isn't the same thing.  I guess it revolves around what you mean by "good."  "Good" in this case is a relative term.  One must always ask "good compared to what?"  If they mean other characters, then yes, magic users have good saving throws versus spells.  The thing is, what really matters is not the other characters.  A probability is a number between 0 and 1.  With 0 meaning I'd bet I'll never happen, and 1 meaning I'd bet it'll always happen.  Ideally, when one makes decisions, it'd be with only the 0-1 scale in mind for assessing their risk of failure.  In practice, though, this person seemed to reveal that what really matter is other people's risk of failure. 

It seems like a statistical version of keeping up with the Jones'.  As as if people aren't going to do something because objectively they'll do well.  They're going to do something because they're more likely to better than they other guy.


  1. This is something I've noticed a lot over the years: people (even gamers) often have odd misconceptions about probabilities, and seem especially attached to them. I remember one conversation with someone who talked about adding instant-kill criticals to D&D, and rejected my arguments that it would increase lethality (and so work against the PCs); because the same rule would apply to the monsters as the PCs. No matter how many counter-points I raised, he always resorted to "no, the same rule applies to both sides, so it's balanced". I don't think he ever actually went ahead with that, thankfully. :)

    Another funny thing I've noticed is the perception of risk. One player seemed totally unconcerned about save-or-die because his character only failed on a natural 1, as if a 5% chance was insignificant. Another player, in a Dark Sun game, had a psionic power that improved his fighting ability but forced a system shock roll (99% in his case) or die - he used that power in every fight, as I recall, with no sign of tension when rolling the dice. It seems to me like about 1% - or certainly in the low single-digit percentiles - is when a risk becomes seen as insignificant to players, even when the cumulative risk actually gets much higher over multiple risks.

    1. Heh.. "balance" is a concept I don't like because in my experience it means different things to different people.

      Regarding risk, 5% isn't that scary and it IS only a game. The 1% is even better. If you're going to quantify risk, you generally multiple the probablility of loss and the loss. If you have effectively nothing to lose (It's only a game!) then the risk taking is ultimately all in good fun and everyone goes home happy. In this sense the GAME part of roleplaying GAME distorts the ROLEPLAYING part, so maybe their characters are behaving with indifference toward their own lives, but when you live in someone's imagination, it's a more dangerous world because they have nothing to lose by you going away! :-)