Originally Posted by

**Jurand of Cracow**
Guys,

I've noticed (and it was reported from the players) that *sometimes *a trigger with very low probability fires very often.

I have a trigger of 2% for a negative trait (in this case Coward) but it fires much more often than expected (from non-representative trials I'd infere 5%). The players report that every character gets it - and it should be 1 in 50 turns (

I've checked a few times if there's no other situations, no other triggers etc - no.

I also doubt that there's a bias perception (we discern only the negative situations) - it's too often reported.

Has this phenomenon been reported in the past?

Any solution? I think I'll make traits starting with 2 points first thresholds - if there's a bias only for the first point...

cheers

JoC

Hmmm, I see no contradiction between the statements "I have a trigger of 2%" and "the players report that every character gets it". After all, 2% with WhenToTest set to CharacterTurnEnd means that I expect the trait to show up during the lifetime of a character who fulfils the conditions for the trigger. Each trigger fires independently for each character, so I don't exactly get what you mean by "every character gets it - and it should be 1 in 50 turns".

In this game, we deal with a geometric distribution. Getting a point in a trait via a trigger is a process following the logic "let the probability of success at an event be p; the probability that the first occurrence of success requires k independent trials is given by

P(X=k) = p(1-p)^(k-1)

which is the geometric distribution. The mean of this distribution is 1/p. In your case, where p=0.02, the mean first occurrence of success is 50 turns. The variance is high though, so giving only the mean first occurrence of success is not that relevant: in this specific case I would rather say that I don't expect this trait to pop up at turn 1, but I'd be surprised if it didn't show up after turn 100, which I guess is within the lifespan of a character.

Without any proper testing it's hard to say something meaningful, unfortunately, so you may be right: after all I guess nobody really knows how the chances of success are calculated, so there might be an error that shows up only at the lower end of the spectrum of probabilities (very typical; boundaries are always critical).

Concerning your other question: it's entirely possible to calculate the difference between one single trigger with 10% chance and 10 triggers with 1% chance. Since each trigger is an independent event, the probability of having no success at all in all 10 triggers is the probability of failure (99%) multiplied by itself ten times, so (0.99)^10=0.904. This means that the probability of getting at least 1 point in your trait is 9.6%, slightly lower than the single trigger with flat 10% chance. Of course this doesn't take into account 1) the possibility of errors in computing low probabilities, as we already mentioned, and 2) the cases in which you aren't dealing with only one level of a trait with threshold 1. The former has no solution apart from testing, the latter needs more specific calculations but it's computable. At least with this method you are able to calculate the expected values for the probabilities, in case you want to do some testing.

I hope this helps, even if I couldn't give a specific answer to your question.