HandofMystra said:
I noticed that it was pretty to easy to compute success probabilities for the different complexities. It seems that the different complexities make little mechanical difference (the lower complexities are a bit more forgiving at lower individual success probabilities than the higher ones) in the success rates, so the only reason you would use one complexity over another is gameplay/flavor.
Thanks for posting this! The results make complete sense now that I think about it.
With 2 successes consistently needed for each 1 failure allowed, an individual probability of success of 0.67 means that the number of 'batches' of 2-for-1 is irrelevant, and that's the p value for which you see the final success probability independent of the complexity. Also, at this point, you need two successes in a row to succeed - 2/3 squared is 4/9 is 0.44.
When your probability on a given try is LESS than 2/3, a lower complexity actually helps you because you need to be lucky to succeed.
When your probability on a given try is MORE than 2/3, a _higher_ complexity helps you, as the law of averages is on your side.
Why is it always 2:1? Other ratios would seriously skew the final chance of success. The way it is with 2:1, a 2/3 chance is neutral. That's 7 on a DC 15 check. Well, that's the standard +5 bonus for trained skill and a typical 2 points for stat bonuses. This makes it balanced right from level one, and will scale perfectly. For that same +7 vs DC 15, requiring 3 successes per one failure would mean your chance of final success would be just 30%. 4:1 would be 20% - and those are with Complexity level 1. Odds would plummet for anything more complex. Conversely, a simple 1:1 ratio would give 67% chance of success, and higher complexity would make it extremely unlikely you would fail. It would probably work fine to tweak a 6:3 challenge to 7:3, or if failure wasn't catastrophic, 6:2.