In the book, Jonah and Tristan pitch an expanded view of Skill Challenges as an effective mechanic for many non-combat encounters and situations. If you haven't read it, I highly recommend the chapter, but the short version is that players make a series of naratively relevant skill checks trying to get 8 successes before 3 failures (the race to the finish and press your luck variants are awesome). They suggest setting DCs in d20 games so a 7 or 8 is required for success depending on the situation.
I worked with a data scientist friend to make a jupyter notebook to run simulations to model the skill challenges from Chapter 4 of Collaborative Campaign Design. We are using the PF2e four degrees of success (10+ and 10-, and 20 or 1 upgrades or downgrades one degree of success). We decided a crit would provide one token and remove one of the other type. The model assumes no use of aid or reroll mechanics (hero points, inspiration, etc). Results below.
i know, i know, reporting averages for asymmetric data, forgive me
BINARY, 8 successes before 3 failures, 10000 simulations
DC6 - 74.9% check success, 68.3% challenge success, 9.3 checks required
DC7 - 70.4% check success, 53.8% challenge success, 9.0 checks required
DC8 - 65.1% check success, 36.9% challenge success, 8.3 checks required
DC9 - 59.8% check success, 22.5% challenge success, 7.5 checks required
RACE, 8 successes, with a variable number of consequences due to failures, 10000 simulations
DC6 - 1.3 average, 1.0 median failures with 11.2 checks
DC7 - 2.1 average, 2.0 median failures with 12.2 checks (histogram shown)
DC8 - 3.2 average, 3.0 median failures with 13.2 checks
DC9 - 4.5 average, 4.0 median failures with 14.3 checks
PRESS, variable success at 2 failures (stopping before risking 3), 100000 simulations
DC6 - 8.4 ave, 6 median successes with 11.9 checks
DC7 - 5.8 ave, 4 median successes with 8.9 checks (histogram shown)
DC8 - 4.2 ave, 3 median successes with 6.9 checks
DC9 - 3.2 ave, 2 median successes with 5.6 checks
I could run other mechanics if they are of particular interest to anyone (5e, pbta, etc) and you help me get the specifics down.