So Jay asserted that proficiency dice are only a small bonus over ability dice. I doubted this - after all they are so much more fun to roll. Being bored at work I decided to do some math. Who doesn’t love math?
The goal of this math was to figure out how many success and avdantage symbols each die could be expected to roll. This would show how much of an advantage the proficency die really was.
Chance of at least one success: 4/8 -> .5
Chance of an additional success: 1 / 8 -> .125
Total chance of success = .5 + .125 = .625 therefore we expect each ability die to generate .625 success on average.
The math is the same for advantage symbols. .625 advantage symbols per ability die rolled.
Proficiency die (we will be counting the triumph symbol as a success):
Chance of at least one success 8/12 = .667
chance of an additional success 2/12 = .167
Total number of success per die = .833
chance of one advantage symbol: 6/12 = .5
chance of an additional symbol: 2/12 = .167
Total number of advantage symbols: .667
Its also worth noting that there is a .083 chance of a triumph symbol. That one is super keen.
My final analysis is that while proficiency dice are definitively better than ability dice the advantage is still to the person who rolls more dice. Conclusion: don’t spend points on skills at chargen.