I'm not sure I buy 'second is the worst' in general either...anything above 1 escalates in how 'bad' it is, it's just also the only way to get more and more successes.
That's not true, though. That' s just mathematically false.
It's like this. Each die has two parts - a good side and a bad side. The good side is a 1/3rd chance of +2 and a 1/3rd chance of +1. The bad side is a 1/3rd chance of -1, but it only unlocks if there are enough successes in the pool to cancel out.
With one die, it's easy - you have no chance of unlocking your negative, so your average payoff is just 1.
With two dice, you have a 2/3 chance that your first die gets a success and thus unlocks your second die's negative... but you
also have a 2/3 chance that your
second die gets a success and unlocks your
first die's negative. So basically, for the second die and the second die only, your cumulative effective "chance to unlock negative" is 4/3.
now, with two dice you have a chance table like so:
431
320
100
which means that you (again) have a 2/3 chance of having at least one success sitting. So your third die has a 2/3 chance of unlocking its negative, but doesn't actually increase the chance of hitting negative for the first two at all.
I suspect that it gets worse from there, but the 2nd die is worse than any later die
could be, and the third is the second best die on the list.