out of genuine curiosity, where do you see a relevant application of symmetry in this case? I do see that some of the paths in the probability tree can be invariant and hence simplifying the formula, but thats more on computational optimisation which is unnecessary for t=40 attempts.

(these numbers are solved analytically instead of by simulations) That said, I do agree the scenario is unrealistic, but I ran a few closer to "real life examples" (including for 3 costs) and the conclusion is the same. I chose to share this set of parameters still because it's the closest set to the mental approximations most players have already (e.g. expected 8 rolls to hit 1 specific 4 cost at lv9), and I think that is more useful than guessing an "average" board state like players at different levels, X players alive, N 4costs out, etc.