"That means that for our posterior from above, if you choose blue, the probability of the majority choosing red is about 0.1817. If you choose red, it's the opposite: the probability that the majority will choose red is 1-0.1817 = 0.8183, over 4 times higher."
It may well be that I don't understand Beta priors, or maybe I just see myself as unique or non-representative. But intuitively, I would not think that my own choice can justify anywhere close to that large of a swing in my estimate of the probabilities of the majority outcome. Maybe I am subconsciously conflating this in my mind with the objective probability that I actually cast the tiebreaking vote, which is very small.
Thank you for making this. I have enjoyed following the D&D.Sci series, even though I don't get around to posting full solutions.
One thing that the series has given me is a better awareness of the limits of data science. Given enough time and effort, you can parse a data set along as many dimensions as you please, but the amount of time and effort needed grows exponentially based on the number of possible variables. If this scenario were a video game, I imagine that just controlling a party through a few different dungeons, and thereby seeing which ene...
Regarding the overall levels of successful teams: I was surprised to see that the total average level of adventurers on victorious teams was 3.69474, and on defeated teams it was 3.477. That's not as big a difference as might be guessed, and it suggests that the precise composition of the team (mix of types of adventurers) matters a lot more than the overall level. This is very helpful, because levels are the primary constraint on our resources.
To get possible insight into the various roles, I calculated the victory rates of teams that lacked a specific ty
If we filter the data based on the encounter which ended an unsuccessful Adventuring party, I notice that the groups foiled by Poison Needle Traps disproportionately had no Rogues.
Filtering by adventurer type, I notice that groups with no Rogues did not do well against dungeons with PNTs.
Thus, I think including at least one Rogue on the team heading for the Lost Temple of Lemarchand is wise.