Another Bayes Theorem question as it would apply to my solo gaming.
So you have Bayes THeorem: (P(A|B) = P(B|A) * P(A))/p(B). I am not sure what to do with p(B|A), p(A) and P(B) when I have no idea of their probabilities, other than to set their odds at 50% to start with. I don't really have a problem with that, but I would like to update their probabilities based on the outcome of that 50/50 roll-- and that I'm not sure how to do best or correctly.
I had a notion of maybe increasing or decreasing their probability by a each time or half a percent, but I really have no clue if that would be good or not. What approaches could one take to this?
I am just going to chime in to say that I really enjoy seeing a post about the applicability of Bayesian statistics to solo RPGs. The intersection of people who know and care about both of these things is super small. Without thinking much about it, I'd say set your priors to some version of 50/50 by default and only update when there's strong evidence that you should.
ReplyDeleteThanks for the suggestion! Still working things out so this helps.
ReplyDeleteI'd say "some halfway-sensible-looking percentage" than just "50/50" if it's supposed to be used for unlikely things such as "is there a dragon in the next room". :-) Presumably if this question even comes up it's because there has been some evidence in the rest of the dungeon to make you think of it, but of course that evidence should be applied on top of a sensible no-evidence prior like 1%.
ReplyDeleteFor estimating the initial prior of "will character E go to bar F tonight", this is just the product of (X:fraction of the population which drink)(Y:fraction of the drinking population which visit bar F)(Z:fraction of the week where a person may go out to drink that day)
Estimate X=70%, Y=1/(N:num bars in city), Z=20%, so the prior is (14%/N). You can call that her initial belief about visiting the bar, and update it as she sees evidence.