by JoeAubrey
Last game I received the starting occupation "Proficient Hunter" (153a) which says "Each time you take an action requiring a dice roll, you can roll up to 4 times instead of 3." My first thought was "whoa, this is amazing." Then I noticed it was worth 2 points, and generally, when a card is less powerful, it's balanced with points.So I wondered: what is the probability of rolling a specific number you want in 3 or 4 rolls of an 8 or 12 sided dice?
I am far from a mathematician, but I found this discussion: https://math.stackexchange.com/questions/1894684/what-is-the...
Probability of receiving a specific result:
1−(1−1/x)^y, where x = number of sides and y = amount of rolls
1−(1−1/x)^y, where x = number of sides and y = amount of rolls
So let's assume you have 1 bow/wood and you take the hunting action. You HAVE to roll a 1. What are the chances of rolling a 1 in three and four rolls?
3 rolls: 33%
4 rolls: 41%
And the same for whaling (12 sided dice and with no resources, only the whaling boat worth one ore)...
3 rolls: 23%
4 rolls: 29%
As you can see, an addition of 8% and 6% when needing a specific number isn't enormous. So perhaps that's why "Proficient Hunter" is worth 2 points. It is nice, though, to see even without that occupation, the chance of success in the worst case scenario is 1/3 and almost 1/4 for Hunting and Whaling.
BUT, I have to think getting a 4th roll is much more powerful for raiding and pillaging or if you have more resource options for all dice actions. Because you don't always need a specific number. A range of numbers could be great. But that math is beyond me. It also gets more complicated when you roll a "successful" number, but decide you want to push your luck towards a better result.
Anyone else willing to take a stab at the value of "Proficient Hunter" for other situations? Or correct me on the half-understood math above?