I haven’t looked much into dependence on time and direction yet, apart from
noticing that the pirates decline in relative frequency
but, I would like some clarification about whether the 100gp budget is for a single set of interventions we’ll use on all trips, or is spent each time on a (potentially varying) arrangement. (edit: I see abstractapplicalready responded to such a question from Measure: it’s a single set obtained up front and not changed.)
My current thoughts:
From looking at the probability distributions, I mostly agree with gjm; my current recommendations are the same as GuySrinivasan’s and Measure’s.
Demon Whale distribution scares the crap out of me, and I probably panic buy all 20 oars allowed. I mostly agree that the distribution looks like it could be peaking near 100% damage, but I am not at all confident of this and think it could be consistent with something growing a lot bigger beyond the cutoff. I expect 250-1000 of the destroyed vessels to have been destroyed by demon whales. While it looks like it will be in control before needing 20 oars, I am uncertain enough to value oars pretty high. Budget spent = 20gp.
Merpeople have a very wierd looking distribution. It doesn’t seem to tailing off at the end, and so (like gjm) I am very uncertain about what happens after the 100% cutoff. I think (like GuySrinivasan) there’s a possibility that it has a multimodal distribution with another peak beyond 100% (not saying bimodal since there even looks like there might be a small peak around 25% distorting the main peak of about 50%, though this could very easily be random). I figure merpeople are responsible for around 200 (assuming no extra peak) or potentially vastly more (assuming an extra peak) of the losses. Merpeople are potentially another solid choice for mitigation imo, unless removing them from the encounter table puts in demon whales in as the substitute. Budget spent = 45+20=65gp
I do not agree with gjm that only about 1% of crabmonster encounters are terminal. The distribution seems to be tailing off very slowly, visually more or less consistent with a triangle-shaped distribution. A simple linear extrapolation would suggest a few percent which I would take as a lower bound. But it might not be linear, but slowing in how it tapers off, so it might be much much more than this. For all I know (apart from the finite number of sinkings) it might not even sum to a finite value. On the other hand, we only really care about crabmonster attacks that do less than 200% damage, since the only relevant intervention reduces damage by 50%. I estimate that between about 50 and about 250 of the destroyed vessels to have been destroyed by the relevant part of the crabmonster damage distribution, with potentially unlimited numbers destroyed by crabmonsters outside that range. Despite the expected max of about 250 mitigatable losses I consider arming carpenters a pretty solid choice for 20gp. Budget spent = 20+65=85gp.
Nessie looks like a pretty straightforward distribution where I assume about 10-20 losses are from the bit of the distribution we can’t see. A single cannon (which is all that we can afford after the other purchases) should suffice. Budget spent = 10+85=95gp.
Conclusion: 20 oars (20gp) + pay off merpeople (45gp) + arm carpenters (20gp) + one cannon (10gp), total 95 gp spent. This is the same plan previously recommended by GuySrinivasan and Measure.
Nothing else looks like it can kill us, unless e.g. some bimodal distribution has one of its humps located entirely within the >=100% zone.
However, stepping out of the pure data analysis and into reasoning about the fantasy world, it seems strange that pirates would bother to attack us if they only ever do 64% damage. They are intelligent, after all. Maybe they run away if in a hard fight, not sticking around to do more damage than that, and take over the ship entirely if they win? I might consider a second cannon (also provides extra insurance in case nessie’s distribution extends further than expected). Dropping 3 oars would provide the funds, and will probably still be enough for the demon whale.
(and...also anticipated by Measure on the pirate theory).
I haven’t looked much into dependence on time and direction yet, apart from
noticing that the pirates decline in relative frequency
but, I would like some clarification about whether the 100gp budget is for a single set of interventions we’ll use on all trips, or is spent each time on a (potentially varying) arrangement. (edit: I see abstractapplic already responded to such a question from Measure: it’s a single set obtained up front and not changed.)
My current thoughts:
From looking at the probability distributions, I mostly agree with gjm; my current recommendations are the same as GuySrinivasan’s and Measure’s.
Demon Whale distribution scares the crap out of me, and I probably panic buy all 20 oars allowed. I mostly agree that the distribution looks like it could be peaking near 100% damage, but I am not at all confident of this and think it could be consistent with something growing a lot bigger beyond the cutoff. I expect 250-1000 of the destroyed vessels to have been destroyed by demon whales. While it looks like it will be in control before needing 20 oars, I am uncertain enough to value oars pretty high. Budget spent = 20gp.
Merpeople have a very wierd looking distribution. It doesn’t seem to tailing off at the end, and so (like gjm) I am very uncertain about what happens after the 100% cutoff. I think (like GuySrinivasan) there’s a possibility that it has a multimodal distribution with another peak beyond 100% (not saying bimodal since there even looks like there might be a small peak around 25% distorting the main peak of about 50%, though this could very easily be random). I figure merpeople are responsible for around 200 (assuming no extra peak) or potentially vastly more (assuming an extra peak) of the losses. Merpeople are potentially another solid choice for mitigation imo, unless removing them from the encounter table puts in demon whales in as the substitute. Budget spent = 45+20=65gp
I do not agree with gjm that only about 1% of crabmonster encounters are terminal. The distribution seems to be tailing off very slowly, visually more or less consistent with a triangle-shaped distribution. A simple linear extrapolation would suggest a few percent which I would take as a lower bound. But it might not be linear, but slowing in how it tapers off, so it might be much much more than this. For all I know (apart from the finite number of sinkings) it might not even sum to a finite value. On the other hand, we only really care about crabmonster attacks that do less than 200% damage, since the only relevant intervention reduces damage by 50%. I estimate that between about 50 and about 250 of the destroyed vessels to have been destroyed by the relevant part of the crabmonster damage distribution, with potentially unlimited numbers destroyed by crabmonsters outside that range. Despite the expected max of about 250 mitigatable losses I consider arming carpenters a pretty solid choice for 20gp. Budget spent = 20+65=85gp.
Nessie looks like a pretty straightforward distribution where I assume about 10-20 losses are from the bit of the distribution we can’t see. A single cannon (which is all that we can afford after the other purchases) should suffice. Budget spent = 10+85=95gp.
Conclusion: 20 oars (20gp) + pay off merpeople (45gp) + arm carpenters (20gp) + one cannon (10gp), total 95 gp spent. This is the same plan previously recommended by GuySrinivasan and Measure.
Nothing else looks like it can kill us, unless e.g. some bimodal distribution has one of its humps located entirely within the >=100% zone.
However, stepping out of the pure data analysis and into reasoning about the fantasy world, it seems strange that pirates would bother to attack us if they only ever do 64% damage. They are intelligent, after all. Maybe they run away if in a hard fight, not sticking around to do more damage than that, and take over the ship entirely if they win? I might consider a second cannon (also provides extra insurance in case nessie’s distribution extends further than expected). Dropping 3 oars would provide the funds, and will probably still be enough for the demon whale.
(and...also anticipated by Measure on the pirate theory).