Mostly not tricky; a few little tricky bits with 1-silver quibbles for expected profits of just half a silver difference. Somehow we don’t care about butchering more for tiiiiny profits, otherwise I’d just skip ’em and forgo a latte to gain back some time to… hm, maybe all this winter stuff means butchering is the most fun thing I could be doing. Nah, I can think of at least something more fun. If I see two possible bids off by small fractions of a silver in expectation, I’m placing the lower bid and getting my theoretically non-existent non-butchering-time equity.
This is well within budget, at 327sp, so we don’t need to worry about saving silver for lucrative late lots. And we expect to lose some of these bids anyway.
Revenue from selling butchered parts is, I think, Snow Serpent: 20+2d6 Winter Wolf: 25+4d6 − 2*age Yeti: 70+1d6 - {age}d6 EDIT: prodded and helped by simon, Yeti is revised to 72+1d6-{age}d6 for me. This is 45x less likely than 72+1d5-{age}d6 by the likelihood, but I’m deciding to say the universe-simplicity-priors against using a d5 there outweigh the 45x.
Your yeti revenue distribution would predict a maximum of 76 at day 0, but we see 77. We also don’t see anything below 73. I suggest 72 + 1d5 at day 0.
The full formula would be then 72 + 1d5 - {age}d6, where these are independent d6 rolls, and not a single roll multiplied by the age (I think this is what you meant, but clarifying since I wasn’t 100% sure on the terminology used). (The other interpretation would lead to too high variation at high ages, I think).
The formulas for Snow Serpent and Winter Wolf look consistent with the data to me.
Yeah I debated that, and some other similar modifications, but in the end my priors on what the natural laws of these worlds look like overrode what looks like it might be a better fit. We shall see...
:facepalm: that’s what I get for switching at the last minute. You’re absolutely right, of course.
I originally had 78 - {age+1}d6 but I figured there was no way that was actually the original formula. I don’t particularly like 71 + 1d6 - {age}d6 either. The means make “-{age}d6” look really good, but I don’t see any “nice” way to start it off. 72+1d5, like you said, looks great distribution-wise but 72 < {20,25} and 1d5 < {all the d6s}. 71+1d6 takes a hit on never rolling a 1 but gets a boost from 1d6 vs 1d5.
OK I calculated the likelihoods of getting the full yeti revenue data set for those distributions and got the following results:
For 78-{age+1}d6 (which is equivalent to 71+1d6-{age}d6):
likelihood ~ 10^-192
For 72 + 1d5 - {age}d6:
likelihood ~10^-189
So the 1d5 version is literally 1000 times better fit to the data, and I doubt that the prior for 1d6 over 1d5 is that strong. Besides, the base value of 72 is a round number in a way, might increase the 1d5 prior a bit. I’d definitely bet on the 1d5 version over the 1d6.
That’s pretty convincing. Let’s try all the maybe-reasonable-ish versions:
71+1d6-{age}d6 has log[10] likelihood of −192.02 72+1d6-{age}d6 has log[10] likelihood of −190.57 72+1d5-{age}d6 has log[10] likelihood of −188.91 71+1d6-{age}d5 has log[10] likelihood of −196.42 72+1d6-{age}d5 has log[10] likelihood of −206.39 72+1d5-{age}d5 has log[10] likelihood of −200.41
Definitively -{age}d6, sure. Now here’s a much tighter question: what about 72+1d6-{age}d6? It takes a x45 hit on the likelihood compared to 72+1d5-{age}d6, which is pretty big, but I think I’m willing to say the chances of using a lone 1d5 right there are a bigger penalty. So my revised guess is 72+1d6-{age}d6.
Mostly not tricky; a few little tricky bits with 1-silver quibbles for expected profits of just half a silver difference. Somehow we don’t care about butchering more for tiiiiny profits, otherwise I’d just skip ’em and forgo a latte to gain back some time to… hm, maybe all this winter stuff means butchering is the most fun thing I could be doing. Nah, I can think of at least something more fun. If I see two possible bids off by small fractions of a silver in expectation, I’m placing the lower bid and getting my theoretically non-existent non-butchering-time equity.
| lot | bid |
|---|---|
|1|56|
|2|21|
|3|18|
|4|24|
|5|36|
|6|24|
|7|18|
|8|18|
|9|24|
|10|22|
|11|21|
|12|18|
|13|27|
This is well within budget, at 327sp, so we don’t need to worry about saving silver for lucrative late lots. And we expect to lose some of these bids anyway.
Revenue from selling butchered parts is, I think,
Snow Serpent: 20+2d6
Winter Wolf: 25+4d6 − 2*age
Yeti: 70+1d6 - {age}d6
EDIT: prodded and helped by simon, Yeti is revised to 72+1d6-{age}d6 for me. This is 45x less likely than 72+1d5-{age}d6 by the likelihood, but I’m deciding to say the universe-simplicity-priors against using a d5 there outweigh the 45x.
Your yeti revenue distribution would predict a maximum of 76 at day 0, but we see 77. We also don’t see anything below 73. I suggest 72 + 1d5 at day 0.
The full formula would be then 72 + 1d5 - {age}d6, where these are independent d6 rolls, and not a single roll multiplied by the age (I think this is what you meant, but clarifying since I wasn’t 100% sure on the terminology used). (The other interpretation would lead to too high variation at high ages, I think).
The formulas for Snow Serpent and Winter Wolf look consistent with the data to me.
Yeah I debated that, and some other similar modifications, but in the end my priors on what the natural laws of these worlds look like overrode what looks like it might be a better fit. We shall see...
And yes, I was using standard https://en.wikipedia.org/wiki/Dice_notation
OK, I see such an argument for the die used, but the base value proposed can’t be correct with that die.
:facepalm: that’s what I get for switching at the last minute. You’re absolutely right, of course.
I originally had 78 - {age+1}d6 but I figured there was no way that was actually the original formula. I don’t particularly like 71 + 1d6 - {age}d6 either. The means make “-{age}d6” look really good, but I don’t see any “nice” way to start it off. 72+1d5, like you said, looks great distribution-wise but 72 < {20,25} and 1d5 < {all the d6s}. 71+1d6 takes a hit on never rolling a 1 but gets a boost from 1d6 vs 1d5.
OK I calculated the likelihoods of getting the full yeti revenue data set for those distributions and got the following results:
For 78-{age+1}d6 (which is equivalent to 71+1d6-{age}d6):
likelihood ~ 10^-192
For 72 + 1d5 - {age}d6:
likelihood ~10^-189
So the 1d5 version is literally 1000 times better fit to the data, and I doubt that the prior for 1d6 over 1d5 is that strong. Besides, the base value of 72 is a round number in a way, might increase the 1d5 prior a bit. I’d definitely bet on the 1d5 version over the 1d6.
That’s pretty convincing. Let’s try all the maybe-reasonable-ish versions:
71+1d6-{age}d6 has log[10] likelihood of −192.02
72+1d6-{age}d6 has log[10] likelihood of −190.57
72+1d5-{age}d6 has log[10] likelihood of −188.91
71+1d6-{age}d5 has log[10] likelihood of −196.42
72+1d6-{age}d5 has log[10] likelihood of −206.39
72+1d5-{age}d5 has log[10] likelihood of −200.41
Definitively -{age}d6, sure. Now here’s a much tighter question: what about
72+1d6-{age}d6?
It takes a x45 hit on the likelihood compared to
72+1d5-{age}d6, which is pretty big, but I think I’m willing to say the chances of using a lone 1d5 right there are a bigger penalty. So my revised guess is 72+1d6-{age}d6.
Nice analysis! But I am not so confident on how strong the prior should be and am somewhat torn on the conclusion.