Above I explicitly noticed that Carver’s bids would distort the distribution, set that aside, then, when I encountered a skewed distribution, failed to think to attribute it to Carver’s bids. But of course that would be the obvious explanation.
I looked at this, and found that the actual distribution does match pretty well what I’d expect if the true distribution of non-Carver bids were a uniform distribution for old carcasses, though the skew effect was only really dramatic for Snow Serpents anyway.
(edit): Assuming this is correct, we can now better calculate the probability of losing if we bid lower.
For Lot 10: 23 v. 22 sp on 7 day wolf, we cut win rate by exactly 1⁄3 going down to 22, the revenue is a bit over 25 by my linear fit or exactly 25 by GuySrinivasan’s formula; meaning, if GuySrinivasan is right then the average profit is exactly the same either way.
For Lot 11: 22 v. 21 sp on 8 day wolf, we exactly halve win rate going down to 21, the revenue is a bit over 23 by my linear fit or exactly 23 by GuySrinivasan’s formula; meaning, if GuySrinivasan is right then the average profit is exactly the same either way.
(edit2): A further note—Even though accounting for Carver’s bids when calculating the old-carcass bid distribution dramatically reduces the loss probability from bidding low on Snow Serpents, it’s still not worth it to bid low on them (since 1⁄8 probability of losing more than makes up for profit going from 9 to 10). However, if the parameters of the problem had been changed a bit, this could have been a nice trap.
(edit3): Or wait—do we actually know that the non-Carver bid distribution for Snow Serpents only goes down to 10? what if it goes down to 8 or lower, but we miss those because carver bids over those? Carver’s bids go down to 9, so we could theoretically see a 9 non-Carver bid, but the data might not include any by coincidence. We can’t possibly see a non-Carver bid below 9. Looking at this—no, if it goes down to 8, the number of non-Carver bids we’d expect to see seems too low—I’m reasonably confident it doesn’t go down that low.
Above I explicitly noticed that Carver’s bids would distort the distribution, set that aside, then, when I encountered a skewed distribution, failed to think to attribute it to Carver’s bids. But of course that would be the obvious explanation.
I looked at this, and found that the actual distribution does match pretty well what I’d expect if the true distribution of non-Carver bids were a uniform distribution for old carcasses, though the skew effect was only really dramatic for Snow Serpents anyway.
(edit): Assuming this is correct, we can now better calculate the probability of losing if we bid lower.
For Lot 10: 23 v. 22 sp on 7 day wolf, we cut win rate by exactly 1⁄3 going down to 22, the revenue is a bit over 25 by my linear fit or exactly 25 by GuySrinivasan’s formula; meaning, if GuySrinivasan is right then the average profit is exactly the same either way.
For Lot 11: 22 v. 21 sp on 8 day wolf, we exactly halve win rate going down to 21, the revenue is a bit over 23 by my linear fit or exactly 23 by GuySrinivasan’s formula; meaning, if GuySrinivasan is right then the average profit is exactly the same either way.
(edit2): A further note—Even though accounting for Carver’s bids when calculating the old-carcass bid distribution dramatically reduces the loss probability from bidding low on Snow Serpents, it’s still not worth it to bid low on them (since 1⁄8 probability of losing more than makes up for profit going from 9 to 10). However, if the parameters of the problem had been changed a bit, this could have been a nice trap.
(edit3): Or wait—do we actually know that the non-Carver bid distribution for Snow Serpents only goes down to 10? what if it goes down to 8 or lower, but we miss those because carver bids over those? Carver’s bids go down to 9, so we could theoretically see a 9 non-Carver bid, but the data might not include any by coincidence. We can’t possibly see a non-Carver bid below 9. Looking at this—no, if it goes down to 8, the number of non-Carver bids we’d expect to see seems too low—I’m reasonably confident it doesn’t go down that low.