My fairly low-effort attempt:

My goal here was roughly to minimize the amount of manual analysis. I used Python to graph the mean revenue by species and age, and also estimate the distribution along which other bidders bid.

Everything seems roughly linear, with perhaps some nonlinearity in winter wolf bids. Given that the sample mean revenue should be an unbiased estimator of revenue, and the probability of winning for a given bid should also be an unbiased estimator, we can use linear regression for each species to estimate revenue, and logistic regression on (age, bid) to estimate the probability of winning a given auction with a given bid. 

Using logistic regression implicitly assumes the distribution is logistic, which might be problematic but seems okay. Since we want to maximize expected profit = p_win(bid) * (revenue - bid), we can throw this into the scipy black-box optimizer to find the bid price that maximizes profit. This gave us the following bids:

One could probably do better by actually looking at the distribution of non-carver winning bids, but I don't know the best way to account for selection (using the distribution directly would create a biased distribution, since they're always higher than the carver bid).

Why would you? The point of the box spread trick is to reduce interest on margin loans, they don't increase your buying power. Selling box spreads without a margin loan just makes you pay small amounts of interest for no reason.

Let's define Levin$${}_f$$ complexity as $$2^l+f\left(t\right)$$, where l is description length and t is execution time

Should this be l + f(t)?

This seems right, thanks.

I'm confused too. Say you sold 10 3200/3400 box spread contracts for $196k a while ago, for a "par value" of $20k per box or $200k total. Since the exact box spread you sold is rarely traded, the best bid in the order book will be the sum of the 4 individual leg bids, and likewise the best ask will be the sum of the 4 leg asks. This makes the spread very wide, maybe $15k bid and $25k ask, and I'm not sure how IBKR values your position, maybe it just takes the midpoint. Let's say it's normally -$197k at some point in time.

Now say someone buys a 3200/3400 box for $25k. I'm guessing that IBKR's algorithm could see the last traded price, decide your position is worth $-250k now, and liquidate you. If you keep an open order to buy back the box for say $16k each, nothing changes and in fact the midpoint price would increase. Maybe the commenter meant to say you should keep an open order to sell more box spreads for slightly above par value?

I agree that closed physical systems aren't optimizing systems. It seems like the first patch given by the author works when worded more carefully: "We could stipulate that some [low-entropy] power source [and some entropy sink] is provided externally to each system we analyze, and then perform our analysis conditional on the existence of that power source."

Then an optimizing system with X bits of "optimization power" (which is log(target states / basin of attraction size) or something) has to sink at least X bits, and this seems like it works. Maybe it gets hard to rigorously define the exact form of the power source and entropy sink though? Disclaimer: I don't know statistical mechanics.

I haven't let one expire yet, but that looks right. I don't anticipate any major problems because none of the sources I've seen mention any, and besides all legs expire on the same day.

Note that the loan value already has to be within margin borrowing power throughout the entire duration of the loan, since your broker takes into account the box spread as a negative-value asset when calculating margin. Box spreads can't get you more borrowing power (it's box spread financing, not box spread borrowing).

My understanding is that each leg of the box spread is marked-to-market, resulting in a small overall capital loss equal to the interest you're paying to the holder of the long box. For example, the market is up this year, so the bullish legs gained value and the bearish legs lost slightly more value. This is how the Interactive Brokers tax forms work; on the section-1256 section of the 1099 form, the line "Unrealized profit or (loss) on open contracts - 12/31/2020" has a loss of about $2000. If interest rates rise so much during a year that the interest is negative, I would expect there to be a small 60/40 capital gain. I could be missing something though.

(For example, imagine a u-shaped craft with a low center of gravity and helicopter-style rotors on each tip. Add a third, smaller propeller on a turret somewhere for steering.)

Extremely minor nitpick: the low center of gravity wouldn't stabilize the craft. Helicopters are unstable regardless of where the rotors are relative to the center of gravity, due to the pendulum rocket fallacy.

Depends whether you're holding it as SPY/VOO or as a mutual fund (assuming you don't mean SPX futures, and SPX itself isn't tradeable). IBKR has somewhat higher margin requirements than the minimums set by the OCC; I think they require 25% maintenance margin for mutual funds and 10-15% for broad-based stock indices.