> Let's start from the other end. Just a pawn and two kings. It's possible to describe some quite succinct rules for when that's a draw versus a win for the side with the pawn. Agreed? Club players know these by heart. You could write that doen as invariants. As long as the side with the pawn stays inside the "green zone" of the state space, there is nothing the other side can do to void mate.
The flaw in this line of reasoning is that it's easy to come up with a theorem that works for KP vs K. However as the number of pieces increases, it becomes impossible to distill all the branches of possible moves into a simple theorem like that. If what you said were possible, endgame would be a simple flowchart, but look at how much time even GM players use in endgame and how often mistakes are made, and you'll recognize Chess endgame is not distillable into a simple flowchart when there are even as few as 7 pieces on the board.
Given the above, the only option is enumeration, if you want to prove that in all cases the outcome is White win or draw.
Tesla IPO'd at 1.7B and is worth 1.4T today. Giving you the benefit of doubt since it would be closer to a 1000x gain rather than the 100x gain that you didn't buy right at IPO, I will point out that there's a world's difference buying in at 1.7B, because there's still room for the stock to 1000x, but there's not much gain to be had buying in at 1.7T valuation.
Even the most highly company in the world Nvidia is less than 3x that valuation, so it's not a good comparison with Tesla's IPO.
Direct indexing will soon be able to provide that functionality of giving you S&P 500 stocks minus A, B and C companies you don't want to hold. However, cheap and reliable direct indexing brokerages aren't out there yet. Hopefully more competitors show up and help lower the prices for everyone.
This reminded me of those booths they have at company holiday parties where they take a photo of you, convert it to a line drawing and have the robot draw it out for you to keep. Very cool hack!
I had this same feeling. Same with reading a biography of Kurt Vonnegut. Before reading it, I thought of them in idealistic ways. They had multiple affairs and weren't such great people, even though they both wrote really, really well.
Even with the sub-heading "It's legal, and that's the problem."*, and even though this kind of cheating is broader than this reply chain from "There is no such thing as too big to fail in China", this is absolutely within bounds for what I asked for :)
* and the not-proof-read AI generated image, that never helps…
+1 The long gap between 2016 when the original article was written in Chinese and 2025, the fact that the Substack article does not cite the original Zhihu article (until someone other than OP linked it in this thread), not linking previously English translations of this article, and the financial incentive of the LLM-translated article being on Substack make OP's claim of authorship of the Chinese article very sus.
Thanks for the info! I don't have a Zhihu account to check myself, but I believe you.
I think it would be helpful to dispel any confusion if you added somewhere on the Substack post (e.g. at the bottom) the above message you are the author of the Zhihu post.
Practically anything you can find online videos for are better than their counterparts from low end restaurants. I have a lot of favs, but most are regional dishes that are not very well known internationally. Pastas are an exception. Cakes too taste a whole lot different and much richer when you do it.
Bogleheads [1] gives better financial advice than HN. Every time I peruse some threads there, I learn something new about personal finance I didn't know about.
The flaw in this line of reasoning is that it's easy to come up with a theorem that works for KP vs K. However as the number of pieces increases, it becomes impossible to distill all the branches of possible moves into a simple theorem like that. If what you said were possible, endgame would be a simple flowchart, but look at how much time even GM players use in endgame and how often mistakes are made, and you'll recognize Chess endgame is not distillable into a simple flowchart when there are even as few as 7 pieces on the board.
Given the above, the only option is enumeration, if you want to prove that in all cases the outcome is White win or draw.