qsort

It's beyond insane that Astra achieves above 50%. Are models allowed to "play against" the specific bot they're up against? What explains the fact that it drops to single-digits against strong bots?

Sure, but you can do Monte Carlo with a double-dummy solver.

The point is that, especially for games perceived as being lower-status like MTG and other board games, I'm more inclined to believe the answer is closer to "nobody is willing to pour in the resources to seriously try" as opposed to "we definitively cannot with current science and technology."

There are very few missing pieces for a game like MTG. The main reasons we don't have a Stockfish for MTG is that it's a PITA to implement the rules and that nobody cares (or at least not enough to make it happen.)

There is nothing that, in principle, makes MTG different from poker or bridge, and we have superhuman engines for both.

I suspect tech has little to do with it: we all mostly miss being 20 years younger and not having gray hair.

Literally the "AI is just computer" argument

Yes, but crucially, in ways that are increasingly decoupled from any practical pattern of usage, considering that I wouldn't see how you can argue that Astra is worse than Opus 5.

One man's modus ponens is another's modus tollens I guess.

I am begging you on my knees to please stop posting this cringe.

The model is just out. It could be good, great even, I don't know. But I do know that this index has Opus 5, one of the worst releases of 26, ahead of Astra. What information are we supposed to deduce from number having gone up?

It's endlessly fascinating how culture, religion and even language influence stylistic choices, even though Chess is a purely abstract game.

The obvious ones: in Western sets the king has a cross on top, and Islamic traditions only use abstract shapes. But I wonder if the "usual" designs aren't at least somewhat influenced by the English language specifically. Bishops have a stylized miter and Rooks are a tower with crenellations, but e.g. in Russian Bishop is "elephant" and Rook is "boat". Even in many other Western European languages "Bishop" as in the piece is not the same as bishop as in the religious office, e.g. "fou" in French, "alfil" in Spanish, "Laufer" in German.

> (This approximation should be familiar to many from an algorithmics class.)

You need both sides though :)

What makes it interesting for estimating algorithmic complexity is that \log{n!} \in \Theta(n \log n). One side is obvious as you note, the other less so, but there's a famous trick to do both at once:

\log{n!} = \log{\prod_{h=0}^{n} h} = \sum_{h=0}^{n} \log{h}

Therefore,

\int_0^n \log{x} dx \le \log{n!} \le \int_0^n \log{x+1} dx

with both integrals trivial by parts.

is claude not a man and a brother

Can't you just describe the group that defines those transformations and use Burnside?

Quoting from the official website:

>>>>>>

The new procedure targets inappropriate behavior by parents and spectators directed at children, coaching staff members, referees, match officials, or other parents and spectators. This includes, but is not limited to:

Verbal abuse (insults or profanity), as well as physical assault or shoving of one’s own children;

Verbal abuse, physical assault, or shoving of staff members of one’s own team;

Verbal abuse, physical assault, or shoving of players or staff members of the opposing team;

Continuous challenging, verbal abuse, physical assault, or shoving of referees and match officials;

Verbal or physical altercations with other parents or spectators.

<<<<<<

If that's the situation in, and it can't be stressed enough, a children soccer game, then yes, abandoning the match is probably the right choice. I assume they are only defining a formal procedure for practices that already exist.