– When played optimally, is pawn race a win for white, black, or a draw?

– Could I beat a grandmaster if he was down a queen? I tried playing Stockfish with it down a Q and a R, and I won easily. (Yeah!) I suspect I could beat it just starting up a queen. But Stockfish plays assuming I’ll play optimally. Essentially it’s just trying to lose gracefully. In contrast, I’m pretty sure the grandmaster would know I’m not good, so he could just complicate the position and tear me apart. Perhaps someone’s already written a chess program called Patzer that plays kinda like me, and then another program called Hustler that can regularly defeat Patzer.

– If I was playing a top player, and my only goal was to last as many moves as possible, and his goal was to beat me in as few moves as possible, how long could I last?

– In bughouse, which is better, 4 bishops or 4 knights?

– How best to set up maharajah to make it balanced? Maybe the non-maharajah team isn’t allowed to promote and they have to win in some prespecified number of moves?

– And then there are the obvious ones:
1. Under perfect play, is the game a draw?
2. How much worse is the best current computer, compared to perfect play?
3. Could a human ever train to play the best computer to a draw? If not, how much worse etc?

– Do you have any good open questions in chess? If so, please share them in the comments.

We were discussing such questions after seeing this amusing article by Tom Murphy on the longest chess game (“There are jillions of possible games that satisfy the description above and reach 17,697 moves; here is one of them”) and also this fun paper comparing various wacky chess engines such as “random_move,” “alphabetical,” and “worstfish” and which begins:
“CCS Concepts: • Evaluation methodologies → Tournaments; • Chess → Being bad at it;
Additional Key Words and Phrases: pawn, horse, bishop, castle, queen, king.” I’ve been told that here’s an accompanying video but I never have the patience to watch videos.

One thing, though. Murphy writes, “Fiddly bits aside, it is a solved problem to maintain a numeric skill rating of players for some game (for example chess, but also sports, e-sports, probably also z-sports if that’s a thing). Though it has some competition (suggesting the need for a meta-rating system to compare them), the Elo Rating System is a simple and effective way to do it.” I know it’s a jokey paper but I just want to remind youall that these rating systems are not magic: you can think of them as mathematical algorithms or as fits of statistical models, but in any case they don’t always make sense, as can be seen from a simple hypothetical example of program A which always beats B, and B always beats C, and C always beats A. Murphy actually discusses this sort of example in his article, so he’s aware of the imperfections of ratings. I just wanted to bring this one up because chess rating is an example of the fallacy of measurement, by which people think that when something is measured, it must represent some underlying reality.

P.S. Also don’t forget Tim Krabbé’s chess records page, which unfortunately hasn’t been updated for over three years (at the time of this writing). Chess games can’t be copyrighted, so the youngest professor nationwide could collect some of this material in a book and put his name on it!

This post is by Phil Price, not Andrew.

As we approach the Olympic Games, this seems like a good time to think about the rules for deciding whether a person is a “woman” when it comes to athletic competition. As I was doing some searches to find some information for the post, I found an excellent piece that puts everything together much better than I would have. Go ahead and read that, then come back here. (The piece is by Christie Aschwanden,  of whom I think very highly; she wrote a book I reviewed here two years ago).

The issue is: if you’re going to have separate divisions for men and women, then you need a way to define “woman.”  A good way of defining this might seem obvious: if the person has a vagina, she’s a she. That’s the way the international sports governing bodies used to do it, but then that was rejected for reasons mentioned in Aschanden’s piece. Well, how about “does the person have two X chromosomes?”  After nixing genitalia as the criterion, this is what they switched to…but then that was rejected for reasons also mentioned in the piece. Currently,  according to the article, “Female athletes who [have] functional testosterone (in other words, not just high testosterone levels, but also functioning receptors that allowed their bodies to respond to the hormone) above a threshold number [are] not eligible to compete unless they [do] something to reduce their testosterone below the threshold.”  (The original sentence is in the past tense, but this is pretty much the current situation too). 

I think it’s safe to say that most people with an interest in how “woman” should be defined for sporting purposes are unhappy with any of the past standards and with the current one. An issue with the current article is, as it says in the article: “People who go through male puberty are taller, have bigger bones and develop greater muscle mass than those who go through female puberty, said William Briner, a sports medicine physician at the Hospital for Special Surgery in Uniondale, New York, during a session on transgender athletes at the American College of Sports Medicine meeting in early June. Men also have more red blood cells than women, and their hearts and lungs are bigger too. Some of these advantages are irreversible [even if testosterone levels are later reduced].”  

Furthermore, although the Olympics focuses only on the best athletes in the world, there’s a need for competition rules that apply at other levels too. High school basketball, for example, needs a way to determine who is eligible to play on the girls’ team. Is it fair for a 17-year-old 6’4″ high school athlete who went through puberty as a male, but then transitioned to female, to be allowed to compete against girls who went through puberty as girls? Viewed one way, being a woman who went through puberty as a male is just another genetic advantage, and we let athletes use their genetic advantages, so there’s no problem with such a person competing on the girls’ team. Viewed another way, it’s not fair to let someone compete as a girl if they got their body by growing up as a boy. 

So what do I think the rule should be? I have no idea. Indeed, I’m not even sure how to think about what the rules are trying to achieve. We have separate competitions for men and women because it would be “unfair” for women to have to compete against men: in most sports the best women wouldn’t stand a chance against the best men, and the average woman wouldn’t stand a chance against the average man. A female sprinter, for instance, would have no chance of reaching the elite level if competing against men. OK, fine…but what about me? I’m a man but I would also have no chance of reaching the elite level if sprinting against other men. Indeed, I would have no chance of reaching the elite level if I were sprinting against women! The fact is, very few people have the genes (and other characteristics) to compete at the elite level. If the point of the rules is to give everyone a reasonable chance to be among the best in the world in a given category, well, that’s not gonna happen, because no matter how you define the categories there will be only a small fraction of people who have what it takes.  By having separate competitions for men and women we can’t really be trying to give “everyone” a chance. So what are we trying to do?

All of this puts me in mind of a statistical principle or worldview that Andrew has mentioned before, that I think he attributes to Don Rubin: most things that we think of as categorical are really continuous. For some purposes (and with some definitions) male/female is indeed categorical — no male can bear a child, for example — but when it comes to innate ability in a sport, what we have is one statistical distribution for men and another statistical distribution for women, and (for most sports) for any reasonable definition of “man” and “woman” the high tail for men will be higher than the high tail for women, but  the bulk of the distributions will overlap. If  Caster Semenya is a woman for sporting purposes, in spite of her XY chromosomes and typically-male testosterone level, then she is at the very top of the sport. If she is a male for sporting purposes, then she is not remotely competitive at the elite level. (Welcome to the club!). Sporting ability is continuous but we have to somehow force people into two categories, assuming we want to continue the current male/female division in competitions. 

It’s said that “hard cases make bad law” but this seems like a sphere in which all of the cases are going to be hard.

This post is by Phil.

Justin Horton writes:

Of course Chess.com are a private company. They have the right, within the law, to have who they want on their site and to ban who they want from their site.

What they don’t have the right to do is to call somebody a cheat without backing it up.

But that is what they have done.

That would annoy me too.

It’s almost Christmas, which makes us think of toys and presents, like . . . videogames for the kids and young adults in your life.

And we have a story for you, all about ethics in video game speedrunning.

Matt Drury writes:

Recently a top player of Minecraft has been exposed as a cheater using a very thorough and well presented statistical analysis of their luck during their play sessions. I was really impressed with the analysis, their dedication to fairness and applying multiple corrections. There’s even implicit attention to the garden of forking paths.

Here’s their paper on the approach and results.

They also published a video with an overview of the methods and results (less details of course).

I know nothing about Minecraft except that it’s a videogame that’s popular with kids. But I guess this might interest some of our readership?

I asked a local expert, who characterized the above-linked paper as “trivial but impressive.” The local expert was not so impressed by the rebuttal offered by the player accused of cheating.

P.S. More here on how this sort of dispute can be resolved.