How about the following statement?

"There is no widely played game for which an Elo rating system shows a larger measurable range of skill than Go."

This is a precise and measurable statement. The standard deviation of the Elo system used in Chess is 200, and the range from the best humans to rank amateurs is 14 times this standard deviation. When the Elo system was adapted to Go, the standard deviation was set to 100, and the range is 29 times the standard deviation.

The possible skill range, of course, measures something how complex the possible strategies are. And Go trounces every other game by this measure.

I think that gives Go a pretty defensible claim to "most complex strategy of any popular board game".

Complex is being used in a different context here though. You are meaning complex as in strategic complexity. The parent (I think) is using it in terms of the games rules. Go is pretty simple in principle: place stones on the board one at a time, and remove enemy pieces completely surrounded by your own. But it's fairly complex to know what exactly constitutes being surrounded. Chess has 6 different kinds of pieces that have different movements, and different kinds of rules depending on the state, and promotion at the end, castling, and en passant. Checkers is a much simpler game because there's only 2 kinds of pieces, and 2 kinds of moves. Strategically, Chess isn't leaps and bounds more complex than Checkers since Carlsen has an Elo rating of 2800 in Chess, and Tinsley had an Elo rating of 2700 in Checkers and I believe it's the same deviation of 200.

Checkers has adjusted its Elo system over time. I believe that it now matches chess except with a floor of a 1000 rating. From http://icheckers.net/ratings/, the current ratings range goes from 1000 to 2297 among active players, and up to 2510 among inactive players.

Even if you use the larger range of inactive players, that's a range of 7.5 times the standard deviation. Which is considerably less than chess.

Tinsley isn't on that list, and I saw it claimed that his rating was 2700: https://en.wikipedia.org/wiki/Marion_Tinsley

Chess has a floor of 1200 for novices. So I'm not sure your point.

The Elo system for Checkers has changed over time. Tinsley had a rating around 2700, but he would not get that rating today.

Chess ratings from the USCF have a floor of 100. What you are thinking of is that they start people at a provisional rating of 1200 and then let them drift to where they belong. But a person who just knows how the pieces move will quickly head down towards that floor.

Know of any resources that help figure out what the Elo SD of a particular game is, and the range? Also, know of anything written about various ways of measuring the complexity of a game? I'd never thought about the number of SDs thing.

By this measure, is there a more complex game than Go, but which is not as widely played?

(Question from someone who does not know anything about board games.)

I ask because a natural question arises: can one engineer a game specifically so that it is extremely difficult for a machine to master compared to a human -- due to some strategic complexity, or some approach that does not lend itself well for current AI models.

edit: looks like there's at least one http://arimaa.com/arimaa/

Probably not.

Even if a game was more potentially complex than Go, it would be hard to establish the dynamic range of Elo ratings unless a lot of people played it, and hard for skill variation to be that high unless a lot of people studied very hard to become very good at it.

Yeah, "deep" is probably a better term than "complex" to describe Go.

For example, Arimaa, which has a more complex ruleset and a bigger game tree. It was designed to be difficult for AI, but in practice the complexity was difficult for humans too, and AI was developed to beat the best humans using classical chess AI techniques and some clever heuristics.

Go is "most complex" only when measured by difficulty of implementing a AI to beat the best humans.

If the human race had collectively had only a decade of Go-playing experience (as was the case with Arimaa), it might have been possible for an AI coded with "classical techniques" to defeat them.

(To be specific, my guess is that we'd have been at the amateur-dan level, and the initial MCTS revolution would have been enough for the computers to win.)

A counter example would be the easiest way to disprove it.

Cones of Dunshire? :)

I haven't met a formidable Cones of Dunshire computer player, AI or otherwise yet, so for now I remain unconvinced :)

what about "most complex board game that is more than a few centuries old"?