Yes, we can easily simulate this, actually.

I just invented a new game called 3-go. To win the game, you play 3 games of go against someone, and have to win at least 2 of them. Simple probabilistic calculation shows that if you have a 60% chance of winning a game of go against someone, then in 3-go you have a 65% chance of winning against that person. This new game of 3-go therefore has a wider Elo range. But of course, 3-go is not harder to learn than go.

Yes, I would be, so long as the betting amount was small enough that I would not have an unacceptable risk--I believe the bet has a slight positive expectation in both cases, though I do realize it has a higher one with the 5dan and 2dan. I would bet $20 without much thought, because I can lose that several times without severe inconvenience. I would not bet $500.

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I just caught this: I'm not concerned to argue that go is harder to master. Indeed, the empirical evidence suggests that go and chess are very close on that metric.

I should state that I consider both chess and go more than deep enough for humans--though Chess does have a problem with opening books. I do not regard the depth that I'm arguing exists in go as much of an argument for it being a better game.

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Mostly my concern is the talk about the ELO ranges being different meaning something.

Maybe the different skill gaps can be pinpointed by way of the game mechanics: Chess and go are both essentially "race games". Meaning the player who makes the most efficient moves wins. Meaning the player who makes less mistakes wins.

A normal game of go lasts about 100 moves longer than a game of chess. Therefor 100 opportunities more to make mistakes. Therefor the gap between the worst possible play and the best possible play has to be greater.

Does that make any sense?

At the risk of un-derailing this thread. Has anyone played any of the GIPF Project series of games?

Three of the six games available are listed above go in the Board Game Geek rankings of Abstract Games.

Yinsh, Tzaar, Dvonn are the three highly-rated GIPF games, while Zertz, GIPF, Punct, Tamsk (replaced by Tzaar) round out the remaining GIPF games.

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Yes, several of them. None of them appealed to me much but to be fair I didn't give them much of a go and it was a good number of years ago.

A propos 3 and Go: Some days ago I invented some Go variation. At first it was just a funny idea.
To test it, I tried it out on the smallest non-trivial board size 3x3.
Some players on KGS enjoyed to participate in my test.

I call it "3x3 Inverse-Go" or (rhyming with 3x3 tic-tac-toe) GigaGo.

You play with normal Go rules, but passing not allowed.
The first player unable to make a legal move ... WINS!

(To try this seems natural for any reader of "Winning Ways" who has thought along the lines of The last one who is able to play is the winner.
So I wonder who invented this before me. And how many )

KGS-player Alast proposed to restrict the number of moves allowed, in order to keep the players from playing forever by avoiding any risk.
This is an interesting addon which I refined a bit so as to balance the burden:
every time the board is "flipped" by taking the last liberty on the board, the number of moves is increased by one. Worked quite well with inital number of 30 moves.

Playing on 4x4 and larger is likewise possible, but it is astonishing how interesting 3x3 can be. Some people loved it and others despised it

Cheers,
Rainer
(GoChild GoRo with 1891645 points)

I love go but backgammon is far more enjoyable. IMO. Every week I have a game night. We usually play 1 game of go and 4-5 games of backgammon. There are dozens of variants for endless fun. Chess used to be on the agenda until I discovered go.

http://aagenielsen.dk/index_nef2.html Hnefatafl is another very old game that I recently learned about. It looks interesting. One thing I like about it is the two sides begin with different strength 'armies'.

So I double-checked this because I had seen that Go was hanging on in the top 50 of BGG (at #48!) whereas the other games aren't. And what msgreg says is true - in the abstract games list, the gipf games are ranked higher, whereas in the games list, go is ranked higher. Looking more closely, the average user rating for go is, 7.78/10, which is higher than any of the gipf games ("tzaar" comes closest, at 7.69). However, apparently this rating is not the rating used to rank games;



This doesn't really explain anything, though, because Go (obviously) has far more ratings than the other abstract games. (It also has more ratings than some of the games that beat it due to re-adjustment on the main chart.) Further, this doesn't explain why on the abstract list the rank is based on a "BGG rating" of 7.370 and on the general list the rank is based on a "BGG rating" of 7.544.

Anyway, there are few things that could be less interesting than the arcana of how a website rejiggers its rankings to keep them interesting and the resulting discrepancies, but I looked into it anyway, so there's your answer.

I can tell you: you're not the only one that looked into it

If your argument that go has a greater depth than chess hinges on the 30k-20k range, then that's just not very impressive. The "depth" required to get from 30k to 20k is surely not a big selling point compared with the overall complexity of both chess and go.

Another argument: 30k-20k and 1k-9d have the same difference in ELO rank. Does that mean there's as much depth in the 30k-20k range as in the 1k-9d range?

Winning probability statistics just aren't related to depth at all.

The thing is that you're making a really selective adjustment. The 30k-20k ranges are pretty quickly passed, but so are the 300-1000 range of chess!

I would never argue that the depth of a game, measured this way, is a good measure of its goodness as a game. But it is measuring something real and important. The depth of both go and chess are extraordinary: each of them has a great many levels, such that a player of a higher level knows more (or plays better) than a player of the previous level.

That's all that it shows, but that is important, even conceding the obvious points that it's not close to being the most important thing about a game, and Herman's point that you can artificially distort the measurements, if you're enough of a smartass.

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Both chess and go have blunder-ranges. I agree you don't learn much go between 30k and 20k, but that is probably true of chess between 300 Elo and 1000 Elo. (I don't know that much about the lowest ranks for chess - 1000 is still super-blunderer, right?)

More importantly, as you learn more about a game, it becomes harder and harder to improve your game sufficiently to squash your peers. In almost any game of skill, beating someone who just learned the rules 90% of the time is not at all hard. Beating that person 90% of the time takes very little familiarity with the game. Beating that third person 90% of the time requires some experience. And we go up and up and up, to the point where beating someone 90% of the time takes years and years of effort, which most people will never put in. -- So hyperpape and I don't think it's the first 1000 Elo points (which take a week or two) that are impressive, but the last 1000 Elo points, which build on three previous blocks of difficulty, each one speaking to greater depth of gameplay than the previous.


If I'm every going to get an intelligent answer to this, it's going to be on L19. How can this be possible? How can a game be deep without that depth translating into people more familiar with the depth pwning noobs? I'm happy to admit that a very deep game might be brand new (Redstone, anyone? ) and lack the player-base to sufficiently explore the depth. Or you could add arbitrary elements of luck into a game to make a new game with a narrower Elo range. Lots of other contingent factors like that are possible. But assuming a game has been adequately explored for a sufficiently long period of time, how could depth not translate into winning?

I'm just having trouble picturing a game where you explore the depth, learn more about the depth, have some quantitative sense of how much depth you've plumbed, but don't think that knowledge will help you improve at the game.

(Maybe we could relate this to the recent Fairbairn-Spight exchange over endgame theory. I took JF's point to be that if miai counting and all the rest don't help you win games, knowledge of miai counting is just a trivial redescription of Go (like that guy who wanted to catalog all possible dango shapes), rather than an exploration of one of its deeper caverns. It looked to me like everyone who participated in that conversation shared that premise, and disagreed about whether miai counting was an understanding of the game that leads to better play.)

Damn, succinctly ninja'ed by hyperpape.

I've heard 1000 Elo described as a bright beginner. Maybe 17/18k EGF perhaps.

I can imagine a game that is very deep in terms of ELO score, but not interestingly deep in the relevant sense. Consider a game where people compete to do mental multiplication of very large numbers. I presume it would have a wider ELO range than even Go or Chess, but there's still something formulaic about it.

Could there be a more typical game with that feature? I'm not sure.

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By the way, I earlier promised Boidhre I would do a direct FIDE-EGF translation.

As we said, Chess has approximately 26 levels where at the player at one level beats a player at the next 35% of the time (from 300 to 2800). The EGF system is slightly annoying in that they are vague about the exact value of one the variables they use in GoR, but the table from which Boidhre got 29.5% per 100 pts suggests that we're talking ~35% per 70 pts. So about 58 levels at 35%.

There are still many, many extra wrinkles. Do we adjust for draws? Do we give Chess an extra 5 levels for Rybka? But I think the basic comparison between two rating systems for different games that share a similar mathematical basis is not hard.

Sure. The issue is that rank is related to what we think of as "depth" in an essentially logarithmic way. Applying the same level of effort that got you from 20k to 19k will only get you from 10k to 9.9k and from 1d to 1.001d or so.

Here's a simple mathematical model. Your "strength" is some number. Your "relative strength" compared to someone else, which is related to winning probability, is your strength divided by theirs. So if your strength is 100, you are twice as strong as someone whose strength is 50. If both of you increase in strength by the same amount, you will no longer be twice as strong. Your chance of winning against them will decrease.

This model is obviously oversimplified, but if you imagine that "strength" represents, for example, the number of hours spent studying go, then it's not that far off. The point is that additional strength gives a smaller advantage when you are already strong.

So we are talking about the essentially linear "depth", but all the evidence we have is from the essentially logarithmic ranks. The same range in ranks may correspond to very different ranges of depth. The problem with converting from one to the other is that we don't have reasonable endpoints. Near the very beginning of the scale, every tiny increase in strength corresponds to gigantic increases in rank, so it's very hard to establish the starting point for rank. This is the reason some go ranking systems start at 30 and others at 20 - both numbers are more or less arbitrary. The number of 100 or 300 for a beginner in chess is just as arbitrary.

At the other end of the ranking scale, we have the opposite problem. Every tiny increase in rank corresponds to gigantic increases in strength and depth. There may be incomprehensible depth between 10d and 10.0001d, and we'll never know.

So simply comparing the rank ranges means ignoring two problems - one, the rank systems don't have a good starting point. Two, we need really good accuracy to capture the depth that's mostly contained at the upper end of the ranking range.

Okay, I misunderstood your point. I'm mainly interested in whether it makes sense to compare games (as in, "I know Go sounds like random game with simple rules, but it's actually much deeper"). I understand that the first step in what you call "relative strength" involves absorbing much less information/ trivia/ experience etc. than the last step. But this is (presumably) true for all games. So comparisons between them all assume something equivalent (that a game is being credited both with an initial level of depth where players avoid blunders, and a final level of depth where players get very close to knowing everything a human being can know about the game).

As for the question about where in the learning curve of a game we find the most depth doesn't really interest me, partly because it seems bound to be muddled up, partly because I'm skeptical that what you call "strength" (and which I might call "effort" or something like that - strength as an absolute quality is a pernicious idea) has such a strong connection to depth.

You might compare the effort of learning a game and the game's depth to the effort of preparing for a mountain trip and the elevation. The difficulty of mountain climbing may go up faster than linearly as you try to climb to higher elevations, but it would be perverse to call your position on the mountain "relative elevation" and the amount of work that went into the climb "elevation".