# What are the maximum number of moves for games of different board sizes?

I know that Go games can technically go on infinitely (pass, move, pass, move, capture, move…), but I’m interested in the max number of moves to more or less settle or fill the board.

I’d like to know this so that I can start making estimations of the length of games using different time controls, and then tournaments. Using this information I can add it to the tournament description to give people an idea how long it will take.

My first idea was to count the number of intersections on the board and use that as the move estimate.
So 9x9 will take 81 moves, 13x will take 169, and 19x will take 361.

Is this a good way to do it? Does anyone have a better idea?

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You can capture stones and play “under” them, also something like ko fight can in theory make the game last infinitely

That being said, most i’ve ever had on 19x19 board was ~340 moves. Longest game i ever had was about 480 moves, but that was on 25x25 board.

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its probably not quite that easy. the average number of moves will be significantly lower than that, and the max number is hard to calculate because of ko situations. the number of moves actually played in a game also depends quite heavily on the players strenght. in my experience weak players dont fill up the board as strong players do.

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A ballpark estimate that I use is 62 points for black and white each. Assuming no captures, that is 118 free intersections at the end (62+56), after 243 moves played. Assume less moves and more points in a moyo game, more moves and less points in a fighting game.

There is really no substitute for actually counting though.
Learn and practice frequent counting, the earlier the better

Edit: This was adressed to the question on the length of games, not the maximum number of moves. Games tend to take an average number of moves on average, not the maximum on average

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As long as you don’t use superko, you can play infinitely long.

If you do use superko, then I suppose the calculations are slightly (but only slightly) complicated.

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Maybe this is a question that can be better answered with statistics. Does anyone know of an easily searchable database of games and the number of moves? If I could get a set of a couple of thousand games per board size that would give me something to work with.

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[quote=“Animiral, post:4, topic:17337, full:false”]
A ballpark estimate that I use is 62 points for black and white each…[/quote]

Where did you come up with 62 stones for (I assume) 19x19? What numbers would you use for 9x and 13x?

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Most 19x games will finish around 250 moves, some get to 300, but rarely if ever reach 350. Longest pro game was 411.

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I suspect knowing the median number of moves would be more useful than the maximum. (assuming annulled games are not included)

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Guesswork, experience and I might have heard it somewhere else - I’m not sure
I have no idea about the smaller boards.

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If you want to know the typical number of moves in a game, you should instead look for the mode (most frequent value in the distribution).

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I suspect mode might be something silly like 5 moves in this instance… Definitely think median or mean are best in this case (opinion)
Edit : for full clarity, I quite like displaying mean, median and mode side by side for comparison sake

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Anyone have a lead on some data I could look at, so I can get the average mode median BMI, or whatnot? OGS data would be preferable.

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Do you really think most games end in 5 moves? I’ve sampled a lot of game histories and 5 move games are almost exclusively the work of thinly veiled sandbaggers. These people are in the minority and even they don’t finish most games in 5 moves, so I think your suspicion is unfounded. :3

Moreover, even if 5 moves was the mode,… that would precisely mean that the typical game ended in 5 moves and whenever someone played a game they should expect a 5 move game.

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Ok, use case.

Say 101 games are played. The first hundred take 1 through 100 moves respectively, and the 101st takes 1 move.

Both the mean and median will return values of roughly 50. But the mode will be 1 because it occurred twice and the others only once.

For this reason, mode presented on its own can easily be misleading as it is very prone to obscure outliers that either the median or the mean normally do a good job of smoothing out.

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I wondered why there are no games <50 appearing in the graph.

I was expecting that there would be some sort of peak in the low numbers due to the perceived large number of games abandoned early.

Then I realised that the graph is not OGS games, it’s Pro games.

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Ignoring completely the original motivation for this question, I did some reading on what the longest game possible is (assuming the superko rule).

First of all an algorithm to make a 361^3 (about 47 million) move game is not too difficult to conceptualise: Black fills the whole board except one point, then white captures, and black will try to fill up the whole board, etc etc, which takes around 2 x (360 + 359 + 358 + … + 1) = 361^2 moves to reach a position where white has filled the entire board except a single point (which should not be the same as black first’s move, because of superko).
Then Black captures, and the whole thing can repeat itself from this starting position, and again, and again, giving another 360 iterations of this strategy, so we’re now at 361^3 moves, and back at a position with only one stone on the board.

For those interested, Tromp and Fanrebäck also published a paper on the combinatorics of go. In that paper it is stated that on a 1xn board, a lower bound for the number of moves is 2^(n+1) - 4.

The same Tromp and Farnebäck found a 2900 move game on a 3x3 board, which therefore visits about 15% of the total number of legal positions.

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You can retrieve them by yourself from OGS, if you know how.

Here is some documentation:
https://ogs.docs.apiary.io/#reference/groups/group-membership

Here is a way to check what the result looks like:
https://online-go.com/api/

Some uses python.

I had some good result with FME but I’m not so clever, so for now I can only download my own games:

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Thanks! I’ll give this a shot when I have some time
: >