What do you think, have two identical games been played?

More formally: From among all games of go that have ever been played, are there two identical by chance? (not counting those times where players intentionally replayed a famous game)

The question could be answered by giving an example pair, but I presume it is not known, so what do you think? Personally my intuition is that no two identical games have been played (on a 19x19 board), but I know that intuition can be misleading, see for example the birthday problem.

If this happened once we will know. Players would have a similar very strong level to follow same patterns so amateurs have much less chances already. But anyway i donāt think that has ever happened.
Next step is to determine how many go positions exist, taking in account it should be realistic, like the result of a game played.

I would bet that I have played the same game more than once (either against the same or different opponents) on the 9x9 board.

On the 19x19 board I think it is much rarer but in my opinion it has already happened several times. I was thinking to games ended by resignation after a mistake in a joseki

It would be fun to see games that are the same up to move 100, letās say, but one player resigned while the other one turned the game around or something.

I donāt think so. Here is a very rough estimate. Suppose for simplicity that at each step, 3 moves are reasonable and can be chosen with equal probability. Then up to move 40, there are about 3^{40} āreasonableā games, which is about 10^{19}.

The birthday paradox says that there exists a constant c>0 such that if we randomly pick cān times a number in {1,ā¦,n}, then one of the numbers will be chosen twice with probability > Ā½.

Suppose that about 10^{10} games have been played, since 10^{10} is approximately the square root of 3^{40} we can guess that there exist two identical games up to about move 40, but the probability to get two identical games up to move 100 is extremely small, unless the players purposely copied another game.

If you put away all the games which have same result as one of the game, like in the Chinese rule where you fill Territories with stones, it looks to me that this approximation will be much smaller as the one we reach yet (simply all the layout possible restricted by legal moves )

I mean what interest us is how many real functional games similar to what we play exist, not a random layout of stones on a grid.

Just always pick the continuation with the most number of moves:

Most common first move is 4-4 top right. Number of games with this first move is 46,099 (out of 82,125 pro games).

4-4 top left is the most common reply with 22,985 games playing that.

Most common third move with the above opening two moves is 3-4 bottom right, which features in 9,715 games.

So we can see already that even on this āmost popularā branch the number of games is approximately halving after each move.

You can repeat this process until there are only two games left and then follow those two games until they diverge. If you do this, you get to this position:

which shows these two games are identical up to move 23.

So that is evidence that you can have identical games up to at least move 23. But that is not to say that there arenāt longer identical examples on Waltheri - that one is just relatively easy to find (basically, always click the ā1ā until the last two games diverge).

I wonder would you be more or less likely to get games that identical for longer with say katago or leelazero self play games, possibly during training for example.

The way human pro study variations, tend to make identical opening repeat more often I think. I remember reading somewhere that lots of pros even research fuseki all the way up to 50 or 60 moves, with various different joseki combinations (where joseki and different sides are like building blocks that can be switch around). A lot of pros who donāt have time or strength to study further would just follow those results sometimes (more or less just switch the sequences)

Talking about complex joseki, big avalanche mainline should be on top (this variation up to this point is 46 already, of total moves 49 identical). Flying knife joseki might surpass it, but waltheri lacking many records in the last 2 years.

Ya, human innovations and studies before AI era were pretty slow.

I wonder with AIās help, making variations used to think not viable (or not good) valid again, does this lead to more diverse fuseki and earlier divergence than before?