After how many moves does a game become unique (statistically)?

Maybe you’re thinking of this:

Extended quotation

argybarg: I found myself wondering today: What is the greatest number of moves into a game that two different professional games have been identical? In other words, game A and game B unfolded identically until, say, move 8. If I had to guess, I would say it would have to be 12, but perhaps someone with a very sophisticated pattern search could find out.

A similar question: What is the farthest into the game that two professional games have resulted in an identical position? This could be later than with the first – say, move 16.

And my last is one for pure speculation: If we had full access to the record of every game played, anywhere, what would the results be for the above questions, only with games played by anyone? Leaving out games played intentionally the same (i.e., replays), I would guess that no two go games have been identical after move, oh, 26.

unkx80: 1st world female tournament, finals games 2 and 3, Rui Naiwei vs Feng Yun. These games are identical in the first 34 moves.

Between the two games, 35 differs by one line, and then 36 to 47 are identical again.

Mef: Looks like unkx80 gave a nice definitive answer to some of your questions, and I think if you compiled a database of every game ever, you’d actually find quite a few similar games. In fact I wouldn’t be suprised if there were games that were the same out to move 50 or more. The problem is that some people play deliberately the same as a previous game because it’s a position they’re comfortable with. For instance, many people always play the low chinese, or maybe they always play the same pincer against the nirensei. Also I know sometimes when pros play a series of games against each other they like to use the exact same opening play as the last time, except that they will try and put their post-mortem analysis to good use, changing the first move in the game they thought didn’t work.

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