361! is a VERY big number. You could probably play games constantly for the next billion years and not repeat one.

No two games have ever been the same, except in cases where both players deliberately set out to reproduce a game.

Suppose we consider only "good" games, allowing us to hugely reduce the size of the game tree. For arguments sake, lets suppose that, on average, there are only two "good" moves that can be played at any point in the game. And suppose that the average game lasts about 270 moves (this is roughly the actual average for professional games). That means that our game tree contains only 2^270 games. Which is an 81 digit number.

Now, suppose every person in the world suddenly finds themselves with the ability to play good games, to find one of those two (on average) good moves within 2 seconds and play it. This means that two such players can finish a game together in about 10 minutes. So every pair of players, doing nothing but sleeping, eating and playing, can play about 100 good games per day. With 7 billion people, that means we are producing 350 billion games per day, 125 trillion per year. 12 quadrillion in a century.

The chance that two of those 12 quadrillion good games are the same is about 0.0000000000000000000000000000000000000000000000001 %

First, the question was not "has two games ever been the same?" But, is it POSSIBLE? You have a non-zero result. It is possible. You might say I am arguing semantics but the possible/impossible choice is stated multiple times in the OP.

Second, somewhere your statistics are flawed. Baduk is not a random process, even between two moves. How many times during lectures does somebody say "This is the only move?" Let's do another analysis.

amnal was kind enough to look up the GoGoD database and find two games that had the same first 41 moves. The way he searched for it doesn't even guarantee that it is the longest sequence in the database... but lets say it is.

The GoGoD database has 68,127 games in the latest version. I will assume amnal has that version.

Lets use your assumption that there are two moves. 2^41. The chance of two games like this appearing in the GoGoD Database are really small, like 0.0000000003%. About the same if you hit a millions jackpot on your first try. I really doubt GoGoD got that lucky

(EDIT: Especially since there's ANOTHER two games with 42 moves.)

Actually, the question was "what is the likelihood". The word possible does not even appear in the original post, the word impossible is used just once.

My statistics are very flawed. Realistically, the tree of good games is many orders of magnitude bigger. Although there are points where there is an "only move", there are also many points where there are a dozen choices that are equally valid. The concept of miai is not nonsense.

I don't know what calculation you used, but assuming every game is a completely independent event, the formula for calculating the probability that two games out of 68000 are the same in a set of 2^41 possible games is:

1 - e^-(68000^2/2^42)

Which is about 0.1%

This is called a Birthday attack in cryptographic terms. The reason that 68000 gets squared here is because each game can match each other game, so there are 68127*68126 pairs of games that might be the same.

Of course, professional games are not independent events. Professionals study each other's games, play the same joseki or fuseki, they copy each other. That makes the probability of matching openings much higher.

Still, don't you think its quite interesting that something that has only a 0.1% chance of happening has happened twice within the set? And maybe more?

No, I don't think so


I don't see "What is the likelihood" at all. It is "Do you think it is possible that 2 games are alike?"

Maybe. Or maybe there is perfect play. We don't know yet. Looking at CrazyStone analysis, typically he strongly prefers only one move most of the time. I think as bots get stronger this becomes very interesting area of research.

Still, don't you think its quite interesting that something that has only a 0.1% chance of happening has happened twice within the set? And maybe more?

There are two more interesting games (if I can get this to work), which also involved mirror go and Go Seigen. Here's the first:

Best wishes.

With the number of players in it and the number of repetitions being done in its advantage, I would say that there is probably a few games that have been repeated already, or how they were played.

Though when you think of it vis-a-vis, the idea seems to far fetched but when you get to it statistically, there is a probability, but not something close to having confidence over.