badukJr wrote:HermanHiddema wrote: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.
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?"
I was referring to the Original Post. The first one, the one where hailthorn explains what he means with his question.
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.
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.
Of course there is perfect play. But, given that there are at least 10^(10^48) possible games, and that there are only 723 possible scores (under area scoring, anything from B+361 to W+361), there are a mindblowing number of games that will result in each score. The number of perfect games is extremely high.
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, because the size of the set, 2^41, is complete and utter nonsense. So that number, 0.1% is completely meaningless.
The important thing, the only thing that is of any meaning at all with respect to the 40 move common openings found, is that pro games are not independent. Therefore, applying statistics to calculate the probability of a common opening is impossible.
