Estimated # of unique chess games
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That's = one noventrigintillion (short scale). 
Is that counting transpositions?
All positions, including transpositions.
Jan 28, 2008
0
#5
does that include positions where my kids put lego figures on the squares as new pieces?
Jan 28, 2008
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#6
heh. my 2 1/2-year-old likes to put his Hotwheels cars on my board.
Includes bughouse/crazyhouse? Heh, that will add some more.
Ah, does it include cheating?
So you're telling me that games of chess are more unique than the infinite universe?
No wonder the game has enduring appeal.
ivoryknight71 wrote:
I just came across something interesting in one of my chess books. The estimated total number of possible unique chess games is 10 to the 120th power: 1, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000. In English, that is a thousand trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion.
For your information, physicists estimate the total number of electrons in the universe is "only" 10 to the 79th power.
What do you mean "the universe" ? The Universe is endless, so I guess the number
of electrons is also endless.
So between igoogoo and igoogoo plex? Now imagine this. A computer that plays against itself repeatedly, essentially forever, but learning as it goes. Initially it simply randomizes for each move (clearly, there are better starting strategies, but let's go with this one). It keeps track of wins and losses, not only overall, but also as a function of which moves were made. Then it modifies the probabilities of future moves so as to be proportional to the empirical probability of winning when that move is played. Would it converge? That is, ultimately, would all probabilities converge to zero or one? Is this the same question as asking if there is a winning strategy?
what happens if you add more squares?.....
Jan 28, 2008
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#13
as for "the universe", i'm only quoting the book. and as for "scientific WAG", you said it: it's a WAG, an estimate, whatever you want to call it. just quoting the author. :)
The question is now, how many of those 10^120 games has been played? Has mankind yet to play them all?
ugh, I wont try
Jan 28, 2008
0
#17
ivoryknight71 wrote:
I just came across something interesting in one of my chess books. The estimated total number of possible unique chess games is 10 to the 120th power: 1, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000. In English, that is a thousand trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion.
For your information, physicists estimate the total number of electrons in the universe is "only" 10 to the 79th power.
That number is only a lower bound on the number of positions possible. The real total is likely much higher.
I would imagine that only a small fraction of those games would be considered "logical". Meaning that if a stragety were to be invoked, and reasoning applied, the number would be cut drastically.
Am3692 wrote: The question is now, how many of those 10^120 games has been played? Has mankind yet to play them all?
If 10 billion people each played a game every second, it would take them more than 10^102 years to play that many games. So, uh, no.
Vance917 wrote: So between igoogoo and igoogoo plex? Now imagine this. A computer that plays against itself repeatedly, essentially forever, but learning as it goes. Initially it simply randomizes for each move (clearly, there are better starting strategies, but let's go with this one). It keeps track of wins and losses, not only overall, but also as a function of which moves were made. Then it modifies the probabilities of future moves so as to be proportional to the empirical probability of winning when that move is played. Would it converge? That is, ultimately, would all probabilities converge to zero or one? Is this the same question as asking if there is a winning strategy?
It will converge, but most likely not to a strategy where the probabilities are zero or one. At each position, it will converge to a probability distribution over the set of optimal moves. If there are more than one optimal move from a given position, then it will most likely assign positive probability to all of them.
I just came across something interesting in one of my chess books. The estimated total number of possible unique chess games is 10 to the 120th power: 1, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000. In English, that is a thousand trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion.
For your information, physicists estimate the total number of electrons in the universe is "only" 10 to the 79th power.