How many different chess positions are there?

#383

"OP's hypothetical assumption that there is a  a perfect single move for every position is obviously false" ++ Yes, that is right: in most positions there are several perfect moves.

"That is what OP is asking for." ++ No: he asked: 
"how many would have to be known to create a theoritical perfect chess computer/player?"
Certainly not all 10^44 legal positions per Tromp and not even all 10^37 positions without promotions to pieces not previously captured per Gourion would have to be known to create a theoretical perfect chess computer / player. The answer to that question is the number of legal, sensible, reachable, and relevant positions, which I estimate at 10^27.

To be precise he asked, " Assuming there is a perfect single move for every position, how many would have to be known to create a theoritical perfect chess computer/player?". Given that the antecedent is false any number would be an answer.

Assuming the antecedent were omitted then he'd be asking for a strong solution. The number of positions would be as noted by Tromp under basic rules but vastly higher under competition rules (though nowhere near as high as the upper bound of 4.8 x 10^44 x 5^(4.8 x 10^44) I gave here which could easily be vastly reduced.)

Your figure of 10^27 is the result of very flawed analysis. (See this thread.)

#385

"Assuming the antecedent were omitted then he'd be asking for a strong solution."
++ No, he would be asking about a weak solution.

"The number of positions would be as noted by Tromp"
++ No, none of the 55958 sampled positions Tromp found legal would have to be known by the theoretically perfect chess computer/player as these would never occur in any game he plays and hence only a tiny fraction of the 4.79 * 10^44 legal positions.
If the theoretically perfect chess computer/player defends 1 e4 e5 and 1 d4 d5 as black and opens 1 e4 as white, then he does not need to know any positions resulting from the Dutch Defence, the King's Indian Defence etc.
The theoretically perfect player would never underpromote to multiple pieces not previously captured and when his opponent tried to do so, that opponent would be checkmated before he could do so multiple times.

"vastly higher under competition rules"
++ No, your observations about competition rules are not relevant at all as previously explained with help from the Laws of Chess, which define when positions are the same and when they are different. The original poster asked about different positions. Even aside from that, the perfect chess computer/player would find means to avoid the draw in a won position and would find other ways to draw in a drawn position. That is what happens in ICCF WC drawn games, 99% of which are perfect play.

Well that's all b*llocks, but I know from experience there's no way to stop you from continuing to spout it, so I'll just leave you to do so.

For those wondering about the amount of possible moves, this video sums it up :
https://www.youtube.com/watch?v=Km024eldY1A

But it is not about the number of positions. The number of positions is 10^44 according to John Tromp and Peter Österlund. But it is the number of total positions, if we want the number of "perfect positions", I think we can't really answer, because if there was 1 perfect move, there would be only 1 game for each opening during the computer championships :
https://www.chess.com/computer-chess-championship

Can we really talk about the "perfect move" when games only differ in our personal preferences (or how the computer is set up) ?

All of the serious numbers in this thread are attempts to determine upper bounds because the perfect Chess automaton would drastically restrict the number of possible positions by making them unreachable. The problem of course, is without that elusive algorithm it's very difficult to even guess the size of the set of positions which it would permit. If we take the example of possible pawn structures, it's reasonable to assume that the vast majority of legal pawn structures would be impossible to construct against the perfect Chess algorithm, because they would be too vulnerable to attack during construction.

#390
"the perfect Chess automaton would drastically restrict the number of possible positions"
++ Yes, that is correct. The vast majority of the 10^44 legal positions or the 10^37 legal positions without promotions to pieces not previously captured are not sensible. The vast majority of the sensible are not reachable in the course of calculation by a perfect automaton. The wast majority of the reachable are not relevant. That leaves 10^17 legal, sensible, reachable, and relevant positions, needed to weakly solve chess.

"without that elusive algorithm it's very difficult to even guess the size of the set of positions"
It is possible without the algorithm. The 10^17 estimate stems from the Gourion paper 10^37 positions without promotions to pieces not previously captured. A sample of 1000 such prositions shows these are not sensible, that leads to an estimated 10^32 sensible positions. Checkers has been weakly solved visiting 10^14 positions and Losing Chess has been weakly solved using 10^9 positions. That leads to an estimated 10^19 reachable positions. Weakly solving only needs a (one) strategy, not all. That leads to 10^17 relevant positions.

There is only one move in every real chess game. Pretend to look at the board while slyly pulling out a gun under the table and blowing your opponents nuts off... game over!

@391

Only 10^44 positions are legal.
Even less make sense: 10^37 is a more sensible number.

13^64 is the number of ways monkeys can put part of 64 boxes of chess men on a chess board. That includes and empty board and a board with 64 white kings and everything in between. It has nothing to do with the game of chess.