chess positions: how many legal ones are there ?

[Christenson]

SM, I take it
you are on board with my given upper bound for three pieces on the board,

and you are on board with my given lower bound, which depends on there always being 46 places to put a pawn of either color for any of the 3612 places to put two kings.

What happens to the upper bound if we recognize that there are only 48 places a pawn can be on the board, not 64?

[science_man_88]

Originally Posted by Christenson

SM, I take it
you are on board with my given upper bound for three pieces on the board,

and you are on board with my given lower bound, which depends on there always being 46 places to put a pawn of either color for any of the 3612 places to put two kings.

What happens to the upper bound if we recognize that there are only 48 places a pawn can be on the board, not 64?

looks to decrease it by 3612*1*14 if I did my math correctly.

[Christenson]

But what if that pawn is black, instead of white? (oh, and run the number through the calculator, too, we are going to use it)

Also, just curious, what name do you use with prime95?

[science_man_88]

Originally Posted by Christenson

But what if that pawn is black, instead of white? (oh, and run the number through the calculator, too, we are going to use it)

Also, just curious, what name do you use with prime95?

I haven't used prime95 in a while.

[science_man_88]

Originally Posted by Christenson

But what if that pawn is black, instead of white? (oh, and run the number through the calculator, too, we are going to use it)

Also, just curious, what name do you use with prime95?

Then it could double things,But to get an accurate (or even an estimate( because we'd have to know they can all legally be done)) a lot of things come into play:

1) 48 squares for the pawn, only if the kings aren't in them already.
2) the amount of legal positions for the opposing king depends on where the king of pawn color is ( if the king is directly behind the pawn, the pawn must have been at that spot at least 1 move since moving into that space, and therefore no matter where it is on the board the other king can't be in the capture zones).
3)if the pawn is in the protection zone and against the wall in some situations it could be just like king on king play.
4) the number of legal positions for a opposing king can be as little as (64-12) = 52.

[science_man_88]

I've been thinking about this for the last few days and I come to this 16( king positions not intruding on the 48 pawn squares)*48(pawn squares) + 48*47 = 3024 positions per side * 52( minimum positions the opponent king has at last calculation) = 314496 as a minimum. and I can almost say with certainty that if I'm correct above I can guess 61 squares at most will be free, from this we get 368928 = 3024*61*2 as a maximum.

[science_man_88]

Originally Posted by science_man_88

I've been thinking about this for the last few days and I come to this 16( king positions not intruding on the 48 pawn squares)*48(pawn squares) + 48*47 = 3024 positions per side * 52( minimum positions the opponent king has at last calculation) = 314496 as a minimum. and I can almost say with certainty that if I'm correct above I can guess 61 squares at most will be free, from this we get 368928 = 3024*61*2 as a maximum.

Sorry not 61, 60 I think, so 3024*60*2 = 362880

[Christenson]

I'm actually working on the exact number of positions with two kings and a pawn, but it's breaking up into a lot (30-60) cases.

[science_man_88]

Originally Posted by Christenson

I'm actually working on the exact number of positions with two kings and a pawn, but it's breaking up into a lot (30-60) cases.

yeah it's hard because for example if you have a pawn in the edge of something like the 8 king move spaces ( so nine total squares use) along the edges you have 2 positions for each I think where the pawn doesn't affect king on king, the hard part is legality( without playing from the beginning). We've also got to consider what color the pawn is.

[diep]

Originally Posted by Christenson

Scienceman, the question I was trying to work was:
How many distinct legal chess positions are there with only 3 pieces on the board. We know there are 3608 ways to legally place the two kings, and we are going to place one other piece. It is correct to note that there are only 62 places where this piece can go, but whether we have 1 piece beyond the 3 we are working with or 30 is temporarily irrelevant. What choices do we have for *each* of those 62 places? Something important is missing from my earlier post, what is it?

I can dig it up from the source code, but 2 kings have 462 configurations to be placed on the board.

You can mirror it 8 times. Just consider the first king confined within the triangle described
starting at the half diagonal
a1-d4-d1-a1 and then also you can reduce the case that the opponent king is on the same diagonal.

[diep]

Originally Posted by science_man_88

yeah it's hard because for example if you have a pawn in the edge of something like the 8 king move spaces ( so nine total squares use) along the edges you have 2 positions for each I think where the pawn doesn't affect king on king, the hard part is legality( without playing from the beginning). We've also got to consider what color the pawn is.

If you want to i can have my program spit it out for you for any number of pawns with 2 kings. It's auto-calculating this.

There is only a 'first king' and a 'second king'.

I'm not reducing attacks of the pawns, as then indeed as someone notices you also have side to move attributes. With pawns you can only mirror left-right.

So it's something like 1806 and then add a pawn. With a pawn there is 3 states of course:

a) both kings are inside the square a2-h2-h7-a7
b) just one king
c) neither king is, in which case they are both somewhere at {a1-h1,a8-h8}

So there isn't 60 states possible or anything like that.