Timeline for What proportion of chess positions that one can set up on the board, using a legal collection of pieces, can actually arise in a legal chess game?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 14, 2013 at 18:26 | comment | added | Joel David Hamkins | @BorisBukh, your nitpick is discussed already in the comments on the question. | |
| Aug 14, 2013 at 18:05 | comment | added | Boris Bukh | A nitpick: a "position" in chess is more than the position of the pieces, it is actually a tuple (position of the pieces, whose turn it is, number of moves since capture/pawn movement, number of times a given position occurred in the past). This proof does not work for this more refined notion of "position". | |
| Aug 4, 2013 at 20:49 | comment | added | Joel David Hamkins | Yes, I agree, but why should that stop us from making some definite calculations in these cases with still lots of pawns? To my way of thinking, there is still a lot we can say about the legal proportion of positions using specific piece collections, if we only make the calculations. | |
| Aug 4, 2013 at 16:14 | comment | added | The Masked Avenger | In the above, I should be more clear and say 6 sets of opposing pawns. | |
| Aug 4, 2013 at 15:56 | comment | added | The Masked Avenger | You can actuallly consider all configurations with 6 black and 6 white pawns present which have not captured. The problem is we still don't know how such legal games stand in relation to all legal configurations. Domotorps consideration of 28 will play a significant role,if for no other reason than helping to determine the set of legal multisets of pieces. | |
| Aug 4, 2013 at 3:56 | comment | added | Joel David Hamkins | Let's start small. Suppose there are 31 pieces, with all 16 pawns present. So at most one of them is out-of-file. But then a similar calculation will kick in to still give a very small proportion of legal positions. Right? And then we can aim to consider 30 pieces with all 16 pawns still present, etc., until the bound isn't much good. | |
| Aug 4, 2013 at 3:28 | comment | added | The Masked Avenger | Good. Now on to the hard part, involving one or more captures. | |
| Aug 4, 2013 at 2:46 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 11 characters in body
|
| Aug 4, 2013 at 2:40 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |