If you click "Read" and click "Chessopedia" there is an article that discusses
"Distinct Chess Positions" and "Total Chess Positions".
The article is titled "Mathematics And Chess". After only two moves for each color there are already 71,852 distinct chess positions or 197,742 total chess positions, which I find amazing.
I don't fully understand the difference between distinct and total chess positions. Is it similar to the difference between combinations and permutations?
Number of Likely Chess Positions
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Mar 23, 2010
0
#23
Also, your king cannot be in double check by two pieces of the same kind unless one of the attacking pieces was just promoted or an en passant capture has just been played. And there is no such thing as a triple check or a quadruple check.
Mar 23, 2010
0
#24
If you are interested, you can check out the puzzle I created about legality.
http://www.chess.com/forum/view/more-puzzles/legal-or-illegal?page=1
I posted my solution on page 2. It has different concepts put into one problem. :)
Boring
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einstein_69101 wrote:
Also, your king cannot be in double check by two pieces of the same kind unless one of the attacking pieces was just promoted. A double check occurs when one piece moves out of the way of another piece such that both pieces attack the king. And there is no such thing as a triple check or a quadruple check.
Good ones, although you can arrive at a double-check with two Queens via en passant:
Mar 23, 2010
0
#28
zxb995511 wrote:
To my knowledge underpromotion to a bishop has been done in maybe 10 games in chess history...
I've done it at least ten times, often twice in the same game. I like mating with clerics.
Ziryab wrote: ...
I like mating with clerics.
I like mating with clerics.
I thought they had to take an oath that prohibited this.
If this has to do also with comparison to 960 you could do the following:
Select a position at random from a standard chess PGN DB - check for its existence in a 960 DB.
Select a position at random from 960 DB - check for its existence in a standard DB.
Repeat a number of times and then compare results.
There is a database of 960 games someone is accumulating at http://www.chess960athome.org/ but its only a few thousand games. (So the entire test above I guess should be repeated a number of times with different random subsets of the same number of games from the standard DB.)
And also for the positions from the 960 DB not found in standard, check for the percentage of such positions that have at least 1 piece in the same space, at least 2 pieces in the same space, at least 3 pieces in the same space, etc. That would indicate the degree of structure in the positions not found in standard chess. That could be compared to the degree of structure in positions from standard not found in 960. And also, the degree of structure of all randomly selected positions from 960 could be compared to that of all randomly selected positions from standard. Just a thought.
Eberulf wrote:
Select a position at random from a standard chess PGN DB - check for its existence in a 960 DB.
Select a position at random from 960 DB - check for its existence in a standard DB.
Repeat a number of times and then compare results.
Instead of just checking for existence, maybe check for frequency of positions similar to a randomly selected position from the other DB. So, iow, select a position at random from one DB, and then compute the weighted average of all positions in the other DB where each position is weighted by its similarity to the position in question, (similarity = # of pieces in same place.)
I've heard 2 different estimations as to the # of possible positions.
10^43 (10 multiplied by itself 43 times for those of you that are math illiterate)
64! (64*63*62*61*60*59... etc).
Idk the validity of these but they're both really big numbers 
zankfrappa wrote:
If you click "Read" and click "Chessopedia" there is an article that discusses
"Distinct Chess Positions" and "Total Chess Positions".
The article is titled "Mathematics And Chess". After only two moves for each color there are already 71,852 distinct chess positions or 197,742 total chess positions, which I find amazing.
I don't fully understand the difference between distinct and total chess positions. Is it similar to the difference between combinations and permutations?
I'd assume so. It would seem that one of these would refer to a distinct order of moves, such as 1.Nf3 Nf6 2.d4 d5 rather than 1.d4 d5 Nf3 Nf6. So, you have to decide whether both of these ways of reaching the same position count or whether order of moves is irrelevant.
Mar 23, 2010
0
#35
TheGrobe wrote:
einstein_69101 wrote:
Also, your king cannot be in double check by two pieces of the same kind unless one of the attacking pieces was just promoted. A double check occurs when one piece moves out of the way of another piece such that both pieces attack the king. And there is no such thing as a triple check or a quadruple check.
Good ones, although you can arrive at a double-check with two Queens via en passant:
Ah, I stand corrected. You are right. We can do a double-check via en passant. :) I think that en passants and immediate pawn promotions are the only times where two pieces of the same kind can give a double-check.
einstein_69101 wrote:
TheGrobe wrote:
einstein_69101 wrote:
Also, your king cannot be in double check by two pieces of the same kind unless one of the attacking pieces was just promoted. A double check occurs when one piece moves out of the way of another piece such that both pieces attack the king. And there is no such thing as a triple check or a quadruple check.
Good ones, although you can arrive at a double-check with two Queens via en passant:
Ah, I stand corrected. You are right. We can do a double-check via en passant. :) I think that en passants and immediate pawn promotions are the only times where two pieces of the same kind can give a double-check.
Could someone please make a diagram to explain this concept of 2 queen double check via en passant?
There are at least hundreds, literally hundreds, of distinct legal chess positions.
thesexyknight wrote:
Could someone please make a diagram to explain this concept of 2 queen double check via en passant?
Scroll up.
dannyhume wrote:
There are at least hundreds, literally hundreds, of distinct legal chess positions.
I'm going to memorize all of them. How hard could it be?
TheGrobe wrote:
dannyhume wrote:
There are at least hundreds, literally hundreds, of distinct legal chess positions.
I'm going to memorize all of them. How hard could it be?
Good luck with that...I think the dudemar who originally wrote the "chunking" paper said "7" items of info was as much as the human brain could typically handle, hence phone numbers. Maybe 10-15 if you are a prodigy, but hundreds? You'd have to be "like that piece of garbage Kasparov. But he's more like an idiot savant. Outside of chess, he knows nothing."
I'd be interested to see what kind of coverage a database of master games might have across the resulting legal positions from the sample set that you pull. You should be able to get a rough idea how many of the legal positions have actually been realized in game play.
Ooh, that's a very interesting idea. Come to think of it, that would be easier to program. I already have a pgn reader, and I know where to get a ton of pgn games, so I could just have it read through the games and spit out the positions. Sort or hash the results and remove duplicates. It would take a lot of time and a fair chunk of storage. I'll have to try a test of that. It would also give me a chance to see just how unlikely it is to underpromote to a double-color bishop.
To my knowledge underpromotion to a bishop has been done in maybe 10 games in chess history...