# Chess 960 pieces

I'm just wondering, how do you you know where to put the pieces at the start of a chess 960 game.If someone explained it to me, then I think it would makea whole lot of sense when my friend does it.

Basically, wherever you want.

To be more precise:

1. They must be on the back rank
2. The King must be between the Rooks
3. This Bishops must be on different colored squares
4. The black pieces must be opposite their white counterparts

A good method for setting it up, is to write the numbers 1-8 on the bottom of the white Pawns, let the black player put the white Pawns on the board to make sure the white player does not know what is on their bottom, and let the white player put the Pawns on the second rank. Then, look on the bottom of each Pawn, and put behind them on the same file in the following order:

1. Behind 1, put a Bishop.
2. Behind the lowest-numbered Pawn on the files of the opposite color, (at most number 5) put the other Bishop.
3. Behind the Pawn with the lowest number that is left, put the Queen
4. Behind the next two lowest-numbered Pawns, put Knights
5. Now three holes are left (behind Pawn 6, 7 and 8). Put the King in the middle hole, the Rooks in the other two.
For white bishop-with a dice roll a number. If it is above 4 roll again. Depending on the number count the white squares from the left. If it is a 1 put it on the first white square etc. Do the same with the black bishop except on the black squares. For the knights roll the dice 2 times. Count out the number of squares for the first roll and place the 1st knight. Do the same for the 2nd and the queen. Put the two rooks on the two outside squares left and the king in the middle.
HGMuller wrote:
A good method for setting it up, is to write the numbers 1-8 on the bottom of the white Pawns, let the black player put the white Pawns on the board to make sure the white player does not know what is on their bottom, and let the white player put the Pawns on the second rank. Then, look on the bottom of each Pawn, and put behind them on the same file in the following order: Behind 1, put a Bishop. Behind the lowest-numbered Pawn on the files of the opposite color, (at most number 5) put the other Bishop. Behind the Pawn with the lowest number that is left, put the Queen Behind the next two lowest-numbered Pawns, put Knights Now three holes are left (behind Pawn 6, 7 and 8). Put the King in the middle hole, the Rooks in the other two.

Unfortunately this doesn't give an even distribution of the 960 starting positions. Positions where the king and the rooks are all on the same color are more likely to come up than other positions.

Ichabod over at bemweeks blog on Chess960 has done an exhaustive analysis of this creative idea for selecting Chess960 starting positions. Apparently Ichabod found that the distribution is not even as Ironic_begar has said:

You can see Ichabod's analysis in the comments to that blog post.

Enjoy 960!

Ichabod wrote:
Got it. The problem with the pawn set up method is that you are placing the rooks and the kings at the same time as everything else. That is, pawns 6, 7, and 8 will always be the rooks and the kings. If the rooks and the kings are all on the same color, there are only four ways to place the bishops. If one of the rooks or the king is on a different color, there are six ways to place the bishop. But the pawn ordering don't know that. There are the same number of pawn orderings whether or not the rooks and king are on the same color. So if they are on the same color, you have the same number of orderings going to fewer possible positions, making those positions more likely.

I took the liberty to quote Ichabod's blog posting here.

I think he is right. Picking the highest numbered Pawn on the remaining color for the second Bishop causes a non-uniformity in the color distribution of the Pawns that were skipped. These become more likely to be on the color of the first-placed Bishop. Which for placing the Queen is no problem (as it is arbitrary which Bishop was placed first), but does make it more likely that Queens and Knights end up on the same color as it should be, in case multiple Pawns where skipped.

I overlooked this effect when I tried to simplify the scheme from a more elaborate method I designed first. Sorry about that. But I still think the more elaborate method would be sound:

On the bottom of the white Pawns, write B, B*, Q, 2 x N, 2 x R and K.

On the bottom of the black Pawns, write ab, cd, ef, gh (each 2x)

Setting up starts as before, each player putting the opponent's Pawns on the board in such a way the opponent cannot see what is on the bottom. Then each player sets up his own Pawns.

1. The white player now reveals the bottom of his Pawns one by one, and puts the pieces behind the correspondingly-marked Pawns. Behind the B* Pawn he does not put a Bishop, however, but steals the black Pawn on the same file from the enemy lines to put behind it.
2. When the white back-rank is filled, the black player reveals the bottom of the stolen black Pawn. This indicates two squares, only one having the opposite color as the other (B) Bishop. (He puts the Pawn back into his own ranks, leaving a hole behind B*.)
3. The piece on that square is replaced by the not-yet-placed Bishop, and  moved to fill the hole behind B*.
4. If the King is not between the Rooks now, it is swapped with the Rook closest to it.
5. The black player mirrors white's piece placement.

This method should give you exactly equal probability for each starting position, as swapping a randomly chosen piece should not affect the distribution. Additional advantages of this method are that you don't have to search for a lowest number, but that each Pawn immediately tells you how to place or swap a piece, and that it is more explicit in mentioning the pieces, rather than having to remember which number corresponds to which piece type. The disadvantage is that it requires writing on the bottom of black Pawns.

HGMuller I just tried your new method out in real life after Ichabod confirms that it is equally distributed. Once you get the idea it is very simple! However there are a couple of very funny problems. There is felt on the bottom of my chess pieces and I cannot find a pen, pencil or crayon that will be visible on my black pieces without permanently marking them  I think someone has a small emerging market for selling Chess960 special chess sets now with felt and a sticker on the bottom of the pieces! I have to admit we needed a five minute break to rest our minds from setting up the pieces before the start of the match!

The issue for me now is that I also need to know the start number that corresponds to the position because the number helps me to remember the ideas I have studied in the past about that position. Therefore we must come up with a manual method to reverse engineer the number from the start position that can be calculated in the head!

Enjoy

Cheers

glider1001 wrote:

HGMuller I just tried your new method out in real life after Ichabod confirms that it is equally distributed. Once you get the idea it is very simple! However there are a couple of very funny problems. There is felt on the bottom of my chess pieces and I cannot find a pen, pencil or crayon that will be visible on my black pieces without permanently marking them  I think someone has a small emerging market for selling Chess960 special chess sets now with felt and a sticker on the bottom of the pieces! I have to admit we needed a five minute break to rest our minds from setting up the pieces before the start of the match!

The issue for me now is that I also need to know the start number that corresponds to the position because the number helps me to remember the ideas I have studied in the past about that position. Therefore we must come up with a manual method to reverse engineer the number from the start position that can be calculated in the head!

Enjoy

Cheers

number each piece like 1 for bishop, 2 for knight, three for rooks, 4 for queen, and 5 for king.  then you just count from a - h and get your number.  11223534 would give a back rank of bishop, bishop, knight, rook, king, rook, and queen for instance.

Unfortunateely the official numbering system (wher 518 is the opening position of standard Chess) is very awkward. To calculate it, you need to do several multiplications with nasty numbers. Basically the number is BishopCode + 16*QueenCode + 96*KnightCode. (16 is the number of different BishopCodes, 96=6*16 multiplies that with the number of different Queen codes. It would have been much smarter to use KnightCode + 10*QueenCode + 60*BishopCode in stead, because there are 10 different KnightCodes, and multiplication by 10 is easy. The official numbering system must have been designed by a computer prgrammer thinking in binary or hexadecimal...)

The individual codes you can get by counting (from the a-file) at the how-manieth position the piece is, starting the count at zero (another computer quirk...). White's black bishop counts 0,4,8,12, the white bishop 0,1,2,3. So with bishops on c1 (4) and f1 (2) you get 6 for the BishopCode. The queen you then count skipping the bishops, a1=0, b1=1, d1=2 (skipping the bishop on c1). Similarly, you count the knight skipping all already placed pieces (bishops, queen and possibly the other knight), the leftmost in decreasing steps starting at 4, (so 0, 4, 7, 9), and the right one staring the count after the left one (because otherwise it would not be the right one, right?). So Nb1 would be 4, and  Ng1 then 1 (e1=0, g1=1, h1=2). So the KnightCode is 5, and you get 6 + 16*2 + 5*96 = 6 + 32 + 480 = 518.

The counting to obtain the individual piece codes isn't so bad, and perhaps you can learn to count 0, 16, 32, 48, 64, 80 for the queen. The multiplication by 96 is a bit of a pain, though, and the KnightCode can run upto 9, so you would have to learn the table of multiplication for 96 by heart (0, 96, 192, 288, 384, 480, 576, 672, 768, 864). Still a pain. How much simpler it would have been to multiply the BishopCode by 60, and count the queen as 0, 10, 20, 30, 40, 50.

The method of numbering the Pawns is attractive because it requires no extra equipment beyond the basic chess set and is unobtrusive during play. It's a pity that the first proposal doesn't work. How about this...

1) Select two Pawns and use the numbers on these to place the Bishops, numbering the four light squares and the four dark squares from left to right, where numbers 5-8 are equivalent to 1-4. Return the Pawns to the set.

2) Place all eight Pawns at random as in the original proposal.

3) Ignoring the Pawns in front of the Bishops, which have already been placed, use the three lowest numbered Pawns to place the Queen and Knights.

4) Place the King and Rooks on the three empty squares with the King between the Rooks.

...If step (1) skews the results because the Pawns are taken at the same time (I'm not sure about this), then select the two Pawns one at a time and return the selected Pawn to the set each time. - Mark

This is one, i know nothing about chess 960 strategy.

bemweeks wrote:

...If step (1) skews the results because the Pawns are taken at the same time (I'm not sure about this), then select the two Pawns one at a time and return the selected Pawn to the set each time. - Mark

Step 1 does skew the results. Consider positions with a and b bishops. You can only get those by picking pawn 1 then pawn 5, or 5 then 1. But for positions with a and d bishops there are four ways: (1, 4), (1, 8), (2, 4), (2, 8).

I would suggest numbering both sets of pawns. Pick a white and a black pawn, use the white pawn to place the light bishop and the black pawn to place the dark bishop. Then mix up and place the white pawns to place the queen and knights. But picking one pawn, putting it back, and picking another pawn would work just as well if you didn't want to number the black pawns.

i want to create game chess960.......but how?

anyone help me plz....