Ratings & Comments

Suppose I have a Rook on d4. Could it move to 4? Or could it only move as far as a4? Likewise, could a Rook on d5 move to 5, or could it only move as far as g5?

I had already answered that before, as follows:

A rook/queen on the rank 4 can only occupy square a4 and not square 4. This applies to the switch h5/5 vice versa.

"So, I gather that the following are all legal moves:

B d1-4, B 4-d1, B e8-5, B 5-e8"

That is absolutely correct.

"So, it looks like the diagonal from 4 to the first rank is a different color than 4, and the diagonal that goes from 5 to the last rank is a different color than 5, and that is how the color changing is done."

By the way: The squares 4 and 5 do not have a uniform color. The squares are each composed of both colors. This is the only way to make a color change possible.

I try to follow. So a Rook cannot go from a4 to 4. And I understood that if there is a piece on a4, it is not possible to have another piece on 4.

At the end I wonder if this game is simply playable. I wouldn't be able to explain it to anyone I'm afraid.

I'm pretty sure that it would be possible to build something interesting on Gernd's idea by melting the cells a4 & 4, as well as h5 & 5. Which was similar to HG's diagram.

Doing this

• only 1 piece allowed on a4/4 or on h5/5
• a Rook on a1 would threat up to b8 AND a8 (as wished by Gernd)
• a Rook on h4 would threat up to a4/4
• a Bishop on d1 would go up to a4/4
• a Bishop on a4/4 would either go to f8 (keeping the color) or to d8 (switching the color).
• a Knight on a4/4 could go to b6, c5, a6, c6, b3, a2, b2, c3 (interesting)
• Chess 66 would have 64 cells which is maybe the real problem.

Dear En Bw, thank you for your comment, which is absolutely correct.

I'm testing my code for Chess66 on Game Courier right now, and with a Knight on a3, I currently have its legal moves as a5, c5, c4, c2, and b1. Because 4 is right above it, it looks like b5 could be another legal move by going over 4 and a5 and turning right to b5. It could be argued that this is illegal because there is a single-direction path from a3 to b5. But if that rules that out, it might also rule out a5 as a legal move, because there is a single-direction path to it through 4.

I don't think that the moves to a5 and b5 are legal since they are on the same line. Merging the squares 4 and a4 would not change that. On the contrary, the possibility of being able to detect movements on the same line or the same diagonal would be diluted.

A rook/queen on the rank 4 can only occupy square a4 and not square 4. This applies to the switch h5/5 vice versa.

That's interesting; given that a rook is allowed to move sideways from 4 onto b4 and beyond, that means that a rook on 4 can threaten a rook on b4 without being attacked back. Is this intentional?

The squares 4 and 5 do not have a uniform color. The squares are each composed of both colors.

Strictly speaking, the colours on the squares are a representational convention and bear no real influence on the game; ‘a bishop can change colour’ is equivalent to saying a bishop can reach the whole board, or in other words all squares are effectively the same colour. But that's a minor quibble

En Bw

I assume you mean me? That's one correct letter out of four, with two more misplaced ;)

I don't think that the moves to a5 and b5 are legal since they are on the same line.

That's one of the few things which changes depending on the knight‐move definition; the definition you've chosen would indeed exclude both destinations, as a queen can reach both of those squares; but the more usual definitions H.G. first brought up (either two othrogonal steps in one direction and one at right angles, or (my preferred expression) one orthogonal and one diagonally outwards — in either order (or not…?) and for some suitable definition of ‘outwards’) would probably allow both moves. Equally the question of whether N h4–g6 is legal, and probably other similar moves, is implicated there. There may be some way of defining the knight move to include only a subset of the moves in question, but that's unltimately for Gerd to decide if he wants to look for (or someone else to contribute if they come up w/ sth).

En Bw

I assume you mean me? That's one correct letter out of four, with two more misplaced ;)

The other one was turned upside-down but left in place. So, they're all there with some mix-ups. :)

I'm done working on Chess66 for Game Courier today. The directions are looking good, but I still have to adapt the Pawns to work with switches, and I still have to prevent double occupancy of the switches. Since Firefox won't remember this after I shut down my computer, here are the moves I've been making to test things out. In the meantime, feel free to check it out, and apart from the issues I just mentioned I still need to work on, let me know if you find any illegal moves it permits or any legal moves it doesn't permit.

1. P c2-c4 
1... p f7-f5 
2. Q d1-A4 
2... q e8-H5 
3. Q A4-a7 
3... p f5-e4 
4. N b1-a3 
4... q H5-e5 
5. P c4-d5 
5... q e5-d4 
6. N a3-c5 
6... p e7-e6 
7. Q a7-a3 
7... b f8-e7 
8. N c5-A4 
8... b e7-g4 
9. P b2-b3 
9... b g4-H5 
10. P b3-b4 
10... q d4-b4 
11. Q a3-g3 
11... p g7-g5 
12. P d5-e6 
12... p g5-f4 
13. Q g3-h7 
13... r h8-h7 
14. N A4-d5 
14... b H5-g6 
15. N g1-h3 
15... n b8-c6 
16. N d5-a4 
16... b g6-h5 
17. N a4-c3 
17... q b4-c5 
18. P e2-e3 
18... b h5-h4 
19. P a2-a3 
19... q c5-h5 
20. N c3-a4 
20... q h5-h6 
21. N a4-c6 // - Check! -
21... p b7-c6 
22. N h3-f4 
22... q h6-e6 
23. N f4-h6 
23... q e6-d5 
24. N h6-f5 
24... n g8-h6 
25. N f5-c4 
25... b h4-e8 
26. P a3-a4

8. N c5-A4

According to my definition, the switch can only be operated from 'below'. After that, the move N c5-A4 would not be possible. N d5-a4 would be possible. However, in my reply to Bn Em I proposed an extension of my definition.

17. N a4-c3 ---> N a4-c2

18. N f5-c4 ---> N f5-d4

"En Bw" - sorry, won't happen again.

"That's interesting; given that a rook is allowed to move sideways from 4 onto b4 and beyond, that means that a rook on 4 can threaten a rook on b4 without being attacked back. Is this intentional?"

That doesn't seem logical indeed.

Assuming a rook is on 4 and an opponent's rook is on e4, my definition means that the rook on 4 can attack the rook on e4, but the reverse is not possible. That's inconsistent. It is probably appropriate to add that the switch can be operated not only from 'below' but also from the side. This would eliminate the inconsistency.

According to my definition, the switch can only be operated from 'below'. After that, the move N c5-A4 would not be possible.

A switch is an overlapping pair of spaces that in some ways operate together as a single space. By their very nature, they operate as a switch only from a given direction. From below, a piece is given two choices for how to continue its vertical movement. However, this property of a switch is not a property of the individual spaces whose overlap constitutes the switch. So, restrictions on movement to A4 have nothing to do with your definition of a switch. They are simply arbitrary restrictions on movement.

There are already other examples of A4 being reachable from above. For example, a Rook or Queen on a8 could move to A4, and a Bishop or Queen on e8 could move diagonally to A4. You have also agreed that it makes sense to let it be reachable from the side.

I'm now going to propose some rule changes. Since the switch can make a piece more powerful, this should be balanced by making a piece using a switch more vulnerable. Allow pieces access to the spaces of a switch from any direction, and when a piece moves to a switch, allow capture of any piece on the switch even if the capturing piece moves to the other space. For example, if a Bishop is on A4, and a Rook moves to a4, consider the Bishop on A4 to be captured.

Currently, the Knight is the only piece whose powers of movement are restricted in the vicinity of a switch. Correct this by allowing a Knight to move to any space that can be reached by a step in an orthogonal direction followed by a step in an outward diagonal direction, or by a step in a diagonal direction followed by a step in an outward orthogonal direction. This is the normal definition for how a Knight moves in Chess and other variants, and it would allow the Knight to also increase its capabilities in the vicinity of a switch.

One last rule change I would suggest is to let Rooks, Queens, and Kings use their ability to move horizontally to switch between the spaces constituting the switch. This would basically involve lifting one more restriction on movement to the spaces making up a switch.

The moves B a4–c2; R a6–4 are legal moves, they are conform to the rules.

Move 17: N a4-c3 doesn't seem legal, but N a4-c2 would be legal.

Move 25: N f5-c4 doesn't seem legal in same way, but N f5-d4 would be legal again.

I have started writing up a brief summary of the rules to appear underneath the board for Game Courier.

Move 17: N a4-c3 doesn't seem legal, but N a4-c2 would be legal.

It looks legal to me. Why wouldn't this move be legal? Meanwhile, a4 and c2 are along a diagonal, and N a4-c2 would definitely be illegal.

Move 25: N f5-c4 doesn't seem legal in same way, but N f5-d4 would be legal again.

N f5-c4 is a perfectly legal Knight move, and I see no reason why it would be illegal. Meanwhile, f5 and d4 are diagonally adjacent, and N f5-d4 is clearly illegal.

When you're examining the moves, be sure to click on Record, paste the moves into the box, and click on View. This will let you view each position. I think you made some wrong judgements, because you got confused about how notation for this game works. Vertical movement shifts to an adjacent file as it goes between the 4th and 5th ranks. So, the space immediately above d4 is e4, for example.

You can agree on almost everything, certainly to make the game playable and programmable. Regardless of that, I can only say my point of view and describe my intentions.

"A switch is an overlapping pair of spaces that in some ways operate together as a single space."

From my point of view it looks different. The square a4 of a switch is an independent square and is completely identical to the square a4 in normal chess. 4 (A4) is a composite square consisting of a half and triangle part of a4 and the new triangle due to board geometry. The new square 4 (A4) gets the same play options as all squares of the game board - 4 (A4) is considered equal.

This means that the squares a4/4 (A4) must first be seen independently. These independent fields get an additional function when they work together and act as a switch, as described.

My intention is therefore not compatible with the proposal to merge fields 4/a4 (A4) as proposed by Jean-Louis.

It is possible to agree on the sides from which the switch should be accessible. We have clarified access from below and from the side, access from above is also not a problem and is already part of my proposal. The only question is whether it is access to the switch as a unit or to the individual square of a switch. According to my intention, the second applies.

"Allow pieces access to the spaces of a switch from any direction, and when a piece moves to a switch, allow capture of any piece on the switch even if the capturing piece moves to the other space. For example, if a bishop is on A4, and a Rook moves to a4, consider the Bishop on A4 to be captured."

As described, access to the switch from all sides is not a problem. It is possible to agree on the proposal, but it does not fit my intention. However, if the game becomes more playable and programmable - so what.

To the Knight: I can't allow anything here, but I can say what my point of view is. If we stick to the fact that the squares of a switch should be seen separately, then knight moves ending on the same line are not possible. However, as the game becomes more playable and programmable, compromises should be possible.

"One last rule change I would suggest is to let Rooks, Queens, and Kings use their ability to move horizontally to switch between the spaces constituting the switch. This would basically involve lifting one more restriction on movement to the spaces making up a switch. "

I have problems with that. I have emphasized that the squares of a switch represent independent squares. This would rather mean that moves between the squares of a switch are possible. The independence of the squares on the one hand and the functionality of a switch on the other compete with each other. Regarding the direct change between the squares of a switch, I tend towards the superordinate function, so a direct change should not be possible. At least that's my intention. But here, too, compromises determine reality.

You're right. I have disregarded the change between the 4th and 5th rank. I fell into my own trap :).

"A switch is an overlapping pair of spaces that in some ways operate together as a single space."

From my point of view it looks different. The square a4 of a switch is an independent square and is completely identical to the square a4 in normal chess. 4 (A4) is a composite square consisting of a half and triangle part of a4 and the new triangle due to board geometry. The new square 4 (A4) gets the same play options as all squares of the game board - 4 (A4) is considered equal.

This means that the squares a4/4 (A4) must first be seen independently. These independent fields get an additional function when they work together and act as a switch, as described.

I didn't say anything different. We're in agreement that the spaces composing a switch are separate from each other. But since they cannot be simultaneously occupied, and occupation of one space blocks movement through the other, and they share a common edge and a common corner, they also function in some ways like the same space.

It is possible to agree on the sides from which the switch should be accessible. We have clarified access from below and from the side, access from above is also not a problem and is already part of my proposal. The only question is whether it is access to the switch as a unit or to the individual square of a switch. According to my intention, the second applies.

Agreed. Use of the switch as a switch is possible only from below. That is due to the nature of how it works. If a piece moves to a switch through a diagonal move or a Knight move, it will have to stop on the switch, which will prevent it from using the switch to alter the direction of its movement. The same is true if a Rook or Queen moves to a switch from the side. It will have to stop there, which will prevent its use as a switch. And if a Rook or Queen moves to a switch from above, it will have only one path through the switch. So, it won't be utilizing the switch as a switch. This shows that access to the spaces composing a switch is a completely different matter than using it as a switch.

"Allow pieces access to the spaces of a switch from any direction, and when a piece moves to a switch, allow capture of any piece on the switch even if the capturing piece moves to the other space. For example, if a bishop is on A4, and a Rook moves to a4, consider the Bishop on A4 to be captured."

As described, access to the switch from all sides is not a problem. It is possible to agree on the proposal, but it does not fit my intention. However, if the game becomes more playable and programmable - so what.

What I'm proposing fits with the rule that both spaces of a switch cannot be occupied at the same time and the rule that occupancy of either space blocks vertical movement through the switch even when that movement would technically be going through the other space in the switch.

To the Knight: I can't allow anything here, but I can say what my point of view is. If we stick to the fact that the squares of a switch should be seen separately, then knight moves ending on the same line are not possible. However, as the game becomes more playable and programmable, compromises should be possible.

We could just say that because of the way that switches affect the geometry of the board, some spaces may be reached by either a vertical move or a Knight move. This would also correct the injustice done to the Knight of making the weakest piece even weaker around a switch while it gives all other pieces greater mobility.

"One last rule change I would suggest is to let Rooks, Queens, and Kings use their ability to move horizontally to switch between the spaces constituting the switch. This would basically involve lifting one more restriction on movement to the spaces making up a switch. "

I have problems with that. I have emphasized that the squares of a switch represent independent squares. This would rather mean that moves between the squares of a switch are possible.

Precisely.

The independence of the squares on the one hand and the functionality of a switch on the other compete with each other. Regarding the direct change between the squares of a switch, I tend towards the superordinate function, so a direct change should not be possible.

Allowing a piece that can move horizontally to move from one space to the other in a switch as a normal move does not affect the functioning of the switch. While the piece is on either space, other pieces can't pass through the switch, and once the piece leaves the switch, pieces will be able to pass through it again.

Just to make sure I fully understand this:

A Bishop on a4 could move along c5-d6-e7-f8 but not b5-c6-d7-e8. For a Bishop on 4 the reverse would be true. But that also means a Bishop on a4 can only be captured from c5-d6-e7-f8 and not from b5-c6-d7-e8.

If this is true the only thing that 'switches' are the connections of 4/a4 to the upper board half. These are either to a5 (f) and b5 (fr), or to a5 (fl), b5 (f) and c5 (fr). And the switch is only in a determined state when 4/a4 is occupied. (And that state has to be chosen as part of the move that occupies it.) When the square is empty you can use all the connections to enter it from above, or to leave it in the same move when you entered it from below.

The intepretation of this that I consider conceptualy the simplest is that 4/a4 is indeed a single square cell, but that the setting of the switch is extra game state. Which can conveniently be indicated by placing the piece that occupies it in the right or left half of the cell, as the distinction only has to be made when the square is occupied. In a computer implementation one could implement the state of the switch through making separate cells of 4 and a4, with only single exits to 5th rank, and duplicate the exits to it from a3 (f), b3 (fl) and b4 (l) so that one connects to 4, the other to a4, both available at any time. But that still would require some 'unnatural' treatment of the spaces 4/a4, to consider one blocked when the other is occupied.

The issue of teh Knight is really an independent one. If the Knight's move is defined 'subtractively', by excluding moves that a Queen can do, its mobility is reduced in the vicinity of the switch, as Q gets extra moves there. In a 'constructive' definition of the Knight move, it would benefit from the switch topology to get extra moves as well.

"A Bishop on a4 could move along c5-d6-e7-f8 but not b5-c6-d7-e8. For a Bishop on 4 the reverse would be true. But that also means a Bishop on a4 can only be captured from c5 -d6-e7-f8 and not from b5-c6-d7-e8.

If this is true the ...."

This is absolutely correct when considering the squares of a switch as separate squares. This looks different if the switch is seen as a unit. But that's a convention that needs to be met. I have already described my intention, but it is not an absolute requirement.

"The issue of teh Knight is really an independent one. If the Knight's move is defined 'subtractively', by excluding moves that a Queen can do, its mobility is reduced in the vicinity of the switch, as Q gets extra moves there. In a 'constructive' definition of the Knight move, it would benefit from the switch topology to get extra moves as well."

Exactly this consideration speaks for a separation of the fields 4/a4. A knight starting from 4 via a5, a6 lands on b6. With a switch as a unit, b6 is on the same line. With 4 as a separate square, b6 is not on the same line. For a4 vice versa. That would be my consideration. I'm thinking of novice players who will notice exactly this inconsistency.