Game Design Competition
A game resurrected from the Shared Pieces Game Design Competition from 2003 is Mark Thompson's Jade. Like Unlur (AG12), Jade was a revisioning of Hex. In Unlur, the two players each have their own kind of piece, although their objectives are different. Jade goes a step further by having the pieces belong to both players equally, although again the game works because the two players have distinct objectives. Jade is playable on Richard's Server. The Richard's Server rules for Jade contains some history, showing that investigation of Jade dates back at least to 2001.
Around the time Jade would have gone into the old AG17, there was some discussion in the community about the phenomenon of "chilling" in Jade. Situations would arise where the action in the game would become focused completely on one pair of spaces, in the sense that the remaining spaces could be filled in with black and white stones in any distribution without affecting the outcome of the game; on the other hand, movement to either of the key spaces would result in immediate loss by the opponent taking the other key space.
I do not know how frequently chilling occurred, but it was thought to be a flaw in Jade. Mark Thompson, author of Jade, spotted Hox in AG21, and suggested to me that the Hox protocol might be a solution to chilling in Jade. We investigated, and we think it is a solution, almost completely, in the sense that chilling can still occur, but only as an extreme outlier. The new game is called "Jed," which means "jade" in Malay. The three-letter name conveniently supports application of the Hox protocol! It is interesting to note that Jed would qualify for three of the four game design competitions we have run: shared pieces, unequal objectives, and now unequal board spaces.
Below, we have reproduced first the original article on Jade by Mark, as it would have gone in the old AG17. Following the Jade article is an Addendum on chilling, the apparent "flaw" of Jade. Then, we give Mark's rules of the new game Jed. A further Addendum follows based on email conversations this spring. ~ Ed.
Around the time Jade would have gone into the old AG17, there was some discussion in the community about the phenomenon of "chilling" in Jade. Situations would arise where the action in the game would become focused completely on one pair of spaces, in the sense that the remaining spaces could be filled in with black and white stones in any distribution without affecting the outcome of the game; on the other hand, movement to either of the key spaces would result in immediate loss by the opponent taking the other key space.
I do not know how frequently chilling occurred, but it was thought to be a flaw in Jade. Mark Thompson, author of Jade, spotted Hox in AG21, and suggested to me that the Hox protocol might be a solution to chilling in Jade. We investigated, and we think it is a solution, almost completely, in the sense that chilling can still occur, but only as an extreme outlier. The new game is called "Jed," which means "jade" in Malay. The three-letter name conveniently supports application of the Hox protocol! It is interesting to note that Jed would qualify for three of the four game design competitions we have run: shared pieces, unequal objectives, and now unequal board spaces.
Below, we have reproduced first the original article on Jade by Mark, as it would have gone in the old AG17. Following the Jade article is an Addendum on chilling, the apparent "flaw" of Jade. Then, we give Mark's rules of the new game Jed. A further Addendum follows based on email conversations this spring. ~ Ed.
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Jade
There are two players, named Cross and Parallel. In the standard game Cross moves first and Parallel moves second. The board is a hexagonal grid in the shape of a parallelogram; the size currently considered best is 9x11, but other sizes and shapes could be used.
A move for either player consists of placing either a Black or White stone onto the board. Either player may use either colour on any turn.
The two players have different objects. The object for Cross is to form a connected group of like-coloured stones (connected group defined as usual in hexagonal-grid connection games such as Hex or Havannah) that touches all four edges of the board. As in Hex, corner cells count as belonging to both the edges that meet there.
There are two players, named Cross and Parallel. In the standard game Cross moves first and Parallel moves second. The board is a hexagonal grid in the shape of a parallelogram; the size currently considered best is 9x11, but other sizes and shapes could be used.
A move for either player consists of placing either a Black or White stone onto the board. Either player may use either colour on any turn.
The two players have different objects. The object for Cross is to form a connected group of like-coloured stones (connected group defined as usual in hexagonal-grid connection games such as Hex or Havannah) that touches all four edges of the board. As in Hex, corner cells count as belonging to both the edges that meet there.
The object for Parallel is to form two connected groups, one of Black stones and one of White, such that both groups touch the same pair of parallel sides.
Passing is not allowed. The player whose objective is completed wins the game, even if the other player placed the final stone.
There are restrictions on opening moves on certain board sizes, which prevent a player from using a “symmetry strategy” for a trivial win: (1) If the board is the same odd number of rows and columns, and if Cross plays first, then Cross may not make his first move on the board’s short diagonal; (2) If the board has one even side and Cross plays first, then Parallel’s first move is not allowed to be in the cell directly opposite Cross’s first move (rotated 180 degrees about the centre of the board).
Note that if the board has an odd number of rows and a different odd number of columns, such as the standard 9x11 board, these rules will not come into play.
Draws are impossible. For if the board were completely filled with Black and White stones, and if the pairs of opposite edges were coloured one pair Black and the other pair White (like a Hex board's edges), then it would form a completed Hex board, and by the familiar proof either Black or White would have won the Hex game. But if the edges were then recoloured White and Black in the opposite sense, it would still form a completed Hex game on which either Black or White would have won. By the win-conditions of Hex and of Jade as described here, if both of these notional Hex games had been won by the same player, then Cross will have won the Jade game; on the other hand, if the two notional Hex games had been won by different players, then Parallel will have won the Jade game. Therefore any filled Jade board must have a winning group for either Cross or Parallel.◾️
There are restrictions on opening moves on certain board sizes, which prevent a player from using a “symmetry strategy” for a trivial win: (1) If the board is the same odd number of rows and columns, and if Cross plays first, then Cross may not make his first move on the board’s short diagonal; (2) If the board has one even side and Cross plays first, then Parallel’s first move is not allowed to be in the cell directly opposite Cross’s first move (rotated 180 degrees about the centre of the board).
Note that if the board has an odd number of rows and a different odd number of columns, such as the standard 9x11 board, these rules will not come into play.
Draws are impossible. For if the board were completely filled with Black and White stones, and if the pairs of opposite edges were coloured one pair Black and the other pair White (like a Hex board's edges), then it would form a completed Hex board, and by the familiar proof either Black or White would have won the Hex game. But if the edges were then recoloured White and Black in the opposite sense, it would still form a completed Hex game on which either Black or White would have won. By the win-conditions of Hex and of Jade as described here, if both of these notional Hex games had been won by the same player, then Cross will have won the Jade game; on the other hand, if the two notional Hex games had been won by different players, then Parallel will have won the Jade game. Therefore any filled Jade board must have a winning group for either Cross or Parallel.◾️
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Addendum 1
Jade was played for a few years in the early 2000's. There was discussion around the phenomenon of "chilling" in Jade, as described above. The game remains ultimately decisive, in that eventually the rest of the board would have to fill up and force the fatal move, which means that the player who moved first will win on an 11x9 board. Here is a concrete example of chilling:
Jade was played for a few years in the early 2000's. There was discussion around the phenomenon of "chilling" in Jade, as described above. The game remains ultimately decisive, in that eventually the rest of the board would have to fill up and force the fatal move, which means that the player who moved first will win on an 11x9 board. Here is a concrete example of chilling:
- If Cross moves to either grey square, Parallel will place a piece of the other colour in the other grey square to win.
- If Parallel moves to either grey square, Parallel will place a piece of the same colour in the other grey square to win.
- The remaining empty blue spaces can be filled with any permutation of black and white pieces, with neither player winning. ~ Ed.
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Jed
Jed is basically Jade with the "hox protocol" for placing stones, as described in the game Hox, by Larry Back, AG21. The board spaces are identified with the letters H, O, and X. Moves must be made in the order ...H-O-X-H-O..., and so on, in a regular cycle. Hox is Hex with the hox protocol; Jed is Jade with the hox protocol, or perhaps we should call it the "jed protocol." Jed is the Malay word for Jade, which conveniently has only three letters! Here is an 9x11 Jed board:
Jed is basically Jade with the "hox protocol" for placing stones, as described in the game Hox, by Larry Back, AG21. The board spaces are identified with the letters H, O, and X. Moves must be made in the order ...H-O-X-H-O..., and so on, in a regular cycle. Hox is Hex with the hox protocol; Jed is Jade with the hox protocol, or perhaps we should call it the "jed protocol." Jed is the Malay word for Jade, which conveniently has only three letters! Here is an 9x11 Jed board:
As with Jade, you need a sufficient quantity of black and white stones. The players take turns to place stones on vacant spaces on the board. Either player can play either colour at any time, as with Jade. The first player begins by placing a stone on any vacant space. Thereafter, stone placement must follow a strict order, ...J-E-D-J-E..., and so, or equivalently, ...Red-Green-Yellow-Red-Green..., and so on. Thus, if a player places a piece on a J(Red)-space, his opponent must immediately follow with a move to an E(Green)-space. Likewise, E(Green) is followed by D(Yellow), and D(Yellow) is followed by J(Red). The players can choose to follow the letters or colours, whichever is easiest to remember, "JED" or the traffic-light order of Red, Green, and Yellow.
One player is Cross, the other is Parallel. The objectives of Jed are identical with that of Jade above, for which the colours and letters are irrelevant. Cross must connect all four sides of the board with a cross of like-coloured stones; Parallel must connect two parallel sides with two lines of opposite colour. Cross may connect the pair of sides the shorter distance apart, or the other pair of sides the longer distance apart. Examples of the objectives of Cross and Parallel are shown above in the rules of Jade, above.
A modified pie rule operates in Jed. The first player moves and declares as either as Cross or as Parallel, and the second player can choose either to reply with a move and play the other role, or adopt the move and the role and return play to the first player.
Those are the full rules of Jed. Other sizes of board of course are possible. It is convenient to have one of the sides divisible by three, so that the board fills with an equal number of J-, E-, and D-spaces. Other sizes are playable, with total number of spaces not divisible by three, but you must be careful which type of space is occupied first in order that it is possible to fill to whole board by the end of the game. ◾️
One player is Cross, the other is Parallel. The objectives of Jed are identical with that of Jade above, for which the colours and letters are irrelevant. Cross must connect all four sides of the board with a cross of like-coloured stones; Parallel must connect two parallel sides with two lines of opposite colour. Cross may connect the pair of sides the shorter distance apart, or the other pair of sides the longer distance apart. Examples of the objectives of Cross and Parallel are shown above in the rules of Jade, above.
A modified pie rule operates in Jed. The first player moves and declares as either as Cross or as Parallel, and the second player can choose either to reply with a move and play the other role, or adopt the move and the role and return play to the first player.
Those are the full rules of Jed. Other sizes of board of course are possible. It is convenient to have one of the sides divisible by three, so that the board fills with an equal number of J-, E-, and D-spaces. Other sizes are playable, with total number of spaces not divisible by three, but you must be careful which type of space is occupied first in order that it is possible to fill to whole board by the end of the game. ◾️
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Addendum 2
The interesting question now is how the hox protocol salvages Jade from the chilling flaw. Suppose the two cells of a chilling pair, as described in the example above, were different types, say, J and E. The player with the next E move would be able to play the E of the chilling pair, knowing her opponent must respond by playing in a D somewhere, after which she can take the J of the chilling pair.
This form of chilling situation is shown in the diagram below left. (J-E-D rotation, or alternatively Red-Green-Yellow rotation)
In regular Jade, X and Y would be a chilling pair: a player could take either space and then immediately lose as her opponent takes the other chilling space. In Jed, however, Player A could take X, Player B must take a green space somewhere, and then Player A can take Y to win. (Player A chooses to play black or white at X, according to whether she is Cross or Parallel.)
The interesting question now is how the hox protocol salvages Jade from the chilling flaw. Suppose the two cells of a chilling pair, as described in the example above, were different types, say, J and E. The player with the next E move would be able to play the E of the chilling pair, knowing her opponent must respond by playing in a D somewhere, after which she can take the J of the chilling pair.
This form of chilling situation is shown in the diagram below left. (J-E-D rotation, or alternatively Red-Green-Yellow rotation)
In regular Jade, X and Y would be a chilling pair: a player could take either space and then immediately lose as her opponent takes the other chilling space. In Jed, however, Player A could take X, Player B must take a green space somewhere, and then Player A can take Y to win. (Player A chooses to play black or white at X, according to whether she is Cross or Parallel.)
In the diagram to the right, however, both spaces of the chilling pair are the same colour, Yellow. The chilling fault still exists. In regular Jade, the whole board is eventually filled up aside from the chilling pair. In this particular situation in Jed, however, a green and red space will be left unfilled before one player or the other is forced to move to X or Y.
Chilling can still occur in Jed. However, the author thinks it will be far less frequent than in Jade. Interestingly, if the first space played to in the game is J, say, then the final sequence in the chill situation must be D-J-E-D. Therefore, from the start the players must know the identity of any future chilling pair. If J is played to first, the chilling pair will be D's; if E is played first, the chilling pair will be J's; if D is played first, the chilling pair will be E's. Perhaps this insight can factor into the play. The first player will always win in a chilling pair situation. The second player will know the colour of the chilling pair and must avoid its creation. Will this influence strategy? Maybe it would at an advanced level.
Chilling can still occur in Jed. However, the author thinks it will be far less frequent than in Jade. Interestingly, if the first space played to in the game is J, say, then the final sequence in the chill situation must be D-J-E-D. Therefore, from the start the players must know the identity of any future chilling pair. If J is played to first, the chilling pair will be D's; if E is played first, the chilling pair will be J's; if D is played first, the chilling pair will be E's. Perhaps this insight can factor into the play. The first player will always win in a chilling pair situation. The second player will know the colour of the chilling pair and must avoid its creation. Will this influence strategy? Maybe it would at an advanced level.
On the standard 9x11 board size, Parallel needs a minimum of 18 stones for a win, whereas Cross needs 19. The difference in number of stones needed to win does not necessarily mean that Parallel has the advantage. Indeed, it was thought initially, in the old days when Jade was played, that Cross rather than Parallel would have the advantage. Mark Thompson says of this,
"It’s been a long time since the 9x11 board dimensions were chosen, and I don’t recall now whether your observation about number of stones for a winning pattern was considered or not. To my best recollection, I didn't feel as confident as other players did that 9x11 was going to prove to be equally balanced: I think it would require much more testing to say. It seemed to me that Cross has an innate advantage on a rhombic board but that Parallel would “clearly” (or is it really clear?) have an advantage on a very long and thin board, and therefore presumably some aspect ratio would provide a reasonably equal game, to the limits of human players, which is all I’d be interested in. (Of course no abstract perfect-information drawless game can ever be balanced if completely analyzed.)
"I’ve forgotten my 20-years-ago reasons for thinking Cross has an advantage, apart from board shaping, but it might be because Cross only needs a group of one colour to be strong, while Parallel needs groups of two colours—though they don’t need to be quite as strong as Cross needs his to be. But this means Parallel has less effective choice about which colour to play each turn: Parallel needs a balance of influence between White and Black, while Cross needs one colour to dominate. Hence Cross may get more benefit from a move switching colours, and using a kind of jiu jitsu to take advantage of the strength Parallel has already invested in that colour."
Either way, Jed offers a different approach to a Hex-type game, involving shared pieces, asymmetrical objectives, and unequal board spaces, surely an unusual combination! ~ Ed.
"It’s been a long time since the 9x11 board dimensions were chosen, and I don’t recall now whether your observation about number of stones for a winning pattern was considered or not. To my best recollection, I didn't feel as confident as other players did that 9x11 was going to prove to be equally balanced: I think it would require much more testing to say. It seemed to me that Cross has an innate advantage on a rhombic board but that Parallel would “clearly” (or is it really clear?) have an advantage on a very long and thin board, and therefore presumably some aspect ratio would provide a reasonably equal game, to the limits of human players, which is all I’d be interested in. (Of course no abstract perfect-information drawless game can ever be balanced if completely analyzed.)
"I’ve forgotten my 20-years-ago reasons for thinking Cross has an advantage, apart from board shaping, but it might be because Cross only needs a group of one colour to be strong, while Parallel needs groups of two colours—though they don’t need to be quite as strong as Cross needs his to be. But this means Parallel has less effective choice about which colour to play each turn: Parallel needs a balance of influence between White and Black, while Cross needs one colour to dominate. Hence Cross may get more benefit from a move switching colours, and using a kind of jiu jitsu to take advantage of the strength Parallel has already invested in that colour."
Either way, Jed offers a different approach to a Hex-type game, involving shared pieces, asymmetrical objectives, and unequal board spaces, surely an unusual combination! ~ Ed.