💡📝Joe Joyce wrote on Mon, Feb 6, 2017 08:43 AM UTC:
The first problem with 4D is that there are far too many crazy diagonals. People cannot come close to visualizing them all. The second is forcing mate. There are too many ways to escape in 4D so that there need to be ways of restricting that 4D freedom to corral and mate a king. This is also a problem in 2D, but not as serious. However, on an infinite board, how many pieces are needed to mate a lone king? You need at least the king and a pair of rooks, the extra rook to provide the effect of a board edge.
I've dabbled in 3D, but find it vastly confusing, and harder to play than Hype. I don't know what the minimum requirement for forced mate is, nor what it takes to force mate on an infinite 3D board. The mating player has to attack 27 squares on 3 adjacent 2D boards with every attacker being defended or out of the king's capture range. For a fully 4D king, 81 squares in a 3x3 array of 2D boards have to be attacked with every attacker being defended or out of the king's capture range.
There seem to be only 2 options, restrict the king, and/or make other pieces powerful enough to capture a 3D or 4D king. Super-powered pieces bring problems of their own, especially in higher-D chess. They are impossible to guard against unless you clog the board with blocking pieces. And pieces with broad movement ability promote chaos in higher-D games. You essentially cannot predict the game state even a couple turns hence. Since the very powerful pieces act like missiles dropping out of the sky onto the target, you need area defense pieces, the equivalent of anti-missile batteries, much shorter range than the missile pieces, but invulnerable to missiles and able to shield neighbors, too. The "Missile Command" comment I made a while back discusses the idea. You'd need something to block the unblockable, a Neutralizer piece. Grin, I think I'd rather work out those ideas on a large 2D board!
The other way is to restrict the pieces in some significant way(s) without totally nerfing the 4D effects. That's basically the way I went here in Hype, along with the tiny board. But the held king rules allow the individual 2D boards to be any size - specifically longer than 5 squares/side - and still allow forced mate with K + 2 of the bishops and/or queen(s) against the lone king. Even on an infinite 2D board, you wouldn't need to add another rook to mate.
It’s a lot later than I wish it was, so I’ll just ask what your general goals are. Your 361 cell board should be big enough, but hex boards limit the number of simple pieces you can have. And my brain just stopped working here. grin, I guess that makes this a cliffhanger.
The first problem with 4D is that there are far too many crazy diagonals. People cannot come close to visualizing them all. The second is forcing mate. There are too many ways to escape in 4D so that there need to be ways of restricting that 4D freedom to corral and mate a king. This is also a problem in 2D, but not as serious. However, on an infinite board, how many pieces are needed to mate a lone king? You need at least the king and a pair of rooks, the extra rook to provide the effect of a board edge.
I've dabbled in 3D, but find it vastly confusing, and harder to play than Hype. I don't know what the minimum requirement for forced mate is, nor what it takes to force mate on an infinite 3D board. The mating player has to attack 27 squares on 3 adjacent 2D boards with every attacker being defended or out of the king's capture range. For a fully 4D king, 81 squares in a 3x3 array of 2D boards have to be attacked with every attacker being defended or out of the king's capture range.
There seem to be only 2 options, restrict the king, and/or make other pieces powerful enough to capture a 3D or 4D king. Super-powered pieces bring problems of their own, especially in higher-D chess. They are impossible to guard against unless you clog the board with blocking pieces. And pieces with broad movement ability promote chaos in higher-D games. You essentially cannot predict the game state even a couple turns hence. Since the very powerful pieces act like missiles dropping out of the sky onto the target, you need area defense pieces, the equivalent of anti-missile batteries, much shorter range than the missile pieces, but invulnerable to missiles and able to shield neighbors, too. The "Missile Command" comment I made a while back discusses the idea. You'd need something to block the unblockable, a Neutralizer piece. Grin, I think I'd rather work out those ideas on a large 2D board!
The other way is to restrict the pieces in some significant way(s) without totally nerfing the 4D effects. That's basically the way I went here in Hype, along with the tiny board. But the held king rules allow the individual 2D boards to be any size - specifically longer than 5 squares/side - and still allow forced mate with K + 2 of the bishops and/or queen(s) against the lone king. Even on an infinite 2D board, you wouldn't need to add another rook to mate.
It’s a lot later than I wish it was, so I’ll just ask what your general goals are. Your 361 cell board should be big enough, but hex boards limit the number of simple pieces you can have. And my brain just stopped working here. grin, I guess that makes this a cliffhanger.