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After all this time, I find VR Parton has already suggested 3 boards for Alice, with player choice of which of the 2 possible destination boards to end upon. And I found it here, on this site, in a spot I didn't know existed. http://www.chessvariants.org/parton/Curiouser&Curiouser.txt I quote from page 10: "Alician Chess can also be played on three boards of identical size. In this case the player has now a choice between two corresponding squares to which the piece that he plays may be transferred, though of course one these may sometimes happen to be occupied, thus allowing no choice." The link above the quote takes one to 31 pages of Parton's thoughts on Alice and various other variants, which he saw as related to Alice. I do not know if he ever made explicit that in Alice with 2 boards, the knights are colorbound, nor that giving one the choice of boards unbinds them. There is a comment on this idea that suggests a standard 8x8x3 3D chess board could be used, but then suggests a modification to 3-board Alice that would re-bind the knights, namely only allowing pieces on the center board to choose which of the other 2 boards to transfer to, and only allowing the top and bottom boards to transfer to the middle. This, I believe, only makes the colorbinding worse. (Sorry, Larry!) Finally, I'd like to point out that the construction of this website presents a lot of "Secret Gardens" that are difficult to find, but once found offer a multitude of surprises.
Another idea about the 3x8x8 3D field. Restricting the King from translating to a similar cell which is attacked on the middle level. So that a King could not move from the bottom level to the top d4 cell if the d4 cell of the middle level was attacked by the opponent. And a player could trap an opposing King with their own. For example, a King on the top a1 cell could pin an opposing King on the bottom b2 cell by simply translating to the b2 cell of the middle level. Neither King would directly attack the other in this position, and the King on the middle level could still 'release' this trap by translating to the top level. This might greatly aid in the endgame.
Larry, Charles, thanks for the comments. I truly appreciate different viewpoints, and every designer likes his/her work discussed. DA3 came about because I was fascinated with the concept of Alice's involuntary move. Chess is the quintessential game of control; you win by moving your totally controlled pieces just so. And Parton took that total control away. Your move wasn't just yours - you had to make an extra move without recourse. If you couldn't, you lost. That was the key idea of Alice, the loss of control over a piece's endpoint. You have total control over the move, but VR Parton controls which board your piece winds up on. The results of Alice's changes include the colorbinding of the knight, the halving of starting piece density, and the extra difficulty in making a move, as you need an extra square to be free to make each move. Those are negative, Positive changes include being able to move 'past' a line of defenders on the opposite board to set up a threat or check on that board after the transfer, and the ability to take a piece and escape to another board, possibly dodging recapture. DA3 mitigates the negative factors, allowing the knights to attack every square on the gameboard, giving 3x the number of squares to move to with a lower starting piece density to allow much easier moves, and taking away the forced part of Parton's involuntary board transfer by giving players a choice of boards to land on. The 'extra board' also enhances the ability to get by defenders and the ability to hit and run. The larger absolute numbers and types of pieces in DA3 allow new options in Alice. The inclusive compound pieces allow multiple board changes in a single move - well, 2 anyhow - at the players' discretion. The larger absolute number of pieces with the 'attacks every adjacent square' property allows a close-in defense of the king that standard Alice cannot. The leaping ability of a large percentage of the pieces also changes the game, allowing new tactics to get past pawns and pieces on the same board... Yeah, well, I do try to give good value for the money, and present a new experience with each game. VR Parton had a brilliant idea. I've had the fortune [good or bad I'll leave up to the reader] to be able to expand on it. I've enjoyed the process. In a sense, what I did was introduce a twist into Alice, which acts somewhat like the twist that makes a paper ring into a moebius strip. It allows the knights to reach both colors of the gameboard as its most obvious characteristic. But I hope the game offers more than just the unbinding of the knights. ;-)
Good point, Charles. Let's simply make the condition for moving from the top to bottom level(or vice versa) predicated on the similar destination cell of the middle level being vacant. So that a move from the bottom level to d4 on the top level is only possible if the d4 cell of the middle level is not occupied. This will allow for blocking an opponent's move or capture, although this tactic might not be utilized that often.
Larry Smith's suggestion for moving between boards would negate the advantages of going from two to three boards in the first place. The whole point is that Knights can return to the same board in an odd number of moves.
Don't know if anyone has pointed this out but-- This game might play nice on the commercial 3x8x8 field. Allowing only transfers to the central level from the top and bottom, but to either top or bottom from the central level. Just a thought.
Thank you for the comment, Daniil. I'll disagree with you to a slight extent, but it's a matter of interpretation, not effect. Alice is 3-dimensional, even if that '3D' effect is achieved by adding 2D and 1D, a gimmick 3D if you will, rather than allowing full 3D freedom on the board. And Directed Alice, which allows a choice of which other 2D board to go to, is 'more fully 3D' than Alice itself is. The switching between boards gives greater freedom of movement than just moving on separate 2D boards alone does. But as I said, it's more semantics than physics. I have considered games similar to what you've suggested here, but not in a chess context, and not much* recently [say the last 30 years.] I've gone to simpler boards over the years - the games are easier to design. ;-) Others have, however. One step toward what you discussed is Chess on the Rainbows. http://www.chessvariants.org/index/msdisplay.php?itemid=MPchessontherain *Did design a 4D wargame with an option of a small 5D 'transfer board' that's connected to all the other 'levels/2D boards'. And each 2D board has terrain, hills, trees, towns, with elevation and blocking rules that apply acroos the levels, so that kinda adds another dimension...
Interesting: Alice chess is not 3-dimensional, but it's moving between several 2-dimensional worlds. So, what about game, where pieces moves between many 0-dimensional worlds (0-dimensional board have only 1 square)? For example, there are several groups of these 'worlds' (cells), each group have certain color. Say, piece A moves from red squares to blue and green suares, from blue squares to purple and yellow squares, and so on, piece B, for example, from red squares moves to yellow, orange and green squares if no more than half of blue squares or no less than half of brown squares are occuppied, and so on? What do you think?
Thank you, Larry, for the kind words. So once again we meet over a Parton variant [a fine place to meet, in my opinion.] At least this time I know it's a Parton variant. :) I can only hope posting this one works as well as posting the last one did. It, too, needs playtesting. The problem of the slippery king in higher dimensional chess is one I've enjoyed working on for a while, although not at first. When I first realized just how slippery the higher-D king is, didn't know how many years of frustration would ensue until, with help, I finally got somewhere. I, too, am curious about just how the king gets checkmated. Certainly my previous solution cannot be employed here; it would be just wrong, very wrong to prevent a king in Alice from moving off the board it's on. But I think the number and right mix of pieces might just suffice for 3D. Don't know how well it would work out in 4D, although I have some ideas for specific pieces to deal with that, too, in case you were thinking of Directed Alice Cubed. The key to mate here might be in the ability of inclusive compound pieces to change boards twice in a move. This gives these pieces a greater range and flexibility than 'normal' Alice pieces. For example, they can step 1 square, move to a specific board, then leap 2 squares and return to the board on which the move started. Or they could use that ability to dodge around obstacles on more than one board, although that might be a relatively rare occurrence. Heh, playtesters wanted.
A very interesting variant. Let me play around with it for a while before rating it properly. Though just for the concept I could rate it better than Good. I wondering how the increase in potential cells will affect play. Particularly when trying to corner the opposing King. This is a common problem with most 3D games, that slippery King. But I can see that the player could also have an increase potential of promotion, so that may solve the problem. Once again, nice idea.
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An interesting concept to extend Alice Chess' idea. I'm inclined to think (but lack the mathematical skill to prove) that the connection between the three boards is a 4D one in disguise - bishops, if they were present, can travel paths one board at a time back onto their original starting board, arriving there on square(s) (e.g. their exact start point) that they wouldn't be able to reach if the variant was truly 3D (like Raumschach is).