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Re: Number of arrays for Fischer Random.

The way that you have had this calculated is strictly correct however it
was overlooked that a mirror image is actually the same position.

For example:
The position B B R K R N N Q is reasonably simply. It is the same to play
in every way as the position Q N N R K R B B.

Hence there are only 480 true variations ( 16 x 20 x 3 / 2 ). This is still
a lot to memorize. I wouldn't recommend trying.

BMunage

Agree with H.G.

Castling makes both positions different, and no symmetrical.

For instance, g-castling (O-O):

In 'B B R K R N N Q' g-castling is accomplished by the King jumping 3 squares, and the Rook moving once.

In 'Q N N R K R B B' g-castling is accomplished by just having the King jump over the f-rook, while the rook stays on the same spot.

Also, b-castling in one of the positions is not equivalent to g-castling on the other.

There is no symmetry because of castling.

If both rook needed to be at least 3 squares one the left (and the other on the right) side of king how many positions would we have?

Some thing that mystifies me, is why the preference for a randomised setup in Chess 960.

A game that had a "zeroeth move" allowing both players to choose their preferred 960 array has potentially richer strategy, and the potential for black to counterract white advantage, by having the "answering" array.

By "richer strategy", it's sounds like you mean,  a predetermined strategy. Doesn't this defeat the point of having a random starting position?

By "richer strategy", it's sounds like you mean,  a predetermined strategy. Doesn't this defeat the point of having a random starting position?

Regression to predetermined strategy would be countteracted by Blacks freedom to choose an answering array.

This gives 921,600 starting positions.

Depending on how much of a counteradvantage Black gains, moves could be staggered-White places a piece, Black answers.

A constructive phase would add to Chesses itinerary, though how much genuine extra depth is added by such pregame metastrategy and how much real nuance these premoves would have I'm not sure.

Your version reduces freedom of array selection, and you artificially reverse moves in placement, forcing Black to place first to further enhance Whites advantage.

"White first move advantage is necessary for strategic tension."

Could you elaborate on this?

All changes in nature depend on potential differences. A waterfall creates energy because there is a difference between high and low. In chess, there is a difference in "altitude", too. White has an advantage, which is converted to either a tactical or strategical initiative. This gives rise to fine pieces of art as well as interesting theory, because the potential serves to energize the game. 

It is possible to design a game in which this potential doesn't exist, but then it isn't Western chess anymore. For instance, I think Shogi and Xiangqi are different in this respect. I don't know about Shogi, but Xiangqi does not have the same status as chess. In China it is regarded as kind of vulgar, although it is great fun.

So that's why I wanted, in the relocation variants, to retain white's first move advantage. Otherwise it isn't chess anymore, and it won't become as popular. The positions chosen are all very natural. There are no awkward positions, as in Chess960.

Moreover, compared with Chess960, in some of the variants the array has been expanded, since there are also non-mirrored positions. Non-mirrored starting positions are congenial with real warfare. See my article, "Relocation variants": http://mlwi.magix.net/bg/relocationvariants.htm
--Mats

The popularity of chess over the other variants is clearly due to its more compact, logical and symettrical design. Its a more modern game, aesthetically more appealing and easier to learn.

To celebrate first move advantage as the central selling point, to be preserved at all costs, is risible. Its a bug, not a feature, as it is in any other strategy game.

As for "tension", white retains move initiative, but against a prepared 960 array of black. The "tension" is now dual.

And as for some 960 arrays being awkward well, yes, but they wouldn't have to play them (in nonrandomised asymettrical).

Johnny, it appears from your comment that you aren't familiar with chess theory. It revolves around white's first move advantage and how to retain it.  As soon as theorists discovers a method to neutralize white's advantage, that particular opening is virtually dead. This has happened to many openings, such as the King's gambit, which is hardly ever played anymore. Were it to happen to all openings, it would mean the death of chess.
--Mats

And yet the entire purpose of Fischer Random and like variants is in eradicating theory based openings altogether...

As a variant that's close to chess, Fischer Random (aka Chess960) does the trick of avoiding all opening theory admirably.

One thing Chess960 lacks compared to chess is ironically usually seen as it's very strength and reason to exist, i.e. that one can't study Chess960 opening theory at home (if that's viewed as desirable/enjoyable), plus book sales thus will suffer, arguably to the detriment of popularizing the variant. This would be partly due to not otherwise having more literature around (i.e. about the opening phase of Chess960).

A way to solve that to some extent is to adopt Kasparov's idea of using the same starting position for a year & then switching to a new one. I'd go farther and suggest not switching the start position for 50 or even 100+ years (chess opening theory took a long time to develop, after all). One drawback of this idea is that the game would be studied to death by, say, 960x100 years from now, whereas never knowing the position one will begin with, as per the rules of Chess960, would avoid such study. However, the lifespan of any board game of skill (e.g. chess) is liable to be finite for one reason or another, IMO.

My estimates for the values of chess pieces applies here too, naturally: P=1; N=3.49; B=3.5; R=5.5; Q=10 and a fighting value of K=4 (though naturally it cannot be traded).

Kevin, you raise a good point about book sales, etc., but as for the "one year per setup" idea, I think Fischer's original plan was to avoid the opening theory discussion altogether.  If everyone studied one particular random setup for a year, I'll bet White's advantage would be exploited even moreso than it is in the standard setup.

With a random setup, determined just before the game starts, you can just look at a random position between two players and enjoy the actual battle of minds in that moment.  The match would be 100% performance-based, instead of being so preparation-based.

@HG,

I remembered seeing a diagram with randomized setup, but I cannot find it anymore.

I don't recall ever doing an Interactive Diagram on Chess960. It would not be able to handle the castling. If there ever has been a Diagram of a shuffle variant, it must have been one with normal castling.

Fischer castling now should work in the Interactive Diagram, including the AI.

<script type="text/javascript" src="/membergraphics/MSinteractive-diagrams/betza.js">
</script>
<div class="idiagram">
  graphicsDir=/graphics.dir/alfaeriePNG35/
  graphicsType=png
  symmetry=mirror
  shuffle=N!BRQK
  pawn::::a2-h2
  knight:N:::b1,g1
  bishop::::c1,f1
  rook::::a1,h1
  queen::Q::d1
  king::::e1
</div>

The Interactive Diagram in the article is not working for me (FireFox:Win 7). I see a narrow black bar where the board is supposed to be. It uses betzaFlex.js as script, (which is not mine).

That's my fork of your script. It was working for me on Firefox with Windows 11, but I got the same results as you did when I tried it on Firefox on Windows 10. Since I use my Windows 10 computer less, I checked whether Firefox was up to date. It was at version 137.0.2, and I updated it to version 138.0.1. Upon doing this, the Interactive Diagram worked as it should. Since Firefox was up to 138.0.3 on my Windows 11 computer, I did another update of Firefox on Windows 10 to bring it completely up to date.

Since Windows 7 is no longer supported by Microsoft, it's possible that it will not support the latest version of Firefox. The first thing you should do is make sure Firefox is up to date. Go to "About Firefox" under the Help menu, where it will check for updates and tell you whether you have the latest version. If you're not up to date, it will try to download the update and ask you to restart Firefox to install it. Note what version you currently have installed and what version you're able to update to. If you cannot update to the latest version, 138.0.3, you may want to consider updating your OS to Windows 10 or replacing your computer. Assuming you can still use the latest version of Firefox, I would hope you are using Windows 7 with 0patch, which will provide you with security updates now that Microsoft is no longer doing that for Windows 7.

FireFox says it is up-to-date, but the reported version is 115.23.0esr (64-bits). The ESR branch apparently is especially made for running on deprecated Windows systems (up to 8.1).

I think it is a bad thing to have pages that don't display correctly on older versions of the browser or OS. Especially since the problem still existed in version 137, which must be a quite recent one if we are now at 138. I can live without an Interactive Diagram for FRC, but it reflects badly on the site if others would encounter this problem.

Do you have any idea what change you made that might cause this? The betzaCSS.js script doesn't seem to have any browser problems on these old systems, and betzaNew.js only has a background problem on Apple devices which seems unrelated. So it must be possible to make a script that runs in this case as well.

BTW, the problem appears on all browsers I tried on this machine (FireFox, Chrome, Edge, the AVG safe browser). So I suppose it has something to do with the plugin JavaScript engine.

I think it is a bad thing to have pages that don't display correctly on older versions of the browser or OS.

Without having the older version in question, I can't really do anything about that. Since you still use Windows 7, maybe you can look into it further.

Do you have any idea what change you made that might cause this? The betzaCSS.js script doesn't seem to have any browser problems on these old systems, and betzaNew.js only has a background problem on Apple devices which seems unrelated. So it must be possible to make a script that runs in this case as well.

The main changes I made were to provide a flexbox layout. The file contains comments about the changes I made, which you can find by searching it for my name. Although it looks like I didn't add a comment about it, I also changed how sections are hidden, replacing "display: none" with "visibility: hidden; height: 0;".

Notably, the timestamp on betzaFlex.js is April 29, 2024, which is before the power button on my Windows 10 computer stopped working and I bought a Windows 11 computer. Therefore, I developed and tested that script on the same Windows 10 computer it wasn't working on today before I updated Firefox. Additionally, I found an archived copy of this page on Archive.org from March 2, 2024 with the Interactive Diagram on the page. So it looks like I added it while I was still using my Windows 10 computer. However, it was not working on Archive.org. So I checked some other diagrams. Most of the ones I checked worked, though Ultima, which uses the same script, did not. You may check whether the Ultima ID is working on your computer.

The Ultima Diagram is working for me. Which makes it even stranger.

I noticed that the link to betzaFlex.js in that case containes an extra &uniqid=4 in the query string, though. So I cannot be sure it is the same script; CloudFlare might cache it as a separate file.

[Edit] If I use the FireFox 'inspector' on the created Diagram it gives a height:0px for the <td> elements of the board (which corresponds to the image we see). The line of code that defines the <td> is

      row = row + '<td id="' + bnr + 'y' + h + 'y' + j + '" style="height: ' + sqrSize + 'px; height: ' + sqrSizeCSS + '; width: ' + sqrSize + 'px; width: ' + sqrSizeCSS +

which is suspect, as the style attribute sets height twice. I will now try to delete the first occurrence in /fergus/betzaFlex.js.