´╗┐ 5x5 chess again thibault please read


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Normajean Yates    (2008-10-30)
5x5 chess again - thibault please read!

Thibault, I know you dont want to start another variant - but since we [meaning ficgs] pushed the theory [and the demise :( ] of the latvian gambit further... and we will have another round of that, so

in 5x5 chess (5x5 board, starting position rnbqk/ppppp/8/PPPPP/RNBQK) [o-o-o etc allowed - all 8x8-chess-type moves allowed] - as far as I know this hasnt been solved yet - far from it; so:

Please consider introducing this some time in the future... ask around to see if there is enough demand... you can consider payment-only tournaments for 5x5 chess....

Plus it will make ficgs academically famous!

[I don't know who suggested this version first: I first read about it more than 25 years ago in a Martin Gardner article - at least then, no theory was known about it.]

Thibault de Vassal    (2008-10-31 00:38:31)
5x5 chess

I'm not convinced yet. The question is : can a computer solve it... That would bury the game, definitely :/ .. Anyway, this variant could be played as hundreds of others, why 5x5 ?

Normajean Yates    (2008-10-31 03:17:50)
replies to thibault's question..

1. No, computers cannot yet. Not even near. Afaik not even 'strongly conjectured to be a white win' or 'strongly conjectured draw' (3x3 chess has been strongly solved - it is not really a game because there is no suitable starting position - but there are complete tablebases for every legal placement of chess pieces on a 3x3 board. I posted the links in a forum thread a few months ago...)

2. Why this variant is special -

if you think about it, 5x5 chess is the smallest notrivial *natural* contraction of 8x8 chess.

Plus - or that is why - it was thought of many decades ago - as far as I remember, when Martin Gardner mentioned it about 25 years ago in his column 'mathematical games' in the USA-based science magazine 'Scientific American', he was merely mentioning it, he hadn't invented it...

I am waiting for one bigchess opponent to time out before going on 15-day chess-leave -- [she (Nicola) would have timed out on 27 Oct but it got extended because of the 7-day addition to clocks owing to server change] --- then I plan to find out the current state of 5x5 - whether some university etc. is researching it, etc. If there are results that indicate forced draw (or win) then I agree that there is not much point in doing it here...

Normajean Yates    (2008-10-31 03:38:44)
similarly,smallest natural *extension*-

similarly, what is the *smallest* natural *extension* of chess? [Again I am reposting this idea - i did it a few months ago]

Think about it this way, as far as way of moving is concerned, [keeping aside pawns for the moment] you have R, B, N moving in essentially different ways. Q = R + B as far as movement is concerned - i.e. a queen can move like a rook or like a bishop, as the player chooses. The movement of the Q is nothing more and nothing less.

So, to extend chess minimally and naturally [therefore extending the symmetry also] IMO the natural choice of new pice would be a piece which I call the superqueen, lets call it U [because S is knight in chess problems and in many non-english roman-script languages..]. The superqueen U moves like a R, a B, or a N, according to mover's choice. In other words, it moves like a Q or a N.

movewise, U = R + B + N = Q + N.

Now keeping symmetry and minimality in mind we get 10x10 chess with the following starting position:


In 10x10 castling O-O and O-O-O, it may be more natural for the king to move *three* squares [and the R crosses the king and goes adjacent to the new position of the king, just like in 8x8 chess.]

Actually long ago (1981-82) we tried this 10x10 a few times with some friends - we used to call *this* 10x10 thing 'big chess' :(

[we used a one-pound coin heads-up and tails-up for white and black superqueen resp.]

But the name bigchess is taken [and bigchess is nice :) ] , so I am just calling it 10x10 chess now..

Alexis Bromo    (2008-10-31 06:56:13)
good idea

I think it's really interesting. I will try to play these variants.

Philip Roe    (2008-10-31 13:24:41)
Chess extensions

There seem to be many ways to extend chess. Most proposals, like yours Normajean, combine the powers of existing pieces. There may be other ways.

I saw it pointed out somewhere that if you put a piece somewhere near the middle of the board, at the center of a 5x5 patch of squares ,the N can go to any square in the patch not covered by a R or B. It was suggested that this might have been the reasoning of the original inventor. This makes even more sense if you consider that under medieval rules the K+Q covered a 3x3 patch.

Along these lines, consider a 7x7 patch and let the new piece go to any square not covered by an existing piece. Such a piece might be interesting. It would cover up to 16 pieces and be a formidable long-range weapon, but perhaps rather helpless at close quarters.

In designing an initial position, I would want to take into account the possibility of early interactions. In regular chess the placing makes such possibilities as the pinning of Nc3 by Bb4 possible. Proponents of FischerRandom call this kind of thing hackneyed, but I find most FR positions sterile because the game has no initial shape.

Thibault de Vassal    (2008-10-31 20:37:59)
10x10 "super" chess

The 10x10 variant seems much more funny but it is not so far from 8x8 chess. Ok, let's say that 5x5 chess is a "natural" variant, but I see no real interest to play it yet as the first 5x5 chess engine will be probably invincible :/

16x16 big chess is too long but IMO the great interest is that the pieces are the same and it is far enough from computer chess (unlike chess 960)... But it is not played enough yet and the more tournament categories, the more variants (..whatever), the less players in each one. This site is firstly dedicated to competition, unlike some other sites that offer tens of variants and it is not compatible IMO :/ .. Big chess & chess 960 + all unrated categories are a lot of chess tournaments already, maybe too many.

Normajean Yates    (2008-10-31 22:52:08)
I love [16x16] bigchess! :)

But disclosure of bias: I am winning my first bigchess (16x16) tournament 6-0 I think ;)

[4-0 I have already, One opp is timing out, and the only remaining opp: well see game 23201... ]

Let me be clear, 16x16 is very nice, need 'far' sight in two senses of the word :), and I would still love it - even if I was losing!

If some genie gave me the option that 'okay, from tomorrow at ficgs there will be no bigchess but there will be 5x5 and 10x10 and Philip Roe's generalisation to 7x7 with a nice initial position worked out -

I'd say no! I want bigchess!

Normajean Yates    (2008-10-31 22:56:28)
re 5x5: thibault's point is well-taken..

Thibault said - "but I see no real interest to play it [5x5 chess] yet as the first 5x5 chess engine will be probably invincible :/"

Well that is true - lack of 5x5 development is because of lack of engine development... good point, and point taken. Best to leave it to universities...

Normajean Yates    (2008-10-31 23:07:40)
small correction + apology to philip..

When I mistakenly said Philip Roe's 7x7 chess -- I meant just what Philip meant - i.e. some variant (10x10?) with two of those pices which can move only to those squares of the 7x7 patch they are at the centre of where it couldn't move were it a 'normal' chess piece. Sorry for the mistake.. and for the correct but perhaps obfuscating expression of the concept in *this* post ... [I took Roe's clear prose and ran an obfuscator on it ;)]

Normajean Yates    (2008-11-01 00:00:10)
a *playable* 3x3 chess :-/

Well as I said 3x3 chess has been strongly solved - by complete set of tablebases - but it is not really a playable game for lack of good starting position - the english wikipedia has links and info on 3x3, 5x5 [it *was* Martin Gardner who proposed it in 1969 acc to wikipedia], 6x6.

(see http://en.wikipedia.org/wiki/Minichess)

Well here is a playable version of 3x3 chess - even 1x3 chess! at least Samuel Beckett would have called it eminently playable!

3x3: 2k/3/K2 w.
1x3: k1K w.

And the kings - wait for Godot!

Normajean Yates    (2008-11-01 00:04:35)
on 5x5 chess experience from wikipedia

the english wikipedia minichess article says that Martin Gardner's 5x5 chess was played by correspondence in italy [doesnt say how many games, players played it, and during which period] - results:
* White won in 40% of games.
* Black won in 28%.
* Draw was in 32%.

Benjamin Block    (2008-11-01 10:05:59)
Looks easy to draw.

Looks easy too draw. And it don┤t need any deep play. How many possible position is that in the game? I think the computer can fix it easy. 300 000 000 poisitons only on 3x3. Not much a computer fix it on 1 sekund.

Normajean Yates    (2008-11-01 23:43:03)
Benjamin Block - I agree

It seems there is some HP product that offers 5x5 chess of various kinds including the one I describled - it is called 'Gardner minichess' now. English-wikipedia 'minichess' entry has a link to that - and in a discussion forum on that HP thing I found - "recent play suggests that Gardner minichess is a draw".

So the first decent engine for it would finish it, it seems, as thibault said earlier in this thread...

Someone modify crafty for 5x5 and check - yawn - I am toooo lazy --- plus crafty [and all later closed source engines I suppose] are too strongly low-level optimised for 8x8 chess --- writing an engine from scratch? Well I know the seven steps [they are/were on an internet in a nice article] --- but I have retired from writing code --- written enough for three lifetimes; no more programming for me.

*Proving* that Gardner-minichess is a draw would be more difficult -- 20-piece tablebases! (okay, in a much smaller space) - that's for the universities --- they have to do something to give out M.S.'s and Ph.D.s - so let them do it :)

[they did it with draughts <called checkers in the USA> - it is solved ie proven to be a draw -- let them try Gardner-minichess now :)]

3x3 - as I said there are complate tablebases now including for positions with pawns on first rank -- so it is very-strongly solved [i.e. given *any* position, the result and the best play for that result are known - in fact online accessible -- instant results of course... you'll find the link on eng-wikipedia -- I have accessed it [3x3 chess site] before but yesteday it seemed to be down - the old link was http://kd.lab.nig.ac.jp/3x3-chess/ but it is broken now...

Normajean Yates    (2008-11-01 23:46:08)
or modify gnuchess...

or any other decently coded open-source chess engine... then optimise -- intoduce latest techniques [what works for 8x8 might not work for 5x5 for low-level optimisation...]

Benjamin Block    (2008-11-02 17:13:30)
We can try

I thinked a bit today. Computer have a bit problem (closed positions.) And humen are long from cleared it. Some cool positons. I played some games vs my self. And it was very funny :UP: The computer will not fix it very fast. First we need to make a openingsbook before the computer can fix the game.
Why not test?

Normajean Yates    (2008-11-03 03:12:58)
It will need writing engine from scratch

Many of the published optimisations : rotated bitboards onwards etc - are specifically for 8x8 - the optimisations is that they combine legal-move generation and best-move genertion : conceptually, at one stage we have a list of 'maybe legal' moves and so on.

The high level optimisations are of course common[to begin, see Aske Plaat's Ph.D. thesis - search for it, it is online - also I have a printed copy - and papers on alphabeta+TranspositionTables]

Rodolfo d Ettorre    (2008-11-04 00:12:23)
5 Queens problem

The queens problem for a 5x5 board has 10 possible solutions, time ago I build a small java application to solve the N queens problem, and I used it for a 5x5 board.

Normajean Yates    (2008-11-04 03:43:33)
Rodolfo, this is not n queens prob!

1. 5 queens prob [none attacking any other] on 5x5 board has ZERO solutions, as is easy to see.
2. n queens problem - fast solution, all solutions, all solutions excluding symmetry etc. is routine exercise after teaching back tracking in a programming course. Also, writing recursive program in lisp, tail recursive program, program with function being called with itself as a parameter [in untyped languages - otherwise you get 'infinite type' error], lazy-eval-function-program [typically for Haskell] - are routine exercises for leaerning a new fundamentally different language for experienced programmers.


nxn queens is 2 minutes programming exercise! Writing a good engine for above is a big project!

Continuing the topic of engines for above (nowadays called Gardner minichess) - we also need some endgame tablebases. That should not be difficult: modifying source code of nalimov tablebase generators. [download tbgen.c - or is it cc (c++)? I have the source - it is GPL anyway...

We are not talking about future ficgs things - we are discussing a point of some academic interest, that is all.

Rodolfo d Ettorre    (2008-11-04 04:20:01)
5x5 Queens problem

There are solutions, one is a1, b3, c5, d2 and e4

Normajean Yates    (2008-11-04 12:13:13)
0h sorry [to rodolfo] :)

Oh sorry - brain tooo fatigued - thats why I am on vacation. Even 4 queens on 4x4 has solutions: a2,b4,c1,d3. [unique upto symmetry -I THINK], Isnt the 5 queens solution also unique up to symmetry? Or can all solutions be obtained by rotation, reflexion or combination of rotation+reflection; of a1, b3, c5, d2 and e4? [JUST DONT FEEL LIKE THINKING IT OUT - BRAIN HAS SHUT OFF...]

Normajean Yates    (2008-11-04 12:28:45)
n queens - number of solutions: n<=15

The following table gives the number of solutions for n queens, both unique (sequence A002562 in OEIS) and distinct (sequence A000170 in OEIS). for n =1 to 15: n queens: no. of solutions:

distinct: 1,0,0,2,10,4,40,92,352,724,2680,14200, 73712,365596,2279184.

up to symmetry: 1,0,0,1,2,1,6,12,46,92,341,1787,9233, 45752,285053.

So the 5 queens prob has two solutions, but the 6 queens prob has only one! [for 5 quuens, by rotating and/or reflecting them you get total 10 solutions which you got.]

Exercise: modify your java applet to give essentially different solutions only i.e. eliminate 'duplicate solutions' i.e. solutions which are identical except for rotation and/or reflexion. First step: e.g. for 5 queens check placement of a-queen on a1,a2, a3 only [a solution with a4 will be a reflexion of a solution ith a2.]

Don Groves    (2008-11-05 08:02:06)
8 x 8 chess variant

There is another way to foil the computers and re-energize chess: A screen is placed between the two sides of the chess board and each player places their pieces on the board in accordance with two rules: (1) one pawn on each file; (2) no piece past its own third rank. Then the screen is removed and the game begins with White's first move.

Opening books become useless (requiring the computer to begin using its clock from the first move) and the usual endgames will rarely occur (although endgame databases are obviously still useful).

Knowing your opponent's tendencies becomes even more valuable than in the normal game.