Progressive Chess

This is the variant where White makes 1 move, Black makes 2 moves, White makes 3 moves, Black makes 4 moves. [and a check ends a series]

Other than above, just like regular chess.

My analysis says it seems probable that White has a forced win.

Comments?

This is quite possible I think.

In normal chess, black is able to counter white's threats by means of prophylaxis. However in this variant, white can have N+1 threats while black can only make N prophylactic moves.

Let's just focus on the queen. In each turn, she can take N opponent's pieces. Black only has N-1 moves. At some point it is impossible to cover all ways which a queen can use to "dig" the way towards black king.

More formal analysis is of course required to prove the hypothesis but it seems unlikely for this game to be drawish.

1.e4 2.e5 Nf6 3.Bc4 Qh5 Qxf7#

1.e4 2.e6 Nc6 3.Qh5 Qxf7+ Qxe8!

1.e4 2.e6 Nc6 3.d4 Bg5 Bxd8 4.Nf6 Nxe4 Nxf2 Nxd1 5.Be7 Bxf8 Bxg7 Bxh8 Kxd1 white will win.

1.e4 2.e6 Nc6 3.d4 Bg5 Bxd8 4.e5 Bg4 Bxd1 Kxd8 5.Bb5 Bxc6 Bxb7 Bxa8 Kxd1 6.Bb4 Nf6 Re8 exd4 Re1#

i do not think 1. e4 is the best move for White and there are better defences for Black.

You might be correct. I am curious to see, please show the variants why e4 is not the best move or how black can set up a better defense. My variations are my first ever thoughts about this kind of chess, so it would be very surprising if I managed to produce the best variants possible.

Yet I thought that 1.e4 was best by test. :-)

i stopped playing this variant due to health reasons but assure you the theory has gone way beyound what anyone would, at first, think are the best lines.

I played a lot of Progressive Chess (by post) about 25 years ago, and at that time the top players were the Italians from the Eteroscacco group. They once published a document with the moves from almost 1,000 games (probably not available online) and 1.d4 and 1.e4 were very much the favoured opening moves. There was no suggestion that White had a forced win.

Progressive was one of the most popular variants in those days - ideal for postal play as games didn't last long. I'm surprised that nowadays it is quite neglected, and I'm not aware of anywhere online that you can play it. Partly because of the extensive opening theory that developed (and the various tricks that were known), I prefer Progressive960. However, castling is rarely desirable in Progressive so you could just use any randomisation.

Variant Chess magazine (published 1990-2010) often featured Progressive Chess. All the issues are available at http://www.mayhematics.com/v/v.htm and the article I wrote for the first issue (page 10) is just one example. 

@MacolmHorne: thank you for provinding those links. I have downloaded two rows of issues and had fun reading some of them.

Interesting article and subtle rule to force a check. It opens new lines of thinking, because you can now put a king voluntarily into the wild as it would force your opponent to prematurely give a check of restrict pieces into their movement until the last move of his turn.

I'm the biggest theoretician in progressive chess, having written software to solve mates, find series, etc. (Bucephalus on github), and spent hundreds of hours analyzing the game, and produced a big series of videos on chessvideos.tv.  

I can't claim absolute certainty, but I still believe the game is a draw after 1.d4 2.d5 c6!, the only series to draw against d4.  1.e4 2.e5 f6 (also probably the only two that draws) is also currently a draw in my analysis after 3.Bc4 Bxg8 f3, 4.Rxg8 Bc5 Bxg1 Bf2+!, where we've been unable to find a win for white. (3.Qf3 Qxf6 Qxd8+ also might be a draw.  Analyzing e5 f6 is complicated).

Game between me and another expert in the game, representing the main line after d4, which is simpler/clearer:  1.d4, 2.d5 c6, 3.Bf4 Bc7 Bxd8, 4.Kxd8 Bf5 Bxc2 Bxd1, 5.Kxd1 e4 Ba6 Bxb7 Bxa8, 6.Kc7 f5 f4 f3 fxg2 gxh1Q, 7.Kd2 Nc3 Nf3 Rxh1 Ng5 Nf7 Nxh8, 8.g5 g4 g3 g2 gxh1Q Qf3 Bg7 Bxh8, 9.Ne2 Ng1 Nxf3 Ne5 Nxc6 Nxb8 Bxd5 Bxg8 a4, 10.Kxb8 Bxd4 Bxb2 Bd4 Bxf2 Bg3 Bxh2 e5 h6 Bf4+, 11.Kd3 Kc4 Kd5 Ke6 Kd7 a5 a6 Bf7 Be8 Bg6 Bh5, 12.Draw agreed

Those guys are a lot like the 19th century (or pre-19th century) of regular chess.  Almost all their openings were wrong/losing, but there are some beautiful games nonetheless (refuting inexact series can still be quite fun).  I still have this document from AISE (PRBASE and Battista) with all the games and annotated a few of them (used to have an online guide for the game on the web years ago when I was a student, but it's long gone).

The Italians particularly loved 1.e4, 2.d5 Nc6?? (losing), 3.Qg4 Qxc8 Qxd8+, 4.Kxd8 dxe4 Nf6 h5!? (the Leoncini Variation, nothing works, so it's a decent try), which was played in a ton of games over the years.  But it just loses to 5.d4 d5 dxc6 Be2 h4!, a novelty I found quickly after taking up the game and played for the first time back in 1998.

The game is really fun in Fischer Random.  I won the 1998 FR progressive chess championship held by chessvariants.com, losing 1 game.  Back then there was a lot of interest in the game, and several big correspondence tournaments were held.  Since then, I've analyzed the game on and off for the last 18 years.

Just to summarize our current (computer-assisted) analysis of progressive chess theory.

1.e4 - draw after 2.e5 f6

1.d4 - draw after 2.d5 c6

1.Everything else - loses trivially to 2.e5 e4 (1.d3 and 1.e3 a bit different but can play normally and exploit fact white can't move one of his bishops).

1.d4 2.c5 cxd4 was really popular with the Italians, but 3.a4 e4 e5! wins easily for white after 4.e6 Qg5 Qxc1 Qxd1+ 5.Kxd1 a5 a6 axb7 bxc8Q+ or 4.e6 d3 dxc2 cxd1Q+ 5.Kxd1 Bg5 Bxd8 Be7 Bxf8.

1.d4 2.d5 Nc6 3.Bf4 Bxc7 Bxd8 wins.

1.d4 2.d5 Nf6 3.e4 e5 Bb5+ wins.

1.d4 2.e5 exd4 3.Bg5 Bxd8 f4! wins.

1.d4 2.d5 c6 3.Bf4 Bc7 Bxd8 or 3.Bg5 Bxe7 Bxd8 both appear to be draws (see game above).  Promotions save black on both the 6 and 8.  3.Qd2 e4 e5!? is the only other try but seems insufficient.

1.e4 2.d5 dxe4 3.d3 dxe4 Qxd8+ wins. (but not 3.Qg4 Qxc8 Qxd8+ 4.Kxd8 e3 e2 exf1Q+ winning for black).  (The Italians tried 4.Kxd8 c6 e5 h5, but white just promotes on f8 and wins.) 4.Kxd8 Bh3 Bxg2 Bxh1 5.e5 Bg2 Bxb7 Bxa8 Bh1, and despite enormous amounts of analysis, we haven't been able to save this line for black.

1.e4 2.d5 e5 3.Qg4 Qxc8 Qxd8+ wins. (but not 3.d4 Bg5 Bxd8 4.Kxd8 Bg4 Bxd1 Bxc2! winning for black.)

1.e4 2.e5 Nh6 3.d4 Bg5 Bxd8 wins.

1.e4 2.d5 d4 3.Qg4 Qxc8 Qxd8+ wins.

1.e4 2.d5 Nh6!? is interesting, likely doesn't work but could use more analysis.

1.e4 2.e5 f6 3.Bc4 Bxg8 f3 4.Rxg8 Bc5 Bxg1 Bf2+ (desperado checks normally bad, but here the extra move appears to save black) 5.Kxf2 d3(d4) Bg5 Bxf6 Bxd8 Against d3: 6.d5 dxe4 exd3 dxc2 cxd1Q Qd4+, and against d4: 6.exd4 d3 dxc2 cxd1Q Qxh1 Qxg2+ both appear to draw.

1.e4 2.e5 f6 3.Qf3 Qxf6 Qxd8+ 4.Kxd8 d5 dxe4 h5 is very complicated and have yet to come to final conclusion (any assessment possible, but gut says black wins or at best white has a miracle draw).

Have lots more analysis, but that's the basics.

Thanks! Cazzeo!

Np.  Would be curious to hear your analysis.  These days I'm more interested in solving the game than playing it.

1.d4 is the more direct move (threatens to get queens off), leading to pretty forcing play (queens off on the 3/4, rooks off on the 5/6, last rooks off on the 7/8, opp bishop draw).  Its forcing nature means most everything that deviates for either side loses.  It may be the best move.

1.e4 is more subtle.  It makes a weakness (opening a line for Bg4 Bxd1), but it threatens mate.  If black plays e5 but not d5, he's letting white play Bg5 Bxd8.  If he plays d5, he's letting white play Qg4 Qxc8 Qxd8.  2.e5 f6 slows down the game and stops white from getting queens off in a "good" way.  This slowing down of the game means both sides have more pieces, but it makes it much harder to figure out what's going on.  Any result is possible.

The only tries I've found to try to keep the game at a fast pace (i.e. take something) are 3.Bc4 Bxg8 f3 (important because it stops queens from coming off until the 5/6 while still taking something), and 3.Qf3 Qxf6 Qxd8+ (gets both queens off early, but both sides have an extra bishop compared to more normal lines, which you would think would favor black.. however, he has no real material grabs on his 4, so it's hard to say for sure).

To go back to a previous post, I don't think we really know what the best first move is.  It may be there's no theoretical difference, or it may turn out 1.e4 wins or loses (or someone finds something to overturn my assessment of 1.d4 2.d5 c6).  The beauty of progressive chess is it only takes one series to overturn an entire line.

Cazzeo

i have not studied the game anywhere near as much as you have. But did come to the sequence 1. d4  2. d5 c6 on my own as maybe holding for Black.

Congratulations on your great analysis and play in Progressive chess!

i am very impressed with Cazzeo's acomplishments in Progressive Chess and Fischer Random Chess. 

It would be great if someone would do a book on the tournament he won and also his analysis of two chess variants.

Or maybe even two books!

You can find some of this using the wayback machine.

CV page for the tournament:

http://web.archive.org/web/20000618043426/http://www.chessvariants.com/pfr98.dir/index.html

My notes on the tournament from my student days:

http://web.archive.org/web/20000519215823/http://www.cs.utk.edu/~hyatt/frpr98/index.html

My page on the 1998 world championship which I organized.

http://web.archive.org/web/20070912051229/http://www.cs.utk.edu/~hyatt/wipcc98/

My online guide to progressive chess (very outdated now, but some of the fascinating theory remains, like that black can checkmate white with two knights, or bishop and knight, but white can't do the same to black):

http://web.archive.org/web/20070910205527/http://www.cs.utk.edu/~hyatt/wipcc98/guide.html

Opening theory way out of date on that one (e.g. 1.e4 2.e5 f6 3.d4 d5 d6? 4.a5 Ra6 Rxd6 Rxd1+! -/+ was found around 2000 or so with Bucephalus).  I hadn't yet found 3.a4 e4 e5 vs. 1.d4, 2.c5 cxd4 either; Linnemann and I found that series in 2010 or so as an improvement to 3.Bd2 e4 e5.

Some of the annotated games in there are quite fun, though.

Just to respond to some of the other comments:

I'd love to write a book on progressive chess someday.  Easily have enough material for one.

Fischer Random is definitely THE WAY to play this game.  It is so fun.  Amazing variant.  Always loved progressive chess, because it's still using the basic chess rules, just changing the move count.

I had to solve some incredibly cool problems in that tournament.  Maybe I'll annotate and post a game or two in a separate thread.

Concerning the game :

 1.d4, 2.d5 c6, 3.Bf4 Bc7 Bxd8, 4.Kxd8 Bf5 Bxc2 Bxd1, 5.Kxd1 e4 Ba6 Bxb7 Bxa8, 6.Kc7 f5 f4 f3 fxg2 gxh1Q, 7.Kd2 Nc3 Nf3 Rxh1 Ng5 Nf7 Nxh8, 8.g5 g4 g3 g2 gxh1Q Qf3 Bg7 Bxh8, 9.Ne2 Ng1 Nxf3 Ne5 Nxc6 Nxb8 Bxd5 Bxg8 a4, 10.Kxb8 Bxd4 Bxb2 Bd4 Bxf2 Bg3 Bxh2 e5 h6 Bf4+, 11.Kd3 Kc4 Kd5 Ke6 Kd7 a5 a6 Bf7 Be8 Bg6 Bh5, 12.Draw agreed

Black could mate in his 8 with the five last moves :

gxf2 , f1=Q , Na6 , Nb4 , Bh6

instead of :

g2 , gxh1=Q , Qf3 , Bg7 , Bxh8