Acceleration chess (also known as Progressive chess)

White moves first, but then Black gets to move twice.  Then White gets to move three times in a row, then Black four times in a row, then White five times in a row, and so on, with continuing escalation as the game proceeds.  You cannot move your King through a check or play another move while your King is in check.  If, in the middle of your sequence, you give check, you lose any remaining moves in your sequence and your opponent moves and enjoys his full sequence.

Here are a few observations:

1. Games will end rather quickly.

2. 1.d4 appears to be a stronger opening move than 1.e4; can you see why?  For one thing, White is threatening to start his next threesome with Bg5, for another his King has some breathing space against some possible checks on f2.  (If Black plays d5 and Nf6 in turn, consider the counter of e4, e5, and Bb5+.  With the next “fivesome” of White he is threatening to advance pawns to e6 and g6 and take on f7.  Qd3 and then Qf5 is another possible threat sequence.)

3. It is often good to give check on the last move of your sequence, if only to tie the hands of your opponent for one move.

4. Sometimes a more exposed King gives you a stronger position, because then the approach toward your King creates a check and ends the sequence of your opponent.  This also means that pawn promotion should not always be to a Queen.

5. The Knight is often better on h3 rather than f3.

“Acceleration chess” is my phrase.  And for the dedicated foursome there is “accelerated Bughouse.”

I thank several individuals at Jane St. Capital for relevant observations on this game plus a bit of play.


"You cannot move your King through a check or play another move while your King is in check." Seems like this variant should have a rather trivial solution for a computer once someone bothers to program up the rules.

"A trivial solution"? I thought this might be the case, and that the game might be solvable with less computation than non-trivial games. But I no longer think so. A grad student of mine studied the game at some length, including writing a program. It does not look to be trivial at all, and some very good human players have studied it and played games into the teens of moves.

Intuitively, you'd expect it to be about the same complexity as Chess, unless for some reason the move grouping causes mate to come systematically sooner or later (I assume sooner is more reasonable, but this certainly isn't obvious). Mind, people are probably playing much less sophisticated progressive chess games, because it isn't well studied so they can't just use memorized patterns, but the game itself isn't obviously simpler.

@Finch, I disagree. Consider the thought experiment in which player white is allowed k moves, then black is allowed k moves and so on. The same number of moves are played and only the grouping differs. Yet the game is trivial for k > 3. Wallingford's comment gives me pause, but discrete optimization has come a long way in the last couple years.

It's a reasonable point. Games may end after fewer moves. I just argue that isn't obvious. I haven't done any deep analysis of that and could be convinced otherwise. You have more time to build up good defenses to the more potent offense you face.

If games don't end in fewer moves, the branching factor, appropriately measured, is about the same as vanilla chess.

By "fewer moves" I mean fewer counting each part of a k-move separately so 1, 1-2, 1-2-3, 1-2-3-4 counts as 10 not 4. It does seem likely that there will be fewer k-moves.

ah, I see.

"If games don’t end in fewer moves, the branching factor, appropriately measured, is about the same as vanilla chess."

Is true, but my hypothesis is that the games do end in both fewer total moves and fewer k-moves. The strategy set gets warped in a way that ends the game earlier (in particular, there are several 4 k-move fool's mates I've found just from playing around).

All Chess variants seem to fail. The reason probably is that people who are interested in Chess tend to really like it and already consider it to be the perfect game, while people who are not interested in Chess are not interested in variants of a game they are not interested in. There are lots of other board games, after all.

By fail, do you mean crazy/bughouse games available every day on FICS?

960 (Fisher Random) certainly isn't as popular as regular chess, but it seems alive and well in places like

As white i often win by foolsmate on the second move

Happens whenever you play both sides.

This suggests chess which is played in different arithmetic sequences:
If the sequence grows linearly, the game will be over quickly. If it grows geometrically, the game will be over within 10 rounds (will white win with a 13 move combination?)
Perhaps the moves could go logarithmically:

don't discount the variants (bughouse is one of the more fun games i've played of any type, vanilla chess has the network effect going for it, which counts for lots given its history, worldwide appeal, etc.). put another way, more players doesn't mean chess is better than go, or vice versa (depending on which has more players).

Any word on other variants, such as alternating double moves? Or the same moves applied to Go?

So it's basically the board game version of A Song of Ice and Fire.

You'll have to explain that one.

I think he means everything dies

Without the check rules, and making victory simply be capture of the king, it looks possibly solvable.

Even with the check rules, the ability to capture pieces and then go back should make captures much more frequent, and thus the game shorter.

I've played progressive chess before, it can be a lot of fun and some of the positions and ideas are uncommonly beautiful. But it would be difficult to persuade a serious chess player to put in the same effort for a game of progressive chess as he would for normal chess, and it's not just because of a lack of familiarity. A game where your opponent always has one more move than yours feels somehow bizarre and arbitrary (even if it isn't!). Much of the attraction of standard chess is in the importance of piece coordination and prophylactic strategic play whereas progressive chess is much more about pure tactics.

I'm a big advocate of Fischer Random though, as it requires much more creativity in the opening phase of the game and to a large extent negates book preparation.

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