How much less or more complex are chess variants than regular chess?

By variants I'm referring to crazyhouse, 3 check, atomic, anti-chess and king of the hill.

And by more or less complex I mean, basically, the number of possible games and 'practical' complexity in learning and playing the game.

At least antichess is less complex: it has been solved!

I imagine the ability to place pieces makes crazyhouse quite a bit more complex than good ol' standard chess.

Here is my guess:

crazyhouse... Insanely more complex than chess, and the most complex variant on here. Every legal chess game, and position is legal in crazyhouse... Then you must add on any pieces off the board can drop in any place...

King of he hill... roughly same as chess with only difference being a king on a center square wins the game... so it is slightly less complex than chess for this reason that either king on a center square is game over. No need to continue from there.

3 check is theoretically as complex as chess, but in practical purposes far less complex as it's 3 checks to win.

Anti-chess least complex, but still very complex. It has a great many forcing lines more so than even atomic, and the board empties out FAST

Atomic... Well it's way different from chess that's for sure. I'd argue it's less complex than chess because of the numerous forcing lines.

Racing kings... I'm going with way less complex than chess. Both sides start on same side, and low on material, no pawns so must be less complex

Horde... I think it's less complex than chess, but still very complex. Both sides only have so many options.

960 is a bit more complex than chess... endgames are same in complexity, but openings are vastly more complex

@lurarose I agree with most of what you have said, but I think KotH and Three check are more complex. the extra win conditions force you to analyze more tactics.

Atomic is less complex when it's played in the regular chess (#518) starting position. We are looking for another one right now.

@EXOprimal the addition of faster wins makes it less complex though. Imagine a variant of 1 check chess. First check wins... Not very complex at all now is it? and white has forced win. So same is true of 3 check. Keep in mind EVERY move played in KoTH, and 3 check is also legal in normal chess.

And as for "complexity" it really depends on if you mean "total legal moves" vs "total playable / reasonable moves"

Yeah I always had in mind that variants like atomic, 3 check and king of the hill were less complex, because there are constraints on your play but otherwise normal play. You can win by checkmate (which is even easier in atomic) or by these other endings. So there are more possible variations to win within the same total possible moves (if they are the same). 3 check and king of the hill for example, would have the same total possible moves, but it in fact would be a bit less because the variant endings will end the game early in a lot of the lines. So these 3 check and king of the hill are less complex.

Atomic has different move rules to normal chess, but due to the explode rule, so I would say the total possible moves in atomic is much less, due to the removal of pieces. There are also much fewer viable openings in atomic, due to its volatility. So there are probably fewer possible games.

If anti-chess is solved and shown to be less complex that would make sense, as the forcing lines will reduce the variability in the moves on offer. Lots of forced lines = less total moves.

I would still argue that Crazyhouse is less complex than regular chess, although its up for debate. The key factor is 1. Does dropping pieces mean there are more total possible moves in the variant? 2. Is the game harder to play because of this? You would have to say that dropping pieces does mean there are more possible moves on the board, and if people weren't trying to win there would be many many more never ending games than regular chess. But does dropping pieces in some situations make those positions less complex? Certainly it does. Does it make some positions more complex? Possibly. But it also just changes the nature of the position, with initiative the key. So I'm not really sure whether crazyhouse is more or less complex.

Another way of looking at 3 check for example, is to say that regular chess is infinite check chess. It doesn't matter how many times you are checked. In that way, it is easier to see three check and other variants are less complex.

Also chess 960 is not more complex in any one game, but as total sport it offers way more potential "games" due to the random starting position. Each "game" would have a similar amount of total moves to original chess, but there are lots of unique games to play.