The Flying Knight

White gets all of his pieces in the beginning and gets one move per turn. Black gets a king knight and a king and 2 moves per turn. (spoilers black will probably win).

It's impossible to checkmate with King and knight

Even if black captures ALL the pieces he won't be able to checkmate!

Because you have no reason to castle and sure not to put your king in the corner - the only place where it can be theoretically checkmated (ok, putting pieces on every free square around the king might work to, which is even more stupid).

Sure it's very hard for white to win - no sane person will exchange his only piece, and no tactics works because of black having 2 moves each time - enough to go out pin or fork. But it's even harder for white to lose, so it's dead draw.

Can you post couple of games won by black with checkmate? Just want to see it.

You have no null move in pgn but you can post it as text, not as diagram - like

1. Nf3 Nf6 2. -- Nh5 3. Nc3 ... etc.

It may be good calculating practice for both sides, but I won't believe checkmate by any side is possible without heavy blunders

I suppose black king can't enter a square under white's control during his double-move, can he?

The black King alone can checkmate white under these rules, right? It doesn't even need the Knight. E.g. white Ke1, black Kd3 would be checkmate, as wherever the white King moves, he would be captured on the next turn by the black King.

It depends if entering a square opponent controls is legal. In classic chess, the king must not go through a square under opponent's control in his castling double-move. I cannot google exact rules and I suppose it is not legal, but I understand that arbitrarily created small-potato chess variant can have different rules.

If white plays 1. e4, 2. Bc4, 3. Qf3, then black could never win, because it is impossible for black cover d1, e1, e2 and f1 with only 2 kings and a knight.

Assuming that:

- Checkmate means checkmate, aka when white king is in check and white to move, and there is no legal move to get him out of check. Thus capturing the white king is NOT checkmate.

- When it is white to move, black's kings may not be in check. (You could say that if there are no legal moves for black to get both kings out of check in his 2 turns, he is checkmated. But this is irrelevant for the fact about "black will probably win").

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So unless there are some additional rules, I fail to see how black will probably win :)

Well, unless it is explicitly forbidden (as in the case of castling in orthodox Chess), I would expect it to be allowed. Being 'in check' is defined as exposing your King to capture, and when it is not your opponent's turn to move, you are obviously not exposed to anything.

Castling is a special case, which should not automatically be generalized to this variant: you are also not allowed to castle out of check, and it was sort of implied by the OP that black could use double King moves here to escape mates while in check. And the rule that double moves are only available to pieces that have not moved yet obviously does not apply here either.

In any case a double-move Knight would not suffer any such restrictions, and should have little problems checkmating the opponent with the aid of its own King, even when this was just a normal King. (E.g. white Ka1, black Kb3, Na3) Double-move pieces are exceedingly strong, as we know from Chu Shogi, where the Lion, which can do two King moves per turn, is worth about 1.6 times as much as a Queen (which itself is enhanced in value because of the larger board).

By that logic delivering checkmate with K + B + N is also impossible once the opponent King moves to e2, as it is impossible to cover d1, e1, f1, d2, e2, f2, d3, e3, f3 all at once with just a King, Bishop and Knight...

Not sure why you mention a second King anyway. Black has only two pieces here, right? And in fact the double-moving King alone already seems able to cover the squares you mention. Or an ordinary King (on d3, covering e2) and a double moving Knight (on e3, covering d1, f1 and e1). So not much of what you wrote seems to make any sense.

I noticed that the OP mentioned "king knight and king", though, and I am not sure if this was a simple typo, or whether 'king knight' means a compound piece.

I read it as:

"Black gets a king, knight and a king. Also black gets 2 moves per turn."

But then again, regardless of what he actually meant, and assume your interpetation of a "king which also has to ability to move as a knight", abiding my assumption, it is impossible for black to win:

"Checkmate means checkmate, aka when white king is in check and white to move, and there is no legal move to get him out of check. Thus capturing the white king is NOT checkmate."

But if capturing the white king implies checkmates too, and black allowed to be in check between his moves, Black should always win, assuming he makes no enormous blunders, as it seems impossible for white to cover the enormous range that black king has.

If black king may not be in check between his moves, white has to cover in the worst case 17 squares. And I mean cover all these 17 squares, because if there is one not covered, he gets additional squares to run to (or stalemate if the only one not covered is the one the black king is standing on).

If black may be in check between his moves, white has to cover in the worst case 61 (!) squares, simply impossible, unless black allowed white to have like 8 queens.

I don't follow your arithmetic. If black is not allowed to 'pass through check', white would have to cover 9 squares in the worst case, the one on which the black King is, and those next to it over which he could escape. And on an edge that would only be 6, and in a corner only 4. Just like in normal Chess.

And with K+R you cannot cover the 9 squares, but we all know that K+R can still force a mate, because you will not be checkmating the opponent in the worst place, but drive him to the best place first. And you only need to cover the single square on which he is to make sure he cannot stay there. So 'worst case' is totally irrelevant.

If black can pass through check, covering 25 squares would be enough to ceckmate him in the middle of the board. But in a corner 9 would suffice, and a King + 2 Rooks could do that. So '8 Queens' seems a gross exaggeration.

OK, clear. And how about passing through check? If white's King is on e1, and black plays his King to e3, is white now in check (if d2, e2 or f2 is empty)?

I don't get that. Why would the black King have to stay two squares away from the white King? Is that an extra rule? It certainly does not follow from the normal checking rules, as the white King is not allowed to do two moves. So Squares at distance two from it are not attacked (if there are no other pieces). So what prevents the black King from going there?

In fact, if passing through check during the double move is not allowed, I don't even see a reason why the Kings cannot approach each other to the same distance as in normal Chess.

If the black King should not be under attack after the first move of the black turn, this also has consequences when you move two different pieces: when in check, the King cannot go to the square where the Knight stands, as you would have to move the King out of check first.

Well, perhaps the problem is that what you say is a bit ambiguous. With 'two squares away' you seem to mean 'one empty square between them', just as in normal Chess, right? At some point you seemed to suggest something different, when you mentioned that the black King's range was larger.

Trying it out will unfortunately not be any help in figuring out how the rules of a variant are. Rules could be anything. Both allowing passing through check and forbidding it will give viable (but different) variants. Obviously when allowed to pass through check, the black advantage would even be bigger.

With reasonable play I don't expect that white would allow himself to be smothered. The most likely progression of a game would be that the black strips white bare with his 'duplex knight' through hit-and-run captures, and then simply mates him in the end-game.

It's pretty important to specify that Black has a kingside knight. If Black has a queenside knight, White has a very limited choice for the first move, because 1... Nc6d4# is mate unless Black plays 1.f3, 1.f4, 1.e3, 1.c3, or 1.Nf6

Also, if White plays 1.f3, there is mate in 2: 1.f3 Nc6d4+ 2. Kf2 Ne6f4#

Having a kingside knight removes the massive advantage of being able to give check on the first move.

The above is pretty clear, but unfortunately you then continue with statements that completely contradict it. There is no rule in standard Chess that specifies the Kings have to stay a cetain distance from each other. Just a rule that says you cannot expose your King to capture at the end of your turn. That they cannot stand next to each other is a consequence from that, not a rule.

The rules you give would certianly allow the black King to be on e3 when the white King is on e1. If you don't want to allow that, you need more than 'just these' rules, because that would be an additional difference with FIDE Chess.

The diagram you give increases my confusion even more. Especially that you state this position is 'clearly illegal'. I don't see anything illegal there. Even with the extra rule that Kings have a 'radius' of 2 squares within which other Kings must not approach, the Kings are at a distance larger than that. So what makes it illegal? What I see is just a position where white is in check, which he will solve by capturing the Knight with his Pawn.

The rule that you have to use both moves offers an interesting new question: what happens if you stalemate yourself on the first move? Like in the diagram below:

I think that should be checkmate, because Black is in check at the start of his turn, and cannot safely escape it following the rules of the game (making two moves).