The Flying Knight

I realise that, just saying that having a queenside knight would make a huge difference to the advantage Black already has.

It's not a normal king, so it is allowed for the black king to give check (and checkmate) as long as the black king is not in check at the end of Black's turn.

That doesn't mean that they have to stay two squares away. It means that the white king has to move away each time they are one square away, and if it can't, it is checkmate. The black king not jumping has no consequence to this.

No, Black just needs to be out of check by the end of his turn.

I would like to check these rules in reliable source.

If the black king can enter check in his first step or not is crucial for white's strategy and overall game balance.

Sounds interesting, but yes, we'd need to know the full rules as the ones listed leave a number of holes, like the one Polar Bear mentioned.

Please don't throw the knight, they are heavy and someone can get hurt if they get landed on

Black just has to be out of check at the end of his turn.

But black doesn't follow the rules, they live outside of it!

Yes, I see you say so. Now prove it and give us reliable link.

So essentially, in an open board you'd need probably need both rooks and the queen to mate?  The king can cross two bishops' diagonals, etc. and escape mating nets.

From the wikipedia article on monster chess, as this is obviously a variant of monster chess (one knight instead of four pawns):

"The white king can move into check on the first move of the turn and move out of check during the second move."(The article has white as the player moving first)

http://en.wikipedia.org/wiki/Monster_chess

OK, so black can approach white just like in normal Chess (1 empty square between them), and then white is in check, (because when he would pass his turn, the black King could now capture the white King), so he has to increase the distance again to two empty squares between them. And when he cannot, because he is driven against the edge, white is checkmated by the black King alone.

In the diagram I gave, could black just step his King to b6?

The black king doesn't need to jump. The king just needs to be out of check by the end of the turn.

True, you already said this. But you are constantly saying things that contradict each other. For one, 'jumping' is moving over an occupied square. Not moving over a square that is attacked.

If the black King is not allowed to pass through check (i.e. be subject to capture in the hypothetical case that black would skip doing his second move), then there is no reason why the Kings should stay further apart than in normal Chess. One empty square between them would be enough. White would not check black then, because he can only do one step. And black would not check white, as he cannot step next to the white King with his first move (as this would be passing through check), and thus can never capture the white King with your King's second move.

Note that not passing through check is an extra rule, in deviation from FIDE rules, which in general only care about the position at the end of the turn.

It is impossible for the side with two to lose if they go first. It gets two moves to white's one, and a win is essentially guaranteed. 

As an example: for algebraic notation I will demonstrate white's two moves as two seperate moves, with the final move being the piece's final placement, and the third move as blacks. Assume black has all pieces and white's king and knight are on starting spots.

1. Nd2 Nd4 e5

2. Nf5 Kd1#

In two moves white can take black's king, no matter where he moves.

The way black could avoid this would be for his first move to guard the f5 square, but with pressure from the king in a few turns it would be inevitable.

I guess this is why black gets the double move, and not white.

The critical issue remains which rules one adopts to restrict the first move of a black move pair. In Monster Chess there are no extra restrictions: this means the black King will be allowed to step to squares attacked by enemy pieces, as it cannot be captured there (because it is not yet white's turn), as long as he ends up unchecked after the second move. This in particular means black can step his King next to the white King, as long as he then steps on. As he can capture the white King from there with his second step, this means white is already in check when the black King is two steps away from him, but that the black King is perfectly safe there, and allowed to deliver such checks. As a consequence, K-vs-K end-games are easily won in Monster Chess.

If the additional rule is adopted that the first black move must be legal under the fiction that it was the only black move, (i.e. 'no passing through check'), then the black King cannot check the white King from a distance of two steps, as he is not allowed to make the first of these steps. Of course the white King cannot capture the black King from this distance either, as it is limited to a single step in the first place. So Kings can approach to the same distance as in FIDE, and neither of them would be in check.

It seems that what the OP describes is neither of this. Which means there is need for yet an additional rule in addition to FIDE and the 'no passing through check' rule.

Black wins easily.  This is a scam to try to win money off of people who think white should have the advantage, but white falls quickly.

Essentially, as I'm understanding, the Black King is upgraded to the powers of the Lion (from Chu Shogi), where it can make two King moves in one turn; and, furthermore, where it can make a capture on a piece adjacent to it only to retreat to any available safe square on its second move. It's nothing new: we all know that a good avoider is placing a piece adjacent to Black's King at all times; and placing a piece where a black King would get there.

How exactly is victory achieved by White, since he/she is up against 2 enemy Kings? Do we do it Ace569er style, where we capture Kings until there's only one left, in which the last King is to be checkmated? Or, do both Kings have to be checkmated at once?

Also, what exactly is the significance of the Knight? If it has already been addressed in the mountain pile which are the posts before me, it would be nice if someone can point it out to me; since I don't have the time to read everything tonight.