The denial rule is designed to balance the white advantage in normal chess (using crazy chess full rules it's a strong defense against an advanced Queen in the early game, but that will be discussed in another post), but if it's used properly it can give black an advantage, even the weak denial version (where Kings moves could not be denied).
Denial in openings:
An interesting way to confuse your opponent is to use the denial in the opening, since openings are almost mechanical it will probably make your opponent stop and rethink it's strategy, remember that it's useless to deny a knight move.
There are two things to keep in mind if you want to use the denial in an opening, first one is that the order of the moves must matter (almost always they fortunately do), the second one is a trap, if you previously know that your opponent will try to force an opening position exchanging the order of the moves you can set a trap exploring the wrong order, keep in mind that the trap will only completely work if it´s set to capture a piece or grant a position in your next move (since you have only one move until you opponent can use denial back), you can also set a trap with a knight, which is immune to denial because they can always take two paths to move or capture in the same position.
Direct denial:
The most common (at least in play tests) use of denial is to counter a capture move or a very bad position (sometimes to prevent a checkmate, but usually one can predict checks a few moves before), it can save your pieces for a while but usually when this happens it's a very bad thing, it's much more interesting to use it in the attack, to force a capture and convert your denial right in a material advantage as soon as you can (this is even better if you are using the soft denial rule).
Veiled advantage:
Another funny thing to do with denial is just not use it until late in the game (even using soft denial rules), when an opponent is building a strategy and you have the denial right he/she needs to build two threads for each move at the same time, while you can focus on only one, and if you happen to use your denial exactly on a bottleneck point of your opponent strategy the things will be very funny (at least for you :-) ).
Black Berserker:
Sometimes a chess game consists in the white attacking and black defending, but, with denial rules the lowest material in the board the stronger is the advantage of the player with the denial right, so if black goes berserker and start trading pieces as soon as possible it raises it's chance to use the denial in promotion races or in checkmates (using strong denial).
End Game:
Using strong denial there are lots of new checkmate possibilities using few material, even in weak denial rules some defenses can be countered (the ones that involve putting a piece in the path to protect the king), so black can save the denial to the end game, even using weak denial a pawn can get to an advanced position and promote faster if there are a race condition.
Anti denial:
The player without the denial right have a little more value for their knights than the player with the denial, then players can use this small temporary unbalance (temporary because when a player uses the denial the values are reversed) to gain some advantage, so white can build a strategy to preserve it's knights if he/she predict the intention of the black to save denial for the end game, but if black discover this strategy it can use the denial soon to gain a small material and force white to lose the advantage.
There are lots of new strategy for each of the crazy chess new moves, but these strategies are somewhat strange to normal chess (but not so strange since the pieces threat ranges are similar), denial alone is a lot of fun :-), mainly if played in fast and timed games.
