What is the Hardest mate to accomplish I think the hardest is the (King+Rook vs King)

King and two bishops vs King

1. 2 Bishop + King vs. King

2.King + Rook vs. King

King + Rook vs. King is actually pretty easy.  The classic ending is always against the side of the board.  Other pieces can complicate it, though.

2 knights vs pawn

Also, from Wikipedia:

"...in May 2006, Bourzutschky and Konoval discovered a KQNKRBN position with an astonishing DTC (Depth to Checkmate) of 517 moves."

This may be the hardest mate (with a known sequence of forced moves) to date.

(KQNKRBN, if you're not familiar with the notation, means King + Queen + Knight vs. King + Rook + Bishop + Knight)

BUT IT can still be hard

Ok, with 6 pieces on the board (including kings) the longest, and therefore probably hardest, checkmate comes from this position:

Interestingly, Wikipedia seems to be incorrect on this matter. (Surprise, surprise!) The longest mate discovered is indeed with KQNkrbn, however it is not 517 moves until mate, but 517 moves until a conversion into a simpler endgame! Namely, KQNkbn. It will in fact take even MORE moves to finish the opponent off. The original position is thus:

i agree with you. one rook with a king and a king is reaaly hard.

bishop + knight + king vs. king

If you have a theoretical forced mate then, such as the 500+ one, does the 50 move rule count? I mean, you are technically attempting to win by normal means...

i at least bet theres a capture in like every 49 moves or so :P

Also, K vs K+ R is a piece of cake. All you need to do is keep cutting the enemy K off from the file/rank, and make waiting moves to achieve the opposition to push him back. Mating with BB or BN is much harder.

Unfortunately not. In the past, FIDE implemented 75- or even 100-move extensions in certain situations, for example queen vs. two bishops. However, these days it is a fixed 50 moves. This is because all endgames that require over 50 moves involve seemingly random moves that are impossible to find by humans in OTB play.

what about  2 pawns + King vs. King ! i have rarely seen this b4 .-----

"i have rarely seen this b4 .----- "

Off topic, but I doubt you've ever seen it before. That position is impossible since Black's only legal last move was Kb8-a8 and in that situation the pawn can't be at a7 (if it was, Black would have been in check from the pawn after the move before as well, which is illegal). It's not important, but I just found your choice of words coupled with the position somewhat ironic and thought others may find it funny as well.

The hardest forced checkmate is this position:

Someday in the far future it may be possible for a computer to "solve" chess. In that case a computer will calculate all variations possible with a forced checkmate in every variation effectively "solving chess".

So therefore this is the hardest mate, albet its not yet (or perhaps/probably never will be) solved. However, that doesnt stop us from trying every day :>

well your your right about that i have rarely seen it before , but like what about this mate- Queen + Rook + King vs. King      Checkmate in the middle of the board-

I'd bet the computations will find that best play ends in a draw.