Perpetual Check

But after 1. Rf8+ Rxf8 2. Ng6+ (supposing we don't play the Kg8 3. Nxe7+, stalemate by perpetual check) if black takes the knight by hg6, then 3. hg6+ Kh8 4. Qh7# because the queen is defended by g6 which also prevents Kf7 and black Rf8 prevents Kf8. So stalemate is actualy black's best hope.

Any flaws in my logic?

3. hg6+ Qxa2

The first thing you need to understand is the nature of "scoring" in chess. There are only three possible outcomes of any match - win, loss, and draw. Any draw is regarded as being better than a loss. So if you are in what appears to be a losing position, and can find a way to get a draw, well, it doesn't matter how many pieces your opponent still has, or how few you have, or what he could have done on the next move - if you can force a draw, it's a draw.

With that said, there are many different ways to draw in chess. Many high-level games end in an agreed draw - neither player thinks he has enough of an advantage to produce a win, so they simply agree to a draw.

Another method is known as "stalemate" - and even as a beginner, you should be aware of this. Stalemate occurs when it is your turn to move, and you're not in check, but you have no legal move. This generally occurs when you have few pieces left, and your king is "boxed in" - unable to move to an adjacent square, because he would be moving into check. (I say "you" and "your", but obviously your opponent can be stalemated as well.)

ANother common form of draw occurs upon "perpetual check". You place your opponent's king in check, he moves out, you check him again, and he returns to the first square.  Obviously, this can go on and on forever, so the rules provide that this constitutes a draw.

Now, in the puzzle above, white is seriously down in material. If white and black exchanged pieces evenly (queen for queen, knight for bishop, rook for rook, and so on), black would still have a rook and a pawn left at the end - more than enough to win the game - so it's time for white to start looking for a way to draw the game, because that's better than a loss.

They gve you the first move (Re8+), and black has no choice; he has to play RxR - he has no other way to get out of check, and you will recall that getting your king out of check is always your first priority.

Your next move is to attack the king, which you do by moving your knight to g6. This looks like a bad move, because black can take the N with the pawn at h7. This gets him out of check, since he has captured the attacking piece.

Now, here comes the fun part. You can play PxP (your pawn at h5 moves to g6). This opens up the h-file for the white queen, which is now attacking the black king - "Check". This is sometimes called "discovered" check - when a piece moves out of the way, and you "discover" that a piece behind it is now attacking your opponent's king).

Black has two choices about getting out of check.  The first is to move the king.  But the only place the black king can go is to g8, and if he goes there, white's next move will be to swoop down to h7, and say "Checkmate" (the queen will be protected by the pawn at g6). So black looks around, and discovers that his queen can take the white queen - thus removing the check, and avoiding the checkmate.

So QxQ it is. But now it's white's turn to move, and guess what? White has three pawns left, but none of them can move. Nor can the white king move. But the white king is not in check, so it's a stalemate.

Now, most chess players can think far enough ahead to see this coming. So instead of taking the white knight with the pawn (P(h7)xN(g6)), black decides to move his king - another way of getting out of check. The only place he can go is to G8. At that point, white moves the knight again - this time to take the pawn at e7. Check again. The king goes back into the corner at h8, the knight comes back to g6 to check again, the king goes to g8, and on and on. So this looks like "perpetual check", and a draw.

But then, this looks like it may be a "busted" puzzle. Once the e7 pawn is taken, wouldn't white's e6 pawn have a place to move (to e7), so the stalemate wouldn't work?

But no - the white pawn at e6 is "pinned" - it can't move because to do so would expose the white king to check from the black bishop on c8.

So - the knight just cycles back and forth, checking the king each time - and you, as white, happily settle for a draw in a game you would otherwise lose. And your opponent grits his teeth, extends his hand, and says - not very graciously - "Nice game".

emmh?

Nice analysis from daxelson. I particularly enjoyed that remark upon the e6 pawn being freed by Ng6xe7+. Nice add-on. Keep up the good job.