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I just want to know when it's a good idea just to say it's a draw vs other times you just keep trying and trying to get a checkmate. …

In general, in chess, the aim is to capture the enemy king and not to have your own king captured. This means that after you make a move your king must not be attacked (=in check), as otherwise your …

This does not seem too difficult. With this in mind, the solution comes almost naturally:

A necessary condition for checkmate is that the king is in check, which is not the case here. The position in question is called stalemate: black does not have any legal moves, but is not in check. …

The final position is a forced win for black in 121 moves starting with 1... Qf4, according to the Shredder Tablebases. While it is objectively a win, it would be very tricky to pull it off in time tr …

In order not to overload the answer to this question, I split off the bishop+two knights part. So the question is: Is it possible to mate with a bishop and two knights without the help of the king?

Work in progress You can convince yourself easily, that mate is only possible in a corner of the board. We distinguish four cases: The corner is the same color as the bishop and the bishop mates Th …

Solving tactics puzzles that end in mate should help a lot. Even if the puzzles are short (2-3 moves), you will learn all kinds of mate positions which is useful because you will know what to aim for …

You posted a different position after my comment and PhishMaster's answer. As for the new position, yes it is mate in 7 starting with Rxc1+. Possible continuations are: Kd2 Rc2+ 2. Ke1 (if 2. Ke3 …

Very difficult is relative and given enough time players of most strength should be able to find a mate in one. I don't have a concrete example, but in my view the following features would make it mo …

If the situation is as in the diagram below, it is stalemate. You correctly noticed that white has no legal moves: any potential move would put the white king into check, which is not allowed. Further …

If I understand you correctly, you want to automatically simplify the mating sequence (final position minus a couple of moves) basically keeping the same mating pattern. I think doing this automatica …

I don't know if any such tool exists. If you want to program yourself you need to watch out for: Change of mating theme: If you remove pieces you might get new/different mates, e.g. in: 6rk/5Npp …

There is no general rule. Most of the time, the middlegame strategy will depend on the position you get out of the opening. Personal preferences can play a role as well, but typically players would p …

Obviously the last white move was 16. Nf3g1+. I note that black needs at least 15 moves to place the pieces as they are: 4 moves to swap queen with rook as they are (various movements possible), 2 …