I am an engineer of electrotechnics. Love to play chess, including its variants. I love to work with math, physics, chemistry, geography, electrical engineering, game programming (already created Tetris, Match Pairs, ...), website design (I created a whole website for a fictional company, including their logo 
), music production, astronomy and science. I often spend hours in programming and playing chess.
I am fascinated about endgames, the patterns of achieving a draw, stalemate or checkmate. Four basic checkmates in the Standard Chess are usually listed:
- king versus king and queen
- king versus king and rook
- king versus king and two bishops of the opposite square color
- king versus king, bishop and knight
And no, learning the king versus king, bishop and knight is not a waste of time, at least according to me, because I had several games in which I was forced to checkmate the opponent's bare king only with my king, bishop and knight, and I knew how to win this endgame, because I learned it! But even some grandmasters fail to learn this endgame, so they fall into a draw or even lose by the clock, leaving the tournament publicly embarrassed.
According to me, there is one more basic checkmate in the Standard Chess:
- king versus king and three knights
And no, learning the king versus king and three knights is not a waste of time, at least according to me, because I had one game in which I was forced to checkmate the opponent's bare king only with my king and three knights (one of my knights came from an underpromoted pawn with check, forking the opponent's king and queen).
And there are actually much more basic checkmates in the Standard Chess. We can checkmate the opponent's lone king without any help of our king:
- king versus two queens
- king versus queen and rook
- king versus queen and bishop
- king versus queen and knight
- king versus two rooks
- king versus rook and two bishops of the opposite square color
- king versus rook and two bishops of the same square color
- king versus rook, bishop and knight
- king versus rook and two knights
- king versus two pairs of bishops of the opposite square color
- king versus two bishops of the same square color, one bishop of the opposite square color and knight
- king versus two bishops of the opposite square color and two knights
- king versus two bishops of the same square color and two knights
- king versus bishop and three knights
- king versus four knights
These basic checkmates can arise in the Horde Chess and some other chess variants. There is a number of basic checkmates involving pawns as well.
I learned most of these basic checkmates, like king versus rook and two knights, king versus rook and two bishops of the same square color and king versus four knights. Three knights or two knights and a bishop can sometimes deliver non-trivial checkmate from certain start positions (checkmate in 12 in the case of king versus three knights, and checkmate in 16 in the case of king versus two knights and bishop), but those two endgames can be a draw as well in other certain start positions, even without king capturing the bishops and/or knights.
There are also many basic stalemates and draws, for example king versus king and two knights stalemate. If other chess pieces from other chess variants are involved (amazon, zebra, camel, princess, elephant, ferz, wazir, ...), the number of basic endgames rises abruptly.