How to avoid making silly errors


the videos stress the concept of undefended pieces and playing basic and fundamental chess

There are basically 3 checks to do before you play a move.
1) after the opponent moves, check if you have a way to win material or checkmate right away. Look at your most forcing moves (checks captures and threats). If you can't then:
2) Check if your opponent is threatening to immediately win material or checkmate. In particular pay attention to all the newly attacked squares from the last move. This also includes uncovering a piece. For example
Black moved the knight, but the main thing this move does is uncover the rook's attack on white's undefended bishop.
If the opponent is not threatening to win something right away then
3) Find a candidate move, and imagine it as if it's been made without actually playing it. Now look for the opponent's checks, captures, and threats again to see if they can immediately punish this move.
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As a newer player, a lot of energy is usually spent trying to find a candidate move that threatens something. This would fit in between steps 2 and 3. It's not important that your moves have a threat, but new players don't really have any other criteria to distinguish between moves... also it lets them win some games right away so it's rewarding.
The point is, usually this takes up most of the mental energy, so the other steps don't get much attention. Another way to say this is, at first doing all this is really hard -- but keep practicing and it does get easier. Eventually to the point that it's practically automatic. Your goal is to find the opponent's checks, captures, and threats on every move, of every game. Everyone does it sometimes, but with a lot of work, you can do it consistently, and your results will improve a lot as a result.

Also, check out the 70 page chapter on "Thought Process" in Dan Heisman's A Guide to Chess Improvement: The Best of Novice Nook. His books, including The World's Most Instructive Amateur Games Book often look at thinking mistakes: he knows most games are won or lost due to giving away pieces. The preface, to the ...Games Book includes this:
"Well, Dan," Howard Stern's familiar bass voice intoned, "now that I am up to 1000, that's about it. I can't seem to beat those 1100's.
"But Howard," I protested, "you're just giving them free pieces and they are taking some of them. They are giving you free pieces and you aren't taking as many of them. If you just stop giving them free pieces and take all of theirs, you will beat them every game...basically, it's as easy as that.
Four years later Howard was rated 1700 ICC (Internet)."
Jeremy Silman's book, The Amateur's Mind, looks at the difference in thinking between masters and lower rated players. But, at 443 pages, it's a long study - I recommend Heisman first.
Does anyone have any exercises or tips about how I might approach my game to cut these daft errors out?! Thank you.