I like to study my games after I've played them. Often, I find myself identifying mistakes and moving on to play another game or study something else. I was wondering if it is worthwhile to continue studying your games beyond the point where the position becomes lost. I'm not talking about extremely lost positions where checkmate is imminent and inevitable, but rather about positions where you are down a minor piece or two and might have a chance at throwing a wrench in your opponents plans and inducing a mistake. It feels like this is a particularly difficult part of the game to study because often times complicating things for your opponent might involve an unsound, but threatening move, something like a bluff in poker. I was hoping some people might have some insights on whether or not it is worth it to study lost positions and how to do so if so. For reference, I am an amateur player who has been playing casually for a few years now.
Yes, these positions can be very rewarding. Sometimes, in endgames, there are stalemate possibilities. In middlegames and even endgames there can be tactical possibilities.
If you are far enough behind in material that a standard approach by your opponent of just swapping pieces is going to yield a straightforward win you need to be inventive to make him work for the victory. You can do this by playing actively and aggressively rather than defensively covering up. Make threats. That way you can sometimes create tactical opportunities to get back in the game.
In endgames there are also positions where the player with the material advantage can not win. Queen against rook and pawn can sometimes not win if the weaker side can set up the correct fortress. Sometimes a queen is not enough against a 7th rank pawn if it is on a rook or bishop file with the king next to it. Learn your endgames and look out for these opportunities in your games both when you are losing the endgame and also when you are winning to make sure you don't let your opponent escape.
Even when you appear completely lost there may be chances to trick an opponent who is playing on autopilot. Make him keep thinking and working for the win!
Don't forget how how psychologically demoralizing it can be when your opponent doesn't resign when they're "supposed" to. It can be worth studying how the quality of one's game changes after one has broken through after a lot of effort and captured that crucial piece, only to have the reward of the win delayed by a pest who is wasting your time by having the audacity to keep going. When losing badly, you win the right to play like a crazy person.
Generally speaking I'd say no -- two pieces down is just too much, there shouldn't be much potential for play left. In the game you'd be better off resigning.
Or is that too easy? If you had the side with the two extra pieces against a really good opponent, would that opponent find ways to put up resistance?
Nowadays there is a way to check that: setup the position with an engine, let it play the weak side, and demonstrate that you can win against it. If you can, then you were right to stop analyzing. If you can't, try to understand how it managed to put up resistance, and analyze your game a bit further to see if you could have done something similar. Then repeat until you beat the engine from the winning side.
And that a try to complicate things might be unsound isn't that relevant anymore if you're already lost.