I find the lesson of little use when "gotcha" hands are created. Holding AA and get into a raising war with a fictitious player holding KK. Yes I've had this happen several times in real games, but not going all in with the best hand pre flop is poor play indeed. Letting the fictitious player catch a K on the turn to bust you teaches no useful lesson that I can see.
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All the hands in the weekly challenges are random, they are not set up. Bad luck sometimes happens, but good luck happens just as often. If you play enough hands on APT, you'll see everything.
Nonetheless, I'd argue hands like this teach a very valuable poker lesson. Poker players on the whole have a huge problem with going on tilt, getting frustrated, letting bad luck affect their future play, etc. It is pretty clear this type of bad luck is frustrating to most players (including you based on your post). Much better to have this type of random bad luck happen in a situation where no money is involved so you can learn how to move past it. That's one of the reasons we created this site, so players can experience every high and low of poker and learn how to move on without losing their shirts in real money games.
As a related note, a lot of players also have a problem with playing poorly after a really lucky break. Assume for a second you were the one who had the KK and hit the K on the river. Many players loosen up after a hand like that and tend to give back some of the winnings. Others tighten up temporarily and potentially miss out on profitable hands. Pay attention to how you react to big wins and big losses. Are you able to keep playing your regular game or does the win or loss mess up your future play?
Allen, you are so right. This is, perhaps, the biggest area where I need help with my game. I can do all of the different types of tilt you mention. But I do think this site is helping.