Gamesmanship
I am teaching the eldest little clowncar to play checkers (I'd rather rip out my teeth with pliers than play Candyland or Chutes and Ladders, but I'll play checkers til the cows come home). Already, she's pretty good. But I'm stumbling across an issue no doubt encountered by countless parents before me: how hard do you try to win?

Clearly, I can't let her win, as she won't learn how to play - no strategy, no planning ahead, no joy of play. Just mindless self-esteem building that won't amount to much because it's false.
At the same time, I don't want to crush her like a grape. No joy of play there either. She'll never want to play again.
I'm gradually - and happily - learning the middle ground here. When she makes a mistake, gently show her the mistake before you take advantage (but take advantage). Occasionally make little clucking noises when she starts to make a bad move. And, throw her a bone every once in a while. Put a checker in harm's way and see if she jumps it. Pass over the occasionally gapingly obvious double or triple jump available to me.
She hasn't beat me yet. But she's caught me off-guard with a jump a couple of times now. And yesterday she even hit me with her first double jump she figured out all for herself.
Few things in life are as satisfying as your first double jump.