So I introduced a handicap system to our games. With Draughts, if I win the game, then I start the next game with one less playing piece. Conversely, if he wins, I add a piece next time. In this way we find an equilibrium where we are roughly equal. I have to play as well as I can to win. He has an incentive to not make simple mistakes. He also gets practice in interesting game positions (such as the end game) and in trying to prevent me getting Kings. He also gets a legitimate sense of achievement when he wins since I'm not just letting him win.
In Chess, our handicap system is similar except he gets to choose the pieces to remove. One interesting aspect for a while is that he was choosing to remove my pawns because he didn't want me promoting them to Queens. I think the system is helping him understand the value of different pieces.
I haven't come up with a similar system for Scrabble yet - we've only played it twice. But interestingly it tests three aspects of learning. First, and obviously, it helps with learning words. It also helps with numbers, since you need to assess word values and add scores. Third, it helps with dexterity, since you need to place your tiles without disrupting the other tiles.
I'm trying to come up with some similar systems for the sports we play, like cricket and soccer. But acquiring a certain minimum level of skill first seems necessary there.
