One of the interesting points about getting people to think about the game outside the game is making it a product. Something I recall from playing 40k (stopped summer of 2019? Near the end of 8th edition) was planning purchases which would help me make up for a shortfall in the traditional arms-race, and when I was ahead in that, options to let me field something different from the successful build that I was getting bored with.
There's also players thinking about how they would play the game differently the next time, but I've noticed wargames, particularly the GW variety, tend to be more of a spectator sport in that you bring your army, set them up, and see what happens. Partly I think that's because the plethora of strategic options overshadows any options for tactics, and being outplayed makes people feel dumb and bad (and being able to blame the dice is key here), so you have a constant cycle of fighting the last battle and trying to build that perfect deck/army/strategy for the next.
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