The luck element of Talisman can be reduced by house ruling that you roll 2 dice for movement rather than 1 die, and the player gets to pick which of those dice he uses for movement. You can do this for a lot of the older style luck-based games.
I hadn't thought of D&D. I did get the new starter pack but the kids were a bit young so I shelved it for another day. In a SHTF world they could role-play living in a fantasy world of offices and commutes and supermarkets