I've been playing Lord of the Rings Risk, in the variant where the Ring moves one territory per turn, requiring a roll of 4 or higher to leave certain territories, and the game ends when the Ring reaches Mt. Doom and is destroyed. At the game's end, victory points are allotted for:
- Territories owned
- Complete regions (="continents") controlled
- Strongholds owned
- Adventure cards played throughout the game
The problem is that once the Ring reaches Mt. Doom, the next player to go has a strong incentive to abandon strategic position and defensibility and just expand as much as he possibly can in order to maximize his points. If the Ring isn't destroyed, then the next player to go does the same thing. If this happens several times, the endgame has a tendency to become a series of ridiculous expansions and contractions that obliterates whatever strategic shape the board had beforehand.
What house rules have others used to avoid these problems?