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We use two variants that make the game more interesting for us.
One is for movement, one is for scoring.
We play that you can change direction during your move. So if you move from a 5 chit, you can go 2 up, 1 left and 2 up again. Diagonals still don't count.
We understood the movement rule that way when the game was explained to us at Spiel and we bought the game on that basis. We tried the correct rule when we found out about it, but thought the game was less fun that way.
Besides the regular majority scoring, we also score the actual pip amounts. Every player compares their pip amount in an area to the following player in the majority ranks and scores one point for every pip they have more than that player. The player with the least amount of pips just gets that many points.
Player A: 10 pips
Player B: 5 pips
Player C: 2 pips
Player A would get 9 points (4 from the majority + 5 compared to player B)
Player B would get 5 points (2 from the majority + 3 compared to player B)
Player C would get 2 points
This adds another layer of tactics to the game, especially towards the end: instead of trying to eke out a majority somewhere, it might be more beneficial to sneak in another area, even if you are in last place there.