You gamble with how many points you have left. Let's say each player starts with 40 points (most games take about 40 moves). You spend anywhere from 0 to however many points you have left to move a piece. If it's early on and there's no chance of conflict, bet 0. If it's an important piece in a crowd, spend more. If there's a conflict, whoever spent more wins that spot.

It might add an element of subterfuge to the game.

> How would two pieces moving to the same square be resolved?

I'd say that the one that has traveled the longest distance wins, and captures the piece that started closer.

(My implicit mental model is that both pieces "depart" from their home squares at the same time and travel at a constant rate, so the closer piece arrives at an empty square, while the more distant piece arrives second and captures the first-arriving piece. This may also encourage more dynamic play)

Maybe highest value price wins, with ties losing both pieces.