Sure, you could use some sort of parabolic formula to give higher places more points.

Using 1 point increments is awful.

Especially for the winner, because playing heads-up is so much more complex than a ring game, the winner should get a decent cut of the cake.

You can take a look at what they use at cardplayer.com and do something with that. Here's the URL: http://www.cardplayer.com/player_of_...oycriteria.php