Convexifying the choice set, an ongoing series

There is a new proposal for chess:

• Slight Win: A player wins slightly if any of the following
  conditions hold:
  d. The opponent offers to concede a slight win and he or she agrees,
  e. He or she stalemates his or her opponent.
  f. Without making a move, a player calls the arbiter and proves that as
  a result of her opponent's last move, the same position has occurred thrice.

The player that wins slightly gets 4/6 points, and the player that loses slightly
get 2/6 points.

Why not go further and allow the players to bargain for a split sum of any magnitude?  "I offer you .5713 to stop playing now…"