One of the most imbalanced things in Magic is deciding who gets to start by the hand of a die roll. 99% of the people who win the die roll decide to play first, and see their chances of winning increased by a pretty large percentage because of it. The fact that the player who is on the play gets to draw a card is simply not enough for people to even consider not starting first.
I personally can't win a die roll if my life denpended on it, and knowing that you have less chance of winning simply because you rarely win die rolls is frustrating. You can tweak or change your deck, but rolling a die is just a random act that rewards people simply because they get lucky... .
What can be done to make this imbalance a little more balanced?
A 'free' mulligan?
A scry?
Drawing an extra card?
Playing two lands on turn 1?

Any suggestions?